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For sustainable building design, performance-based optimization incorporating parametric modelling and evolutionary optimization can allow architects to leverage building massing design to improve energy performance. However, two key challenges make such applications of performance-based optimization difficult in practice. First, due to the parametric modelling approaches, the topological variability in the building massing variants is often very limited. This, in turn, limits the scope for the optimization process to discover high-performing solutions. Second, for architects, the process of creating parametric models capable of generating the necessary topological variability is complex and time-consuming, thereby significantly disrupting the design processes. To address these two challenges, this paper presents a parametric massing algorithm based on the subtractive form generation principle. The algorithm can generate diverse building massings with significant topological variability by removing different parts from a predefined volume (food4rhino.com/node/2974). Additionally, the algorithm can be applied to different building massing design scenarios without additional parametric modelling being required. Hence, using the algorithm can help architects achieve an explorative performance-based optimization for building massing design while streamlining the overall design process. Two case studies of daylighting performance optimizations are presented, which demonstrate that the algorithm can enhance the exploration of the potential in building massing design for energy performance improvements.
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sustainability
Article
Subtractive Building Massing for Performance-Based
Architectural Design Exploration: A Case Study of
Daylighting Optimization
Likai Wang 1, Patrick Janssen 2, Kian Wee Chen 3, Ziyu Tong 1,* and Guohua Ji 1 ,*
1School of Architecture and Urban Planning, Nanjing University, Nanjing 210093, China;
dg1436002@smail.nju.edu.cn
2School of Design and Environment, National University of Singapore, Singapore 117566, Singapore;
patrick@janssen.name
3Andlinger Center for Energy and the Environment, Princeton University, Princeton, NJ 08544, USA;
chenkianwee@gmail.com
*Correspondence: tzy@nju.edu.cn (Z.T.); jgh@nju.edu.cn (G.J.); Tel.: +86-13805178067 (Z.T.);
+86-13605192392 (G.J.)
Received: 15 November 2019; Accepted: 4 December 2019; Published: 6 December 2019

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Abstract:
For sustainable building design, performance-based optimization incorporating parametric
modelling and evolutionary optimization can allow architects to leverage building massing
design to improve energy performance. However, two key challenges make such applications
of performance-based optimization dicult in practice. First, due to the parametric modelling
approaches, the topological variability in the building massing variants is often very limited. This, in
turn, limits the scope for the optimization process to discover high-performing solutions. Second, for
architects, the process of creating parametric models capable of generating the necessary topological
variability is complex and time-consuming, thereby significantly disrupting the design processes.
To address these two challenges, this paper presents a parametric massing algorithm based on the
subtractive form generation principle. The algorithm can generate diverse building massings with
significant topological variability by removing dierent parts from a predefined volume. Additionally,
the algorithm can be applied to dierent building massing design scenarios without additional
parametric modelling being required. Hence, using the algorithm can help architects achieve an
explorative performance-based optimization for building massing design while streamlining the
overall design process. Two case studies of daylighting performance optimizations are presented,
which demonstrate that the algorithm can enhance the exploration of the potential in building massing
design for energy performance improvements.
Keywords:
parametric massing algorithm; building massing design; performance-based optimization;
design exploration; subtractive form generation principle; passive energy savings; daylighting
1. Introduction
Recent decades have witnessed rapid urbanization in China, which has fed the demand for more
energy-ecient buildings moving towards a more sustainable future. While engineering methods,
such as system control, renewable energy generation, and high-performance materials, have been
widely applied in the building sector, the contribution made by architectural design remains limited.
This issue has raised widespread concerns in architecture and increased the awareness of embracing
performance-based design or performative design in architectural design [
1
,
2
]. In performance-based
design for energy sustainability, building massing design can play a role in energy performance
improvement [
3
5
]. A good building massing design can make the building adapt to the surrounding
Sustainability 2019,11, 6965; doi:10.3390/su11246965 www.mdpi.com/journal/sustainability
Sustainability 2019,11, 6965 2 of 20
urban environment and take advantage of climate resources, such as sun, light, and wind. As a result,
the building can benefit from passive energy savings by leveraging daylighting, passive heating or
cooling, and natural ventilation.
In sustainable architectural design, there are certain widespread building massing design strategies
for passive energy saving, such as atriums, courtyards, and stilts. With these strategies, it is possible
to achieve a moderate improvement in passive energy saving by following certain rules-of-thumb or
guidelines [
6
]. However, the full exploitation of applying these strategies for progressive energy saving
is not trivial. Because of the uncertainty resulting from the interaction between the climate conditions
and the specific surrounding urban environment, the application of these strategies in building massing
design for each project must be site-specific [
7
]. In this regard, a systematic exploration of a broad
range of building massing design alternatives can help to identify the appropriate application of these
strategies for the project.
In the past, building massing design exploration has mostly been partial and limited as
manually generating many dierent configurations and combinations of these strategies is tiring
and time-consuming. Recent progress in parametric modelling and evolutionary optimization
is considered a possible solution to these challenges. This allows architects to undertake
automated performance-based optimization as a means of building massing design exploration.
Parametric modelling allows for a design space (solution search space) to be defined, encompassing a
large number of design variants for evolutionary optimization to explore. Evolutionary optimization
evolves the population of building massing design and aims to identify the computed optimal solution
with the desired energy performance [810].
In the last decade, a growing body of research literature has developed around eorts to apply
performance-based optimization to maximize the potential of building massing design in passive energy
savings [
11
,
12
]. Despite many successful applications in the literature, applying performance-based
optimization for building massing design exploration is still challenging. While certain barriers
have been identified by other researchers, such as the lack of easy-to-use optimization tools and the
problematic integration of optimization with architectural design [
13
15
], another critical barrier is the
lack of topological variability among the variants oered by these techniques in the design space.
The lack of topological variability means that the building massing design variants generated by
the parametric model show little or no topological dierentiation to the change of parameters. Thus,
despite a large number of design variants, the design space may actually only cover a small subset of all
possible design alternatives, which excludes many other competitive alternatives from being explored
by the optimization process. In order to overcome the lack of topological variability in the design
space, this research proposes a parametric algorithm to generate building massing designs based on a
subtractive form generation principle. The process starts with a solid building block defining the basic
volume of the building massing. By removing dierent parts from the building block, the generated
building massings show significant topological variability, which can imply dierent configurations
and combinations of various passive energy-saving strategies in the building massing design.
To place the research in context, we first discuss the progress that has been made in parametric
modelling for building massing design before going on to describe the details of the proposed algorithm.
We then present two case studies with associated results. We conclude the paper by discussing the
relative eectiveness of this algorithm and some limitations.
Parametric Modelling for Building Massing Design
Parametric models describe design by explicit rules and parameters [
16
]. Often, the rules encoded
are rigorous but inflexible. This often results in the design space defining a family of design variants that
are all very similar with limited topological variability [
10
,
17
19
]. The lack of topological variability is
often overlooked as architects may use parametric models to describe a specific design strategy for
each optimization. Hence, the fact that the design space only includes similar design variants is seen
as acceptable, since they are all derived from the same strategy. A case in point is that for building
Sustainability 2019,11, 6965 3 of 20
massing design optimizations aimed at daylighting or passive solar energy, many researchers or
architects create parametric models to describe building blocks with central internal courtyards [
20
,
21
].
With such models, the shape of the courtyard can typically be changed by formal transformation
operations, such as rotation, twisting, and slanting [
22
,
23
]. The result of the optimization may
show remarkable improvements by identifying the fittest shape of the courtyards. However, such
optimization nonetheless leaves many other competitive solutions unexplored, for example, the one
characterized by features, such as stilts and solar envelopes.
In order to overcome the lack of topological variability, other researchers have proposed
sophisticated parametric modelling approaches to oering discrete formal variability of the generated
building massing. One commonly used approach is to include several massing algorithms, respectively
describing dierent building massing forms in one parametric model, and select one of these algorithms
to create the building massing each time [
6
,
24
,
25
]. This approach is often used in design problems at the
urban scale, and the desired urban form diversity can be simply achieved by varying permutations and
combinations of dierent forms over multiple buildings. Nault et al. [
6
] and Xiaodong et al. [
25
] used
this approach to create neighborhood-scale and urban block design based on a set of basic building
forms for energy-daylighting optimization and outdoor thermal comfort optimization. Another
approach is to create building massings composed of various small mass units. By arranging and
rearranging these mass units, the algorithm can generate dierent spatial configurations [
26
29
].
This approach is also widely used in conjunction with thermal-zone layout optimization to achieve
better energy eciency [
30
,
31
]. Buildings generated by this approach typically have a cellular-look
massing. However, due to the parametric approach, the arbitrary arrangement of the mass units often
results in many chaotic design variants [28].
Applying the two approaches mentioned above is technically demanding and consumes a
great amount of time and eort. The former requires laborious developments of dierent massing
algorithms [
19
], while the latter requires complex constraint handling to ensure the designs generated
are meaningful [28,29,31].
Regardless of the diculty in developing massing algorithms capable of oering desired
topological variability, another drawback shared by common performance-based optimization exercises
is that a large amount of parametric modelling is required for dierent projects. Hence, although
there are approaches to generating building designs with high topological variability, architects may
still struggle with such a complex parametric modelling task, which further results in significant
interruptions to the design process. This issue has been drawing concern recently [
6
,
19
,
22
,
32
].
The reusability of the parametric model, therefore, becomes a critical issue for minimizing the
interruption to the design process [
6
,
33
]. Ideally, it should be possible to reuse parametric models
in dierent design contexts [
9
,
34
]. However, this merit is often overshadowed as highly customized
parametric models are often built on architects’ preferences and biases. The designs generated by such
customized parametric models are often too specific or unique to be reused in other design contexts.
In contrast, this research explores the idea that it may be possible to reuse a parametric model
for dierent design contexts if generic design (building massing) strategies can be represented by the
parametric model [
35
]. Recently, a few studies have attempted to develop design support systems,
including predefined generic building forms, to reduce the eort and time invested in parametric
modelling, thereby allowing architects to carry out streamlined performance-based optimization
processes without the interruption of parametric modelling [
6
,
25
]. However, as pointed out in these
studies, oering sucient topological variability in the design generated, again, presents a significant
challenge for developers.
In contrast to the existing approaches, the proposal of using the subtractive form generation
principle in parametric building massing algorithms may have some advantages in overcoming the
challenges related to the lack of topological variability and low reusability:
First, the subtractive form generation principle is one of the most generic and widely applied
massing strategies in architecture. This strategy can fit many dierent common types of building
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designs [
4
]. Using this principle ensures that, with simple constraints, most of the building
massings generated have acceptable and reasonable architectural features. In addition, by
removing dierent parts from a predefined building volume, the subtracted building massing can
show great topological variability. These two advantages can eciently overcome the weaknesses
identified above.
Second, many passive energy-saving strategies for building massing design, such as courtyards,
stilts, and solar envelopes, can be schematically described as removing (subtracting) parts from
a building block [
3
,
35
], which complies with the subtractive form generation principle. Thus,
with dierent parts removed, the subtracted building massing can be recognized as dierent
combinations and arrangements of these passive energy-saving strategies imposed in the building
massing design.
Third, the subtractive form generation approach allows for easy customization of the types of
building design features that are generated. Architects can tune the types of features by adjusting
various global parameters associated with the subtractors. For example, such parameters may
include the size, position, and number of subtracting parts.
2. Methods
2.1. Overview of Proposed Algorithm
The proposed algorithm generates building massings according to a subtractive form generation
principle. The algorithm starts with a maximal building volume and then creates building massing
design variants by subtracting parts of this volume. By varying the number of parts to be removed as
well as their positions and dimensions, alternative massings with significant topological variability can
be generated. The core of the algorithm is to define the part to be removed, which is referred to as the
“subtractor” in this paper. The definition and formation of the subtractor consist of three basic steps:
(1) Initialization of a maximal volume and the subtractors, (2) constraining the position and size of
the subtractors, and (3) aligning the subtractors. In addition, there is one optional step to generate
building cores.
In order to be able to provide control over the features of the building massing after subtraction,
several initialization parameters are provided. These parameters are assigned before the optimization
process starts and remains fixed throughout the process. Other parameters, referred to as the
optimization parameters, are changeable and modified by the evolutionary algorithm during the
optimization processes. The initialization parameters include: (1) the dimension of the maximal
volume, (2) the number of subtractors, (3) the size constraint of the subtractor, and (4) the boundary
constraint regulating the relationship between subtractors and the maximal volume. The optimization
parameters define the dimension and spatial position of each subtractor. Moreover, two optional
initialization parameters are: (1) Specifying the footprint of the maximal volume, and (2) turning on or
othe generation of building cores.
Once the initialization parameters have been assigned, the algorithm can generate building
massing variants by varying the optimization parameters list, and these variants can then be sent to
various energy simulation tools for performance evaluation. An evolutionary algorithm can be used
to evolve building massing designs by iteratively changing optimization parameters and receiving
corresponding performance feedback from simulations. The overall building massing creation and
iterative evolutionary processes are illustrated in Figure 1.
2.2. Generative Steps
The generative process consists of three main generative steps related to the subtractors:
Initialization, constraints, and alignment. Finally, a fourth step can also optionally be added, to
insert building cores.
Sustainability 2019,11, 6965 5 of 20
Sustainability 2019, 11, x FOR PEER REVIEW 5 of 21
Figure 1. Schematic diagram of the building massing creation and evolutionary optimization process.
2.2. Generative Steps
The generative process consists of three main generative steps related to the subtractors:
Initialization, constraints, and alignment. Finally, a fourth step can also optionally be added, to insert
building cores.
2.2.1. Subtractor Initialization
The first step is to initialize the maximal volume and the subtractors. The shape of the maximal
volume is a rectangular block by default, and its dimension is defined by the number of column
gridpoints in the x- and y-directions and the number of floors in the z-direction, which are assigned
by architects (Figure 2-a). Changing the dimensions allows different types of buildings to be
generated, e.g., high-rise or low-rise buildings. Two types of subtractors—vertical subtractors and
horizontal subtractors—are created based on values in the optimization parameters lists. Vertical
subtractors have an aims to create features related to design strategies, such as atriums and
courtyards (Figure 2-b). In contrast, horizontal subtractors aim to create features, such as stepped
(cascade) roofs, empty floors, and stilts, in the building massing (Figure 2-c). Using these two types
of subtractors, the building massing is generated by removing the parts occupied by these subtractors
from the maximal volume (Figure 2-d).
Figure 2. The creation of the building massing by two types of subtractors: (a) generating maximal
volume, (b) vertical subtractors, (c) horizontal subtractors, and (d) assembling of vertical and
horizontal subtractors.
Figure 1.
Schematic diagram of the building massing creation and evolutionary optimization process.
2.2.1. Subtractor Initialization
The first step is to initialize the maximal volume and the subtractors. The shape of the maximal
volume is a rectangular block by default, and its dimension is defined by the number of column
gridpoints in the x- and y-directions and the number of floors in the z-direction which are assigned by
architects in the initialization parameters (Figure 2a). Changing the dimensions allows dierent types
of buildings to be generated, e.g., high-rise or low-rise buildings. For each building massing design
variant, two types of subtractors—vertical subtractors and horizontal subtractors—are created based on
values in the optimization parameters lists. Vertical subtractors have an aims to create features related
to design strategies, such as atriums and courtyards (Figure 2b). In contrast, horizontal subtractors
aim to create features, such as stepped (cascade) roofs, empty floors, and stilts, in the building massing
(Figure 2c). Using these two types of subtractors, the building massing is generated by removing the
parts occupied by these subtractors from the maximal volume (Figure 2d).
Sustainability 2019, 11, x FOR PEER REVIEW 5 of 21
Figure 1. Schematic diagram of the building massing creation and evolutionary optimization process.
2.2. Generative Steps
The generative process consists of three main generative steps related to the subtractors:
Initialization, constraints, and alignment. Finally, a fourth step can also optionally be added, to insert
building cores.
2.2.1. Subtractor Initialization
The first step is to initialize the maximal volume and the subtractors. The shape of the maximal
volume is a rectangular block by default, and its dimension is defined by the number of column
gridpoints in the x- and y-directions and the number of floors in the z-direction, which are assigned
by architects (Figure 2-a). Changing the dimensions allows different types of buildings to be
generated, e.g., high-rise or low-rise buildings. Two types of subtractors—vertical subtractors and
horizontal subtractors—are created based on values in the optimization parameters lists. Vertical
subtractors have an aims to create features related to design strategies, such as atriums and
courtyards (Figure 2-b). In contrast, horizontal subtractors aim to create features, such as stepped
(cascade) roofs, empty floors, and stilts, in the building massing (Figure 2-c). Using these two types
of subtractors, the building massing is generated by removing the parts occupied by these subtractors
from the maximal volume (Figure 2-d).
Figure 2. The creation of the building massing by two types of subtractors: (a) generating maximal
volume, (b) vertical subtractors, (c) horizontal subtractors, and (d) assembling of vertical and
horizontal subtractors.
Figure 2.
The creation of the building massing by two types of subtractors: (
a
) generating maximal
volume, (
b
) vertical subtractors, (
c
) horizontal subtractors, and (
d
) assembling of vertical and
horizontal subtractors.
The number of subtractors, defined by architects, is an important factor aecting the topological
variability of the generated building massings. Figure 3shows the generated building massings with
dierent numbers of subtractors. It can be noticed that when the number of subtractors increases,
subtractors become merged and turn the negative volume subtracted from the building mass into a
Sustainability 2019,11, 6965 6 of 20
complex topological configuration. By changing the number of subtractors, architects can control the
overall topological variability and configurational complexity of the generated building massings.
Sustainability 2019, 11, x FOR PEER REVIEW 6 of 21
The number of subtractors, defined by architects, is an important factor affecting the topological
variability of the generated building massings. Figure 3 shows the generated building massings with
different numbers of subtractors. It can be noticed that when the number of subtractors increases,
subtractors become merged and turn the negative volume subtracted from the building mass into a
complex topological configuration. By changing the number of subtractors, architects can control the
overall topological variability and configurational complexity of the generated building massings.
Figure 3. Generated building massings based on different numbers of subtractors: V indicates vertical
subtractors, H indicates horizontal subtractors.
As the accumulated negative volume subtracted by all subtractors is dynamically changed by
varying the optimization parameters, the gross area of the subtracted building massing varies
accordingly. The gross area is a critical functional requirement in architectural design. Therefore,
although a building massing may have excellent energy performance, it is of little relevance if its
gross area is too low or too high. The algorithm, therefore, adjusts the maximal volume to create a
building massing close to a target gross area by iteratively increasing or decreasing the number of
column grid spans and floors. With the maximal volume adjusted, the appearance of subtractors also
varies as some subtractors may be deactivated due to the size constraint, which is described in Section
2.2.2 (Figure 4). The adjustment of building massing is executed during the building massing creation
process and is independent of the evolutionary optimization process. At the same time, in order to
give some additional control, architects are able to freeze certain dimensions (x, y, or z).
Figure 4. Generated building massings with different target gross areas.
The maximal volume that is a rectangular block may not fit into irregular building plots or satisfy
architectural intentions. Therefore, the algorithm provides an initialization parameter to specify the
footprint of the maximal volume, which is achieved by removing a fixed part from the building
massing. As shown in Figure 5, this operation can create maximal volumes with an L-shaped or U-
shaped footprint.
Figure 5. Generated building massings with different footprints: (a) rectangular footprint, (b) L-
shaped footprint, and (c) U-shaped footprint.
2.2.2. Subtractor Constraints
The second step is to constrain the size and position of subtractors according to the values in the
optimization parameters list. In order to prevent over-large or over-small voids from appearing in
Figure 3.
Generated building massings based on dierent numbers of subtractors: V indicates vertical
subtractors, H indicates horizontal subtractors.
As the accumulated negative volume subtracted by all subtractors is dynamically changed
by varying the optimization parameters, the gross area of the subtracted building massing varies
accordingly. The gross area is a critical functional requirement in architectural design. Therefore,
although a building massing may have excellent energy performance, it is of little relevance if its gross
area is too low or too high. The algorithm, therefore, adjusts the maximal volume to create a building
massing close to a target gross area by iteratively increasing or decreasing the number of column grid
spans and floors. With the maximal volume adjusted, the appearance of subtractors also varies as some
subtractors may be deactivated due to the size constraint, which is described in Section 2.2.2 (Figure 4).
The adjustment of building massing is executed during the building massing creation process and
is independent of the evolutionary optimization process. At the same time, in order to give some
additional control, architects are able to freeze certain dimensions (x, y, or z).
Sustainability 2019, 11, x FOR PEER REVIEW 6 of 21
The number of subtractors, defined by architects, is an important factor affecting the topological
variability of the generated building massings. Figure 3 shows the generated building massings with
different numbers of subtractors. It can be noticed that when the number of subtractors increases,
subtractors become merged and turn the negative volume subtracted from the building mass into a
complex topological configuration. By changing the number of subtractors, architects can control the
overall topological variability and configurational complexity of the generated building massings.
Figure 3. Generated building massings based on different numbers of subtractors: V indicates vertical
subtractors, H indicates horizontal subtractors.
As the accumulated negative volume subtracted by all subtractors is dynamically changed by
varying the optimization parameters, the gross area of the subtracted building massing varies
accordingly. The gross area is a critical functional requirement in architectural design. Therefore,
although a building massing may have excellent energy performance, it is of little relevance if its
gross area is too low or too high. The algorithm, therefore, adjusts the maximal volume to create a
building massing close to a target gross area by iteratively increasing or decreasing the number of
column grid spans and floors. With the maximal volume adjusted, the appearance of subtractors also
varies as some subtractors may be deactivated due to the size constraint, which is described in Section
2.2.2 (Figure 4). The adjustment of building massing is executed during the building massing creation
process and is independent of the evolutionary optimization process. At the same time, in order to
give some additional control, architects are able to freeze certain dimensions (x, y, or z).
Figure 4. Generated building massings with different target gross areas.
The maximal volume that is a rectangular block may not fit into irregular building plots or satisfy
architectural intentions. Therefore, the algorithm provides an initialization parameter to specify the
footprint of the maximal volume, which is achieved by removing a fixed part from the building
massing. As shown in Figure 5, this operation can create maximal volumes with an L-shaped or U-
shaped footprint.
Figure 5. Generated building massings with different footprints: (a) rectangular footprint, (b) L-
shaped footprint, and (c) U-shaped footprint.
2.2.2. Subtractor Constraints
The second step is to constrain the size and position of subtractors according to the values in the
optimization parameters list. In order to prevent over-large or over-small voids from appearing in
Figure 4. Generated building massings with dierent target gross areas.
The maximal volume that is a rectangular block may not fit into irregular building plots or satisfy
architectural intentions. Therefore, the algorithm provides an initialization parameter to specify the
footprint of the maximal volume, which is achieved by removing a fixed part from the building
massing. As shown in Figure 5, this operation can create maximal volumes with an L-shaped or
U-shaped footprint.
Figure 5.
Generated building massings with dierent footprints: (
a
) rectangular footprint, (
b
) L-shaped
footprint, and (c) U-shaped footprint.
2.2.2. Subtractor Constraints
The second step is to constrain the size and position of subtractors according to the values in the
optimization parameters list. In order to prevent over-large or over-small voids from appearing in
the building massing, the horizontal dimension of subtractors is restricted by the size constraint, by
which architects specify the upper and lower size limit of subtractors in the unit of column-grid span
numbers. When the size of a subtractor does not satisfy the size constraints, a number of operations are
Sustainability 2019,11, 6965 7 of 20
used to automatically modify the subtractors. When the size is above the upper limit, the dimension of
the subtractor is decreased to the upper limit. When the size is below the lower limit, the subtractor
is deactivated, and the corresponding part is not subtracted from the building massing (Figure 6).
Note that the size constraint does not guarantee that all subtracting parts appearing in the building
mass are satisfactory. When two or more subtractors are merged, it can turn into a large void in the
maximal volume that could exceed the upper boundary.
Sustainability 2019, 11, x FOR PEER REVIEW 7 of 21
the building massing, the horizontal dimension of subtractors is restricted by the size constraint, by
which architects specify the upper and lower size limit of subtractors in the unit of column-grid span
numbers. When the size of a subtractor does not satisfy the size constraints, a number of operations
are used to automatically modify the subtractors. When the size is above the upper limit, the
dimension of the subtractor is decreased to the upper limit. When the size is below the lower limit,
the subtractor is deactivated, and the corresponding part is not subtracted from the building massing
(Figure 6). Note that the size constraint does not guarantee that all subtracting parts appearing in the
building mass are satisfactory. When two or more subtractors are merged, it can turn into a large
void in the maximal volume that could exceed the upper boundary.
Figure 6. The size constraint in the horizontal direction: assuming the size constraint is 2 to 5, (a)
before size being constrained, and (b) after size being constrained.
Apart from the user-defined size constraint in the horizontal direction, another constraint, which
is hard-coded in the algorithm, restricts the size of subtractors in the vertical direction. In order to
differentiate vertical and horizontal subtractors, two different constraints are subject to the two types
of subtractors. For the vertical subtractors, the top and bottom faces are automatically aligned to the
maximal volume if the displacement between the face and the maximal volume is less than 30% of
the total height of the building (Figure 7-a). At the same time, for each vertical subtractor, at least one
face has to satisfy this constraint, or else the subtractor is deactivated. For horizontal subtractors, the
vertical size of every subtractor has to be less than 30% of the total height of the building but should
also not be smaller than one floor. For any horizontal subtractors violating this condition, the
algorithm automatically changes the size to make it satisfactory (Figure 7-b).
Figure 7. The size constraint in the vertical direction.
Apart from the size constraint, users also define the boundary constraint, which determines
whether vertical subtractors can break through the outer face of the maximal volume in the horizontal
direction. When the constraint is deactivated, any face of a vertical subtractor close to the face of the
maximal volume is aligned to one of the faces of the maximal volume so that it creates a vertically
open void running through the maximal volume (Figure 8-a). In contrast, the boundary remains
intact when the boundary constraint is activated, and any vertical subtractor close to the face of the
maximal volume is moved away from the face of the maximal volume (Figure 8-b).
Figure 6.
The size constraint in the horizontal direction: assuming the size constraint is 2 to 5, (
a
) before
size being constrained, and (b) after size being constrained.
Other than the user-defined size constraint in the horizontal direction, another constraint, which
is hard-coded in the algorithm, restricts the size of subtractors in the vertical direction. In order to
dierentiate vertical and horizontal subtractors, two dierent constraints are subject to the two types
of subtractors. For the vertical subtractors, the top and bottom faces are automatically aligned to the
maximal volume if the displacement between the face and the maximal volume is less than 30% of
the total height of the building (Figure 7a). At the same time, for each vertical subtractor, at least one
face has to satisfy this constraint, or else the subtractor is deactivated. For horizontal subtractors, the
vertical size of every subtractor has to be less than 30% of the total height of the building but should
also not be smaller than one floor. For any horizontal subtractors violating this condition, the algorithm
automatically changes the size to make it satisfactory (Figure 7b).
Sustainability 2019, 11, x FOR PEER REVIEW 7 of 21
the building massing, the horizontal dimension of subtractors is restricted by the size constraint, by
which architects specify the upper and lower size limit of subtractors in the unit of column-grid span
numbers. When the size of a subtractor does not satisfy the size constraints, a number of operations
are used to automatically modify the subtractors. When the size is above the upper limit, the
dimension of the subtractor is decreased to the upper limit. When the size is below the lower limit,
the subtractor is deactivated, and the corresponding part is not subtracted from the building massing
(Figure 6). Note that the size constraint does not guarantee that all subtracting parts appearing in the
building mass are satisfactory. When two or more subtractors are merged, it can turn into a large
void in the maximal volume that could exceed the upper boundary.
Figure 6. The size constraint in the horizontal direction: assuming the size constraint is 2 to 5, (a)
before size being constrained, and (b) after size being constrained.
Apart from the user-defined size constraint in the horizontal direction, another constraint, which
is hard-coded in the algorithm, restricts the size of subtractors in the vertical direction. In order to
differentiate vertical and horizontal subtractors, two different constraints are subject to the two types
of subtractors. For the vertical subtractors, the top and bottom faces are automatically aligned to the
maximal volume if the displacement between the face and the maximal volume is less than 30% of
the total height of the building (Figure 7-a). At the same time, for each vertical subtractor, at least one
face has to satisfy this constraint, or else the subtractor is deactivated. For horizontal subtractors, the
vertical size of every subtractor has to be less than 30% of the total height of the building but should
also not be smaller than one floor. For any horizontal subtractors violating this condition, the
algorithm automatically changes the size to make it satisfactory (Figure 7-b).
Figure 7. The size constraint in the vertical direction.
Apart from the size constraint, users also define the boundary constraint, which determines
whether vertical subtractors can break through the outer face of the maximal volume in the horizontal
direction. When the constraint is deactivated, any face of a vertical subtractor close to the face of the
maximal volume is aligned to one of the faces of the maximal volume so that it creates a vertically
open void running through the maximal volume (Figure 8-a). In contrast, the boundary remains
intact when the boundary constraint is activated, and any vertical subtractor close to the face of the
maximal volume is moved away from the face of the maximal volume (Figure 8-b).
Figure 7. The size constraint in the vertical direction.
Apart from the size constraint, users also define the boundary constraint, which determines
whether vertical subtractors can break through the outer face of the maximal volume in the horizontal
direction. When the constraint is deactivated, any face of a vertical subtractor close to the face of the
maximal volume is aligned to one of the faces of the maximal volume so that it creates a vertically
open void running through the maximal volume (Figure 8a). In contrast, the boundary remains intact
when the boundary constraint is activated, and any vertical subtractor close to the face of the maximal
volume is moved away from the face of the maximal volume (Figure 8b).
Deactivating the boundary constraint permits radical changes in the building massing. Figure 9
presents generated building massings with the boundary constraint deactivated. As it can be
seen, massing design variants consisting of two or more completely separate buildings can emerge.
These types of massing design variants allow the optimization process to explore beyond solutions
characterized by one building massing. Such an expansion to the solution space may benefit the
building energy performance, for example, by allowing for inter-block shading among buildings [3].
Sustainability 2019,11, 6965 8 of 20
Sustainability 2019, 11, x FOR PEER REVIEW 8 of 21
Figure 8. Generated building massings with or without the boundary constraint activated: (a) the
boundary constraint disabled, (b) the boundary constraint enabled.
Deactivating the boundary constraint permits radical changes in the building massing. Figure 9
presents generated building massings with the boundary constraint deactivated. As it can be seen,
massing design variants consisting of two or more completely separate buildings can emerge. These
types of massing design variants allow the optimization process to explore beyond solutions
characterized by one building massing. Such an expansion to the solution space may benefit the
building energy performance, for example, by allowing for inter-block shading among buildings [3].
Figure 9. Examples of massing designs generated with the boundary constraint deactivated.
2.2.3. Subtractor Alignment
Alignment is an important approach by which architects regulate the massing elements to
maintain geometric order [35]. However, arbitrary placements of subtractors can result in poor
alignment. For example, two subtractors may be positioned close together, creating a space between
the two subtractors that may be too narrow to be of any use. Thus, in the horizontal direction, the
parallel faces from different subtractors are aligned to be co-planar when the distance between the
two faces is less than a half span of one column grid (Figure 10-a). Similarly, the faces of two partly
overlapping subtractors are also aligned in the same way to avoid small jagged faces in the void
merged by two or more subtractors (Figure 10-b). Lastly, when a subtractor has a face close to the
maximal volume’s boundary, the face is aligned to the boundary (Figure 10-c). Note that the last
alignment operation only applies to vertical subtractors if the boundary constraint is deactivated.
Figure 10. The procedures of alignment: (a) aligning two separated subtractors, (b) aligning two partly
overlapping subtractors, and (c) aligning a subtractor to the maximal volume.
In architectural design, apart from the alignment among massing elements, the placement of the
face of massing elements (walls or facades) typically also aligns with grid lines defined by the
modulus related to the column grid. Hence, the faces of all subtractors are aligned to its nearest n/4
(n could be 0) position in between two adjacent columns (Figure 11). With the constraints and
operations mentioned above, many commonly unwanted features that may appear in the building
massing when using parametric approaches are excluded.
Figure 8.
Generated building massings with or without the boundary constraint activated: (
a
) the
boundary constraint disabled, (b) the boundary constraint enabled.
Sustainability 2019, 11, x FOR PEER REVIEW 8 of 21
Figure 8. Generated building massings with or without the boundary constraint activated: (a) the
boundary constraint disabled, (b) the boundary constraint enabled.
Deactivating the boundary constraint permits radical changes in the building massing. Figure 9
presents generated building massings with the boundary constraint deactivated. As it can be seen,
massing design variants consisting of two or more completely separate buildings can emerge. These
types of massing design variants allow the optimization process to explore beyond solutions
characterized by one building massing. Such an expansion to the solution space may benefit the
building energy performance, for example, by allowing for inter-block shading among buildings [3].
Figure 9. Examples of massing designs generated with the boundary constraint deactivated.
2.2.3. Subtractor Alignment
Alignment is an important approach by which architects regulate the massing elements to
maintain geometric order [35]. However, arbitrary placements of subtractors can result in poor
alignment. For example, two subtractors may be positioned close together, creating a space between
the two subtractors that may be too narrow to be of any use. Thus, in the horizontal direction, the
parallel faces from different subtractors are aligned to be co-planar when the distance between the
two faces is less than a half span of one column grid (Figure 10-a). Similarly, the faces of two partly
overlapping subtractors are also aligned in the same way to avoid small jagged faces in the void
merged by two or more subtractors (Figure 10-b). Lastly, when a subtractor has a face close to the
maximal volume’s boundary, the face is aligned to the boundary (Figure 10-c). Note that the last
alignment operation only applies to vertical subtractors if the boundary constraint is deactivated.
Figure 10. The procedures of alignment: (a) aligning two separated subtractors, (b) aligning two partly
overlapping subtractors, and (c) aligning a subtractor to the maximal volume.
In architectural design, apart from the alignment among massing elements, the placement of the
face of massing elements (walls or facades) typically also aligns with grid lines defined by the
modulus related to the column grid. Hence, the faces of all subtractors are aligned to its nearest n/4
(n could be 0) position in between two adjacent columns (Figure 11). With the constraints and
operations mentioned above, many commonly unwanted features that may appear in the building
massing when using parametric approaches are excluded.
Figure 9. Examples of massing designs generated with the boundary constraint deactivated.
2.2.3. Subtractor Alignment
Alignment is an important approach by which architects regulate the massing elements to maintain
geometric order [
35
]. However, arbitrary placements of subtractors can result in poor alignment.
For example, two subtractors may be positioned close together, creating a space between the two
subtractors that may be too narrow to be of any use. Thus, in the horizontal direction, the parallel
faces from dierent subtractors are aligned to be co-planar when the distance between the two faces is
less than a half span of one column grid (Figure 10a). Similarly, the faces of two partly overlapping
subtractors are also aligned in the same way to avoid small jagged faces in the void merged by two
or more subtractors (Figure 10b). Lastly, when a subtractor has a face close to the maximal volume’s
boundary, the face is aligned to the boundary (Figure 10c). Note that the last alignment operation only
applies to vertical subtractors if the boundary constraint is deactivated.
Sustainability 2019, 11, x FOR PEER REVIEW 8 of 21
Figure 8. Generated building massings with or without the boundary constraint activated: (a) the
boundary constraint disabled, (b) the boundary constraint enabled.
Deactivating the boundary constraint permits radical changes in the building massing. Figure 9
presents generated building massings with the boundary constraint deactivated. As it can be seen,
massing design variants consisting of two or more completely separate buildings can emerge. These
types of massing design variants allow the optimization process to explore beyond solutions
characterized by one building massing. Such an expansion to the solution space may benefit the
building energy performance, for example, by allowing for inter-block shading among buildings [3].
Figure 9. Examples of massing designs generated with the boundary constraint deactivated.
2.2.3. Subtractor Alignment
Alignment is an important approach by which architects regulate the massing elements to
maintain geometric order [35]. However, arbitrary placements of subtractors can result in poor
alignment. For example, two subtractors may be positioned close together, creating a space between
the two subtractors that may be too narrow to be of any use. Thus, in the horizontal direction, the
parallel faces from different subtractors are aligned to be co-planar when the distance between the
two faces is less than a half span of one column grid (Figure 10-a). Similarly, the faces of two partly
overlapping subtractors are also aligned in the same way to avoid small jagged faces in the void
merged by two or more subtractors (Figure 10-b). Lastly, when a subtractor has a face close to the
maximal volume’s boundary, the face is aligned to the boundary (Figure 10-c). Note that the last
alignment operation only applies to vertical subtractors if the boundary constraint is deactivated.
Figure 10. The procedures of alignment: (a) aligning two separated subtractors, (b) aligning two partly
overlapping subtractors, and (c) aligning a subtractor to the maximal volume.
In architectural design, apart from the alignment among massing elements, the placement of the
face of massing elements (walls or facades) typically also aligns with grid lines defined by the
modulus related to the column grid. Hence, the faces of all subtractors are aligned to its nearest n/4
(n could be 0) position in between two adjacent columns (Figure 11). With the constraints and
operations mentioned above, many commonly unwanted features that may appear in the building
massing when using parametric approaches are excluded.
Figure 10.
The procedures of alignment: (
a
) aligning two separated subtractors, (
b
) aligning two partly
overlapping subtractors, and (c) aligning a subtractor to the maximal volume.
In architectural design, apart from the alignment among massing elements, the placement of the
face of massing elements (walls or facades) typically also aligns with grid lines defined by the modulus
related to the column grid. Hence, the faces of all subtractors are aligned to its nearest n/4 (
n could be 0
)
position in between two adjacent columns (Figure 11). With the constraints and operations mentioned
above, many commonly unwanted features that may appear in the building massing when using
parametric approaches are excluded.
Sustainability 2019, 11, x FOR PEER REVIEW 9 of 21
Figure 11. Alignment operation of the face of subtractors to the axes: assuming the size constraint is
2 to 5, (a) before being aligned to axes, and (b) after being aligned to axes.
Despite the fact that the number of subtractors is predefined as an initialization parameter, the
various operations applied during the building massing generation process can cause the actual
appearance of the number of parts being subtracted from the building massing to vary significantly.
As a result, building massing with different topological complexity can be generated, from the one
without any part removed to that with the largest number of parts permitted removed. As such, the
generated building massings may present various combinations and arrangements of different
passive design strategies, such as several smaller courtyards or one large courtyard (Figure 12).
Figure 12. Examples of massing designs generated with the same number of subtractors.
2.2.4. Building Cores
As widely applied to modern building design, building cores can serve as circulation,
evacuation, and structural supports. In this consideration, the algorithm provides an optional
operation to create building cores. The principle for creating these cores is based on the footprint of
the building massing and complies with the firefighting evacuation regulation in China. In China,
the door-to-door distance from a room to its closest evacuation stair and the distance of any point in
the room to its closest exit door to corridors should be no more than 22 m. Since the proposed
algorithm does not subdivide the floor plan into rooms, the calculation of the number and position
of the building cores is simplified to fulfill a requirement that every face of the maximal volume’s
footprint to its closest cores is no more than 35 m. When the position of the cores is determined, the
column grid cell containing or close to (equal or less than half of the column-grid span) the center
point of any core is turned into the building core. After the building cores have been generated, all
subtractors are also required to align with these cores (Figure 13).
Figure 13. Generated building massings with or without building cores: (a) building core generation
disabled, (b) building core generation enabled.
2.3. Implementation
In order to facilitate the ease of use, the algorithm was implemented as a plug-in component
(Figure 14-a) in Rhino-Grasshopper, which is one of the most popular 3D and parametric modelling
tools in architecture [36]. A user interface (Figure 14-b) was also integrated into the component for
architects to specify the initialization parameters and other attributes related to the building massing
design, such as floor height, span size (width), and facade types. As to the facade type, only curtain
walls and strip windows are provided in the current implementation, which could be further
expanded in the future. With the component and the user interface, architects can interact with the
Figure 11.
Alignment operation of the face of subtractors to the axes: assuming the size constraint is 2
to 5, (a) before being aligned to axes, and (b) after being aligned to axes.
Despite the fact that the number of subtractors is predefined as an initialization parameter, the
various operations applied during the building massing generation process can cause the actual
Sustainability 2019,11, 6965 9 of 20
appearance of the number of parts being subtracted from the building massing to vary significantly.
As a result, building massing with dierent topological complexity can be generated, from the one
without any part removed to that with the largest number of parts permitted removed. As such, the
generated building massings may present various combinations and arrangements of dierent passive
design strategies, such as several smaller courtyards or one large courtyard (Figure 12).
Sustainability 2019, 11, x FOR PEER REVIEW 9 of 21
Figure 11. Alignment operation of the face of subtractors to the axes: assuming the size constraint is
2 to 5, (a) before being aligned to axes, and (b) after being aligned to axes.
Despite the fact that the number of subtractors is predefined as an initialization parameter, the
various operations applied during the building massing generation process can cause the actual
appearance of the number of parts being subtracted from the building massing to vary significantly.
As a result, building massing with different topological complexity can be generated, from the one
without any part removed to that with the largest number of parts permitted removed. As such, the
generated building massings may present various combinations and arrangements of different
passive design strategies, such as several smaller courtyards or one large courtyard (Figure 12).
Figure 12. Examples of massing designs generated with the same number of subtractors.
2.2.4. Building Cores
As widely applied to modern building design, building cores can serve as circulation,
evacuation, and structural supports. In this consideration, the algorithm provides an optional
operation to create building cores. The principle for creating these cores is based on the footprint of
the building massing and complies with the firefighting evacuation regulation in China. In China,
the door-to-door distance from a room to its closest evacuation stair and the distance of any point in
the room to its closest exit door to corridors should be no more than 22 m. Since the proposed
algorithm does not subdivide the floor plan into rooms, the calculation of the number and position
of the building cores is simplified to fulfill a requirement that every face of the maximal volume’s
footprint to its closest cores is no more than 35 m. When the position of the cores is determined, the
column grid cell containing or close to (equal or less than half of the column-grid span) the center
point of any core is turned into the building core. After the building cores have been generated, all
subtractors are also required to align with these cores (Figure 13).
Figure 13. Generated building massings with or without building cores: (a) building core generation
disabled, (b) building core generation enabled.
2.3. Implementation
In order to facilitate the ease of use, the algorithm was implemented as a plug-in component
(Figure 14-a) in Rhino-Grasshopper, which is one of the most popular 3D and parametric modelling
tools in architecture [36]. A user interface (Figure 14-b) was also integrated into the component for
architects to specify the initialization parameters and other attributes related to the building massing
design, such as floor height, span size (width), and facade types. As to the facade type, only curtain
walls and strip windows are provided in the current implementation, which could be further
expanded in the future. With the component and the user interface, architects can interact with the
Figure 12. Examples of massing designs generated with the same number of subtractors.
2.2.4. Building Cores
As widely applied to modern building design, building cores can serve as circulation, evacuation,
and structural supports. In this consideration, the algorithm provides an optional operation to create
building cores. The principle for creating these cores is based on the footprint of the building massing
and complies with the firefighting evacuation regulation in China. In China, the door-to-door distance
from a room to its closest evacuation stair and the distance of any point in the room to its closest exit
door to corridors should be no more than 22 m. Since the proposed algorithm does not subdivide the
floor plan into rooms, the calculation of the number and position of the building cores is simplified to
fulfill a requirement that every face of the maximal volume’s footprint to its closest cores is no more
than 35 m. When the position of the cores is determined, the column grid cell containing or close to
(equal or less than half of the column-grid span) the center point of any core is turned into the building
core. After the building cores have been generated, all subtractors are also required to align with these
cores (Figure 13).
Sustainability 2019, 11, x FOR PEER REVIEW 9 of 21
Figure 11. Alignment operation of the face of subtractors to the axes: assuming the size constraint is
2 to 5, (a) before being aligned to axes, and (b) after being aligned to axes.
Despite the fact that the number of subtractors is predefined as an initialization parameter, the
various operations applied during the building massing generation process can cause the actual
appearance of the number of parts being subtracted from the building massing to vary significantly.
As a result, building massing with different topological complexity can be generated, from the one
without any part removed to that with the largest number of parts permitted removed. As such, the
generated building massings may present various combinations and arrangements of different
passive design strategies, such as several smaller courtyards or one large courtyard (Figure 12).
Figure 12. Examples of massing designs generated with the same number of subtractors.
2.2.4. Building Cores
As widely applied to modern building design, building cores can serve as circulation,
evacuation, and structural supports. In this consideration, the algorithm provides an optional
operation to create building cores. The principle for creating these cores is based on the footprint of
the building massing and complies with the firefighting evacuation regulation in China. In China,
the door-to-door distance from a room to its closest evacuation stair and the distance of any point in
the room to its closest exit door to corridors should be no more than 22 m. Since the proposed
algorithm does not subdivide the floor plan into rooms, the calculation of the number and position
of the building cores is simplified to fulfill a requirement that every face of the maximal volume’s
footprint to its closest cores is no more than 35 m. When the position of the cores is determined, the
column grid cell containing or close to (equal or less than half of the column-grid span) the center
point of any core is turned into the building core. After the building cores have been generated, all
subtractors are also required to align with these cores (Figure 13).
Figure 13. Generated building massings with or without building cores: (a) building core generation
disabled, (b) building core generation enabled.
2.3. Implementation
In order to facilitate the ease of use, the algorithm was implemented as a plug-in component
(Figure 14-a) in Rhino-Grasshopper, which is one of the most popular 3D and parametric modelling
tools in architecture [36]. A user interface (Figure 14-b) was also integrated into the component for
architects to specify the initialization parameters and other attributes related to the building massing
design, such as floor height, span size (width), and facade types. As to the facade type, only curtain
walls and strip windows are provided in the current implementation, which could be further
expanded in the future. With the component and the user interface, architects can interact with the
Figure 13.
Generated building massings with or without building cores: (
a
) building core generation
disabled, (b) building core generation enabled.
2.3. Implementation
In order to facilitate the ease of use, the algorithm was implemented as a plug-in component
(Figure 14a) in Rhino-Grasshopper, which is one of the most popular 3D and parametric modelling
tools in architecture [
36
]. A user interface (Figure 14b) was also integrated into the component for
architects to specify the initialization parameters and other attributes related to the building massing
design, such as floor height, span size (width), and facade types. As to the facade type, only curtain
walls and strip windows are provided in the current implementation, which could be further expanded
in the future. With the component and the user interface, architects can interact with the building
massing creation process and observe the change in the renewed building massing instantly in the
Rhino-Grasshopper environment. The timely visual feedback of the generated building massings
allows architects to undertake parameter tuning to exclude unwanted or unsuitable features in the
building massing and ensure that these features do not appear in evolutionary optimization.
The implementation in the Rhino-Grasshopper environment takes advantage of the Visual
Programming Language, where no coding is required. It allows architects, even computational design
novices, to use the algorithm and establish a performance-based optimization system for building
massing design in a plug-and-play fashion. The implementation of the proposed algorithm is part
of an integrated evolutionary design toolkit, which also embeds a diversity-driven evolutionary
Sustainability 2019,11, 6965 10 of 20
algorithm [
37
]. As such, a performance-based optimization system can be established simply by
connecting the component of this building massing algorithm and the evolutionary algorithm with
various building performance simulation tools, such as DIVA, Ladybug, Honeybee, Archsim, etc. [
38
].
Sustainability 2019, 11, x FOR PEER REVIEW 10 of 21
building massing creation process and observe the change in the renewed building massing instantly
in the Rhino-Grasshopper environment. The timely visual feedback of the generated building
massings allows architects to undertake parameter tuning to exclude unwanted or unsuitable
features in the building massing and ensure that these features do not appear in evolutionary
optimization.
Figure 14. (a) Component implemented in Rhino-Grasshopper, (b) the user interface.
The implementation in the Rhino-Grasshopper environment takes advantage of the Visual
Programming Language, where no coding is required. It allows architects, even computational
design novices, to use the algorithm and establish a performance-based optimization system for
building massing design in a plug-and-play fashion. The implementation of the proposed algorithm
is part of an integrated evolutionary design toolkit, which also embeds a diversity-driven
evolutionary algorithm [37]. As such, a performance-based optimization system can be established
simply by connecting the component of this building massing algorithm and the evolutionary
algorithm with various building performance simulation tools, such as DIVA, Ladybug, Honeybee,
Archsim, etc. [38].
2.4. Case Studies
2.4.1. Design Setting
To demonstrate the efficacy of the proposed algorithm, two case-study performance-based
optimization processes for building massing design were carried out. The two case studies
respectively describe a high-rise slab-type building design and a middle-rise deep plan building
design (Figure 15). The difference between these two building design objects is to clarify the
capability of the proposed algorithm to handle different settings of building massing design. For both
case studies, the energy performance objective was to maximize daylighting for passive energy
savings.
Figure 14. (a) Component implemented in Rhino-Grasshopper, (b) the user interface.
2.4. Case Studies
2.4.1. Design Setting
To demonstrate the ecacy of the proposed algorithm, two case-study performance-based
optimization processes for building massing design were carried out. The two case studies respectively
describe a high-rise slab-type building design and a middle-rise deep plan building design (Figure 15).
The dierence between these two building design objects is to clarify the capability of the proposed
algorithm to handle dierent settings of building massing design. For both case studies, the energy
performance objective was to maximize daylighting for passive energy savings.
Sustainability 2019, 11, x FOR PEER REVIEW 11 of 21
Figure 15. Plan and aerial view of the building plot: the orange block indicates the building being
designed.
The building plot for the two case studies is located at the campus of Nanjing University in
Nanjing City, Jiangsu Province, China. Several high- and middle-rise buildings surround the building
plot and cast shadows on the plot (Figure 16), thereby presenting a significant challenge in achieving
desired daylighting. Without the assistance of performance-based optimization, architects may
conceive high-performing solutions by manual trial and error. However, this is not only time-
consuming and laborious, but the solution is likely to be prejudiced due to architects’ cognitive biases.
Figure 16. Sun path of the building plot (winter solstice).
For the optimization objective, the fitness evaluation considers both the energy reduction
resulting from daylighting and the gross area of the building massing. For the energy reduction from
daylighting, annual lighting energy (LE) consumption is taken as the performance indicator, and the
general objective of the evolutionary optimization is to minimize this value. At the same time, the
gross area of the building massing considers a penalty function in the fitness calculation. While the
proposed algorithm can automatically adjust the dimension and floor number of the building
massing to make the gross area close to the required target value, there could be an unacceptable
gross area difference if the original difference is too large. Hence, the difference is considered a
penalty function to punish unsatisfactory design variants. In this regard, the value of lighting energy
increases proportionally with the increase in the difference between the actual gross area and the
required gross area. Therefore, even with low lighting energy, the building massing still receives an
Figure 15.
Plan and aerial view of the building plot: the orange block indicates the building
being designed.
Sustainability 2019,11, 6965 11 of 20
The building plot for the two case studies is located at the campus of Nanjing University in Nanjing
City, Jiangsu Province, China. Several high- and middle-rise buildings surround the building plot and
cast shadows on the plot (Figure 16), thereby presenting a significant challenge in achieving desired
daylighting. Without the assistance of performance-based optimization, architects may conceive
high-performing solutions by manual trial and error. However, this is not only time-consuming and
laborious, but the solution is likely to be prejudiced due to architects’ cognitive biases.
Sustainability 2019, 11, x FOR PEER REVIEW 11 of 21
Figure 15. Plan and aerial view of the building plot: the orange block indicates the building being
designed.
The building plot for the two case studies is located at the campus of Nanjing University in
Nanjing City, Jiangsu Province, China. Several high- and middle-rise buildings surround the building
plot and cast shadows on the plot (Figure 16), thereby presenting a significant challenge in achieving
desired daylighting. Without the assistance of performance-based optimization, architects may
conceive high-performing solutions by manual trial and error. However, this is not only time-
consuming and laborious, but the solution is likely to be prejudiced due to architects’ cognitive biases.
Figure 16. Sun path of the building plot (winter solstice).
For the optimization objective, the fitness evaluation considers both the energy reduction
resulting from daylighting and the gross area of the building massing. For the energy reduction from
daylighting, annual lighting energy (LE) consumption is taken as the performance indicator, and the
general objective of the evolutionary optimization is to minimize this value. At the same time, the
gross area of the building massing considers a penalty function in the fitness calculation. While the
proposed algorithm can automatically adjust the dimension and floor number of the building
massing to make the gross area close to the required target value, there could be an unacceptable
gross area difference if the original difference is too large. Hence, the difference is considered a
penalty function to punish unsatisfactory design variants. In this regard, the value of lighting energy
increases proportionally with the increase in the difference between the actual gross area and the
required gross area. Therefore, even with low lighting energy, the building massing still receives an
Figure 16. Sun path of the building plot (winter solstice).
For the optimization objective, the fitness evaluation considers both the energy reduction resulting
from daylighting and the gross area of the building massing. For the energy reduction from daylighting,
annual lighting energy (LE) consumption is taken as the performance indicator, and the general
objective of the evolutionary optimization is to minimize this value. At the same time, the gross area
of the building massing considers a penalty function in the fitness calculation. While the proposed
algorithm can automatically adjust the dimension and floor number of the building massing to make
the gross area close to the required target value, there could be an unacceptable gross area dierence if
the original dierence is too large. Hence, the dierence is considered a penalty function to punish
unsatisfactory design variants. In this regard, the value of lighting energy increases proportionally with
the increase in the dierence between the actual gross area and the required gross area. Therefore, even
with low lighting energy, the building massing still receives an unfavorable fitness value when the gap
between its gross area and the target value is too large. The fitness function can be described below:
f itness =LE × 1+|Aactual Atarget
Atarget
|!, (1)
where LE indicates the lighting energy consumption, and A
actual
and A
Target
indicate the actual gross
area of the building massing and the required target gross area.
The annual lighting energy consumption is calculated by a Radiance-based simulation tool, called
DIVA [
39
], in Rhino-Grasshopper. In order to ensure each simulation can be finished in a reasonable
timeframe, the lowest simulation quality is adopted, which means that the Radiance engine calculates
a lower number of bounces of rays for the simulation. Using a higher quality makes the simulation
too time-consuming, since there might be thousands of simulations involved in one evolutionary
optimization process. Moreover, although the lowest quality degrades the accuracy of the simulation,
the bias to the overall optimization result is not significant. This is because the fitness ranking among
high-performing and low-performing design variants calculated by the lowest simulation quality
corresponds to that calculated by the higher quality according to our observation. With the lowest
simulation quality applied, each simulation lasts from 1 to 2 min (HP Z440 Workstation with a Xeon
4-core CPU). The typical time for one evolutionary optimization process reaching the required number
of design generations and performance evaluations (4980, to be exact, in the case study) is around 4 to
5 days. While the time consumed by the optimization process cannot satisfy the time constraint set
by practice, this can be addressed with an increase in computational power and incorporating other
approaches, such as parallel computing and cloud computing.
With regard to the optimization algorithm, the case study uses a newly developed hybrid
evolutionary algorithm designed to support explorative design optimization, called SSIEA (steady-state
Sustainability 2019,11, 6965 12 of 20
island evolutionary algorithm) [
37
]. This algorithm can yield several high-performing solutions, while
the solutions also have enhanced design dierentiations. The algorithm integrates an island-model
approach and a steady-state replacement strategy into a standard evolutionary algorithm to increase
diversity in the design population and improve the search eciency. The island model allows the
algorithm to launch multiple parallel search processes to evolve several “niching” subpopulations.
For each subpopulation, it is guided to focus on a dierent region in the design solution space.
The separation and multitude of subpopulations counteract the exploitative natural inherited in the
standard evolutionary algorithm and prevents the optimization from producing a family of very similar
design solutions due to the genotypic similarity. At the same, the steady-state replacement strategy
speeds up the optimization process by increasing the evolutionary pressure on each subpopulation. We
examined the algorithm in a previous study [
37
], which indicates that this algorithm can significantly
outperform the standard genetic algorithm. Incorporating this algorithm with the proposed building
massing generation algorithm can retrieve several high-performing solutions from the optimization
process. Furthermore, these solutions have significant topological dierentiation due to the genotypic
diversity in the individuals from dierent subpopulations. The diversity in the result enhances the
feedback from optimization, which helps architects discover underlying compromises and trade-os
characterizing the design problem.
For the setting of SSIEA, six subpopulations (islands) are set for the optimization process in
order to achieve a relatively high diversity in the optimization result. Each subpopulation has 50
individuals as the initial size, and, thereby, the overall initial population size is 300. In each iteration,
10 individuals are randomly selected from each subpopulation, and six higher-ranking individuals are
selected as parents by tournament selection to reproduce an equal number of ospring individuals by
crossover and mutations. With all ospring individuals evaluated by simulations, the 10 originally
selected individuals compete against the ospring individuals, and inferior ones are then replaced
by higher-ranking ospring individuals. Lastly, 130 iterations are set as the termination criteria, so
that there are 4980 design generations and evaluations in each optimization process as a result, which
ensures that the design can be suciently evolved.
2.4.2. Initialization Parameters
With the proposed algorithm, the first step is to specify the initialization parameters. In order to
widen the scope of exploration, the boundary constraint is deactivated to achieve a relatively radical
change in the generated building massings. Then, we specify the parameters related to the attribute of
two building massing designs, including total floor numbers, numbers of column grids in the x- and
y- directions, floor heights, and column-grid span sizes. For the second case study, the building plot
shown in Figure 15 is not suitable for a rectangular footprint, and, therefore, an L-shaped footprint
is set for the maximal volume and divides the building massing into a west wing and a south wing.
This part of the setting will be presented at the end of this section together with other initialization
parameters in the user interface.
Apart from the parameters mentioned specifying the attributes of the building massing design,
we also compare three initialization parameter setups varying the size constraints and the number of
subtractors (Table 1). For the first case study, Figure 17 illustrates the generated building massings
for the three initialization modeling parameter setups. From the first row in Figure 17, it can be seen
that if the number of subtractors and the size constraint are set too small, the building massings will
not embody significant topological variability. This is despite the fact that the boundary constraint
is deactivated, which will improve topological variability. For the other two setups, the features
appearing in the generated building massings are mostly similar as shown in the second and third rows
in Figure 17. Considering that a larger number of subtractors applied to the third setup expands the
search space and increases the search diculty for evolutionary optimization, the second initialization
parameter setup is selected for the subsequent execution of the optimization process.
Sustainability 2019,11, 6965 13 of 20
Table 1. Initialization parameters.
Number of Subtractors Size Constraint
Vertical Subtractors Horizontal Subtractors Vertical Subtractors Horizontal Subtractors
Setup 1 2 3 [2, 3] [2, 3]
Setup 2 3 4 [3, 4] [3, 5]
Setup 3 4 5 [3, 5] [3, 5]
Sustainability 2019, 11, x FOR PEER REVIEW 13 of 21
With the proposed algorithm, the first step is to specify the initialization parameters. In order to
widen the scope of exploration, the boundary constraint is deactivated to achieve a relatively radical
change in the generated building massings. Then, we specify the parameters related to the attribute
of two building massing designs, including total floor numbers, numbers of column grids in the x-
and y- directions, floor heights, and column-grid span sizes. For the second case study, the building
plot shown in Figure 15 is not suitable for a rectangular footprint, and, therefore, an L-shaped
footprint is set for the maximal volume and divides the building massing into a west wing and a
south wing. This part of the setting will be presented at the end of this section together with other
initialization parameters in the user interface.
Apart from the parameters mentioned specifying the attributes of the building massing design,
we also compare three initialization parameter setups varying the size constraints and the number of
subtractors (Table 1). For the first case study, Figure 17 illustrates the generated building massings
for the three initialization modeling parameter setups. From the first row in Figure 17, it can be seen
that if the number of subtractors and the size constraint are set too small, the building massings will
not embody significant topological variability. This is despite the fact that the boundary constraint is
deactivated, which will improve topological variability. For the other two setups, the features
appearing in the generated building massings are mostly similar as shown in the second and third
rows in Figure 17. Considering that a larger number of subtractors applied to the third setup expands
the search space and increases the search difficulty for evolutionary optimization, the second
initialization parameter setup is selected for the subsequent execution of the optimization process.
Table 1. Initialization parameters.
Number of Subtractors Size Constraint
Vertical subtractors Horizontal subtractors Vertical subtractors Horizontal subtractors
Setup 1 2 3 [2, 3] [2, 3]
Setup 2 3 4 [3, 4] [3, 5]
Setup 3 4 5 [3, 5] [3, 5]
Figure 17. Random sampling generated building massings by the initialization parameter.
For the second case study, Figure 18 shows the generated building massings, also based on the
three initialization parameter setups. In this case, the second setup in Table 1 is selected as it results
in reasonable topological variability. In contrast, the generated building massings by the first setup
(the first line in Figure 18) are relatively similar. For those generated by the third setup (in the third
line in Figure 18), the possibility of creating two separate building massing entities may be not
suitable for the functional requirement in this case due to the lack of accessibility and connectivity.
Figure 17. Random sampling generated building massings by the initialization parameter.
For the second case study, Figure 18 shows the generated building massings, also based on the
three initialization parameter setups. In this case, the second setup in Table 1is selected as it results in
reasonable topological variability. In contrast, the generated building massings by the first setup (the
first line in Figure 18) are relatively similar. For those generated by the third setup (in the third line
in Figure 18), the possibility of creating two separate building massing entities may be not suitable for
the functional requirement in this case due to the lack of accessibility and connectivity.
Sustainability 2019, 11, x FOR PEER REVIEW 14 of 21
Figure 18. Random sampling generated building massings by the initialization parameter.
The process of setting up the optimization algorithm is straightforward for the user and does
not require any parametric modelling to be performed. Instead, the user only needs to fill in certain
initialization parameter settings in a graphical user interface (GUI). Based on the above parameter
setup, the user interface for the two case studies is filled out as below (Figure 19). The difference in
the settings on the user interface between the two case studies is highlighted. The basic attributes
specify the parameters related to floor numbers, span numbers, etc. For the second case study, a fixed
cut volume in the building massing is set to create the L-shaped footprint.
Figure 19. The setting on the user interface.
3. Results
3.1. Case Study 1
The first case study describes a slab-type high-rise office building with a target gross area of
45,000 m2. We take the building massing shown in Figure 15 without any part removed as the
benchmark. The gross area of the benchmark building massing is 43,740 m2. The LE of the benchmark
building massing is 813,811 kWh, and the fitness after being penalized by the gross area difference is
836,597.
Figure 20 shows the elite individual in each subpopulation found by the optimization process.
In this case study, the surrounding buildings prevent a large amount of daylight from reaching the
building massing (Figure 16) and cast shadows on the facade of the building, which can undermine
the daylighting quality on the floor with windows frequently shaded by the shadow. In order to
improve daylighting, three dominant features can be found among elite individuals. First, stilts
appear in the building massing of Elite1, Elite4, and Elite5, which raise the overall building mass.
Raising the building mass reduces the space close to the ground, which naturally has worse
daylighting quality due to heavy daylight obstructions by the surrounding buildings.
Figure 18. Random sampling generated building massings by the initialization parameter.
The process of setting up the optimization algorithm is straightforward for the user and does
not require any parametric modelling to be performed. Instead, the user only needs to fill in certain
initialization parameter settings in a graphical user interface (GUI). Based on the above parameter
setup, the user interface for the two case studies is filled out as below (Figure 19). The dierence in the
settings on the user interface between the two case studies is highlighted. The basic attributes specify
the parameters related to floor numbers, span numbers, etc. For the second case study, a fixed cut
volume in the building massing is set to create the L-shaped footprint.
Sustainability 2019,11, 6965 14 of 20
Sustainability 2019, 11, x FOR PEER REVIEW 14 of 21
Figure 18. Random sampling generated building massings by the initialization parameter.
The process of setting up the optimization algorithm is straightforward for the user and does
not require any parametric modelling to be performed. Instead, the user only needs to fill in certain
initialization parameter settings in a graphical user interface (GUI). Based on the above parameter
setup, the user interface for the two case studies is filled out as below (Figure 19). The difference in
the settings on the user interface between the two case studies is highlighted. The basic attributes
specify the parameters related to floor numbers, span numbers, etc. For the second case study, a fixed
cut volume in the building massing is set to create the L-shaped footprint.
Figure 19. The setting on the user interface.
3. Results
3.1. Case Study 1
The first case study describes a slab-type high-rise office building with a target gross area of
45,000 m2. We take the building massing shown in Figure 15 without any part removed as the
benchmark. The gross area of the benchmark building massing is 43,740 m2. The LE of the benchmark
building massing is 813,811 kWh, and the fitness after being penalized by the gross area difference is
836,597.
Figure 20 shows the elite individual in each subpopulation found by the optimization process.
In this case study, the surrounding buildings prevent a large amount of daylight from reaching the
building massing (Figure 16) and cast shadows on the facade of the building, which can undermine
the daylighting quality on the floor with windows frequently shaded by the shadow. In order to
improve daylighting, three dominant features can be found among elite individuals. First, stilts
appear in the building massing of Elite1, Elite4, and Elite5, which raise the overall building mass.
Raising the building mass reduces the space close to the ground, which naturally has worse
daylighting quality due to heavy daylight obstructions by the surrounding buildings.
Figure 19. The setting on the user interface.
3. Results
3.1. Case Study 1
The first case study describes a slab-type high-rise oce building with a target gross area of
45,000 m
2
. We take the building massing shown in Figure 15 without any part removed as the
benchmark. The gross area of the benchmark building massing is 43,740 m
2
. The LE of the benchmark
building massing is 813,811 kWh, and the fitness after being penalized by the gross area dierence is
836,597.
Figure 20 shows the elite individual in each subpopulation found by the optimization process.
In this case study, the surrounding buildings prevent a large amount of daylight from reaching the
building massing (Figure 16) and cast shadows on the facade of the building, which can undermine
the daylighting quality on the floor with windows frequently shaded by the shadow. In order to
improve daylighting, three dominant features can be found among elite individuals. First, stilts appear
in the building massing of Elite1, Elite4, and Elite5, which raise the overall building mass. Raising the
building mass reduces the space close to the ground, which naturally has worse daylighting quality
due to heavy daylight obstructions by the surrounding buildings.
Sustainability 2019, 11, x FOR PEER REVIEW 15 of 21
Figure 20. Elite individuals of natural daylighting (south-west aerial view).
Second, cases, such as Elite2, Elite5, and Elite6, appear as a tower-type building massing. The
reason for this is that tower-type building massing increases the indoor floor area at a higher altitude
where there are fewer daylight obstructions due to surrounding buildings. Figure 21 illustrates the
natural lit space in a cross-sectional direction. Note that the natural-lit space (warmer red-colored
areas) increases as the floor level is raised. The first and second features suggest that the overall
performance of daylighting can be improved by manipulating the building massing in the vertical
direction—either reducing the proportion of lower floor levels as in Elite1 or increasing the
proportion of higher floor levels as in Elite6. In contrast, the third feature manipulates the building
massing in the horizontal direction. All elite individuals tend to have a stepped footprint, which can
enlarge the spacing with the south high-rise building as well as increase the facade area exposed to
daylight [40].
Figure 21. Daylight autonomy analysis by floors.
The effect of the optimization on daylighting is significant. The elites achieve an average 96%
improvement compared with the benchmark building massing. It means that, for this case study, the
performance of daylighting is sensitive to the change in the building massing. This finding also
suggests that while there is great potential in building massing design to achieve better daylighting,
inappropriate building massing design can also lead to much intensive lighting energy consumption.
Lastly, the elites with a tower-like massing may be inappropriate when a rigorous urban planning
code regulates the height of the building. However, this helps to enhance the tendency of raising the
building massing for better daylighting for this case study.
3.2. Case Study 2
The second case study describes a middle-rise deep-plan building for multi-purpose use with a
target gross area of 100,000 m2. Similar to the first case study, the building massing without any part
removed is taken as the benchmark, as shown in Figure 15. The gross area of the benchmark building
massing is 102332 m2. The LE of the benchmark building massing is 1.9334 × 106 kWh, and the fitness
after being penalized by the gross area factor is 1.9785 × 106. Compared with the first case study, the
change in the building plot allows the south wing of the building to be exposed to direct sunlight
without obstructions by other buildings (Figure 16). Thus, the building massing should react
differently compared with the first case study.
Figure 22 shows the elite individual in each subpopulation. As the deep-plan building is
unfavorable to daylighting, a common approach reflected in the elite building massing to overcome
this drawback is to reduce the depth of the floor plan by inserting subtractors. This approach can
Figure 20. Elite individuals of natural daylighting (south-west aerial view).
Second, cases, such as Elite2, Elite5, and Elite6, appear as a tower-type building massing.
The reason for this is that tower-type building massing increases the indoor floor area at a higher
altitude where there are fewer daylight obstructions due to surrounding buildings. Figure 21 illustrates
the natural lit space in a cross-sectional direction. Note that the natural-lit space (warmer red-colored
areas) increases as the floor level is raised. The first and second features suggest that the overall
performance of daylighting can be improved by manipulating the building massing in the vertical
direction—either reducing the proportion of lower floor levels as in Elite1 or increasing the proportion
of higher floor levels as in Elite6. In contrast, the third feature manipulates the building massing in
the horizontal direction. All elite individuals tend to have a stepped footprint, which can enlarge the
spacing with the south high-rise building as well as increase the facade area exposed to daylight [
40
].
The eect of the optimization on daylighting is significant. The elites achieve an average 96%
improvement compared with the benchmark building massing. It means that, for this case study,
the performance of daylighting is sensitive to the change in the building massing. This finding also
suggests that while there is great potential in building massing design to achieve better daylighting,
Sustainability 2019,11, 6965 15 of 20
inappropriate building massing design can also lead to much intensive lighting energy consumption.
Lastly, the elites with a tower-like massing may be inappropriate when a rigorous urban planning
code regulates the height of the building. However, this helps to enhance the tendency of raising the
building massing for better daylighting for this case study.
Sustainability 2019, 11, x FOR PEER REVIEW 15 of 21
Figure 20. Elite individuals of natural daylighting (south-west aerial view).
Second, cases, such as Elite2, Elite5, and Elite6, appear as a tower-type building massing. The
reason for this is that tower-type building massing increases the indoor floor area at a higher altitude
where there are fewer daylight obstructions due to surrounding buildings. Figure 21 illustrates the
natural lit space in a cross-sectional direction. Note that the natural-lit space (warmer red-colored
areas) increases as the floor level is raised. The first and second features suggest that the overall
performance of daylighting can be improved by manipulating the building massing in the vertical
direction—either reducing the proportion of lower floor levels as in Elite1 or increasing the
proportion of higher floor levels as in Elite6. In contrast, the third feature manipulates the building
massing in the horizontal direction. All elite individuals tend to have a stepped footprint, which can
enlarge the spacing with the south high-rise building as well as increase the facade area exposed to
daylight [40].
Figure 21. Daylight autonomy analysis by floors.
The effect of the optimization on daylighting is significant. The elites achieve an average 96%
improvement compared with the benchmark building massing. It means that, for this case study, the
performance of daylighting is sensitive to the change in the building massing. This finding also
suggests that while there is great potential in building massing design to achieve better daylighting,
inappropriate building massing design can also lead to much intensive lighting energy consumption.
Lastly, the elites with a tower-like massing may be inappropriate when a rigorous urban planning
code regulates the height of the building. However, this helps to enhance the tendency of raising the
building massing for better daylighting for this case study.
3.2. Case Study 2
The second case study describes a middle-rise deep-plan building for multi-purpose use with a
target gross area of 100,000 m2. Similar to the first case study, the building massing without any part
removed is taken as the benchmark, as shown in Figure 15. The gross area of the benchmark building
massing is 102332 m2. The LE of the benchmark building massing is 1.9334 × 106 kWh, and the fitness
after being penalized by the gross area factor is 1.9785 × 106. Compared with the first case study, the
change in the building plot allows the south wing of the building to be exposed to direct sunlight
without obstructions by other buildings (Figure 16). Thus, the building massing should react
differently compared with the first case study.
Figure 22 shows the elite individual in each subpopulation. As the deep-plan building is
unfavorable to daylighting, a common approach reflected in the elite building massing to overcome
this drawback is to reduce the depth of the floor plan by inserting subtractors. This approach can
Figure 21. Daylight autonomy analysis by floors.
3.2. Case Study 2
The second case study describes a middle-rise deep-plan building for multi-purpose use with
a target gross area of 100,000 m
2
. Similar to the first case study, the building massing without any
part removed is taken as the benchmark, as shown in Figure 15. The gross area of the benchmark
building massing is 102,332 m
2
. The LE of the benchmark building massing is 1.9334
×
10
6
kWh, and
the fitness after being penalized by the gross area factor is 1.9785
×
10
6
. Compared with the first case
study, the change in the building plot allows the south wing of the building to be exposed to direct
sunlight without obstructions by other buildings (Figure 16). Thus, the building massing should react
dierently compared with the first case study.
Figure 22 shows the elite individual in each subpopulation. As the deep-plan building is
unfavorable to daylighting, a common approach reflected in the elite building massing to overcome
this drawback is to reduce the depth of the floor plan by inserting subtractors. This approach can result
in two dominant features found among these elite building massings. First, light wells appear in Elite1
and Elite5, which allow daylight to reach the inner part of the building. Second, there is a setback in
the south wing of the building massing (the blue-colored volume shown in Figure 23), which allows
the floor plan to become thinner and escape from the shadow cast by the south-west high-rise building.
Apart from these two features, horizontal carve-outs appearing in the south wing of Elite1 and stepped
roofs in Elite6 also help to reduce the depth of the floor plan and increases the facade area exposed to
daylight. Similar to the first case study, stilts also appear in Elite1 and Elite4 due to the same reason
explained in the first case study.
In summary, the elite building massing achieves an average 95.6% improvement in the overall
performance compared with the benchmark building massing. Concerning the features, thin plans
stand out in this case study as deep-plan buildings are naturally inferior in daylighting performance.
In contrast, courtyards, as a commonly adopted strategy for daylighting, do not appear in this case
study, which is mostly because a courtyard often occupies a large amount of building floor area, and
its contribution is not suciently significant to oset its disadvantage of a loss of floor area. Last, but
not least, Elite1 shows a mixture of dierent passive energy-saving strategies, including self-shading,
stilts, and light wells. It suggests that synergizing these strategies allows for significant progressive
improvement. Such mixtures of strategies are challenging to conceive by human architects and unlikely
to be found when the optimization is confined to building massing with limited topological variability.
Sustainability 2019,11, 6965 16 of 20
Sustainability 2019, 11, x FOR PEER REVIEW 16 of 21
result in two dominant features found among these elite building massings. First, light wells appear
in Elite1 and Elite5, which allow daylight to reach the inner part of the building. Second, there is a
setback in the south wing of the building massing (the blue-colored volume shown in Figure 23),
which allows the floor plan to become thinner and escape from the shadow cast by the south-west
high-rise building. Apart from these two features, horizontal carve-outs appearing in the south wing
of Elite1 and stepped roofs in Elite6 also help to reduce the depth of the floor plan and increases the
facade area exposed to daylight. Similar to the first case study, stilts also appear in Elite1 and Elite4
due to the same reason explained in the first case study.
Figure 22. Elite individuals of daylighting (south-east aerial view).
Figure 23. Set-back in the south wing of the building massing (south-east aerial view).
In summary, the elite building massing achieves an average 95.6% improvement in the overall
performance compared with the benchmark building massing. Concerning the features, thin plans
stand out in this case study as deep-plan buildings are naturally inferior in daylighting performance.
In contrast, courtyards, as a commonly adopted strategy for daylighting, do not appear in this case
study, which is mostly because a courtyard often occupies a large amount of building floor area, and
its contribution is not sufficiently significant to offset its disadvantage of a loss of floor area. Last, but
not least, Elite1 shows a mixture of different passive energy-saving strategies, including self-shading,
stilts, and light wells. It suggests that synergizing these strategies allows for significant progressive
improvement. Such mixtures of strategies are challenging to conceive by human architects and
unlikely to be found when the optimization is confined to building massing with limited topological
variability.
4. Discussion
The two case studies allowed the efficacy of the proposed algorithm to be investigated under
different design settings, in terms of surrounding buildings and building design objects.
Strengthened by the explorative character of the proposed evolutionary algorithm, the optimization
process successfully explored and evaluated different building massing variants and identified
multiple high-performing solutions for each design scenario. Due to the extensive topological
variability, the building massings retrieved from the optimization present significant design
differentiation. The difference among these elite variants helps to reveal performance trade-offs and
compromises. At the same time, without the need to perform any actual parametric modelling, the
process of carrying out performance-based optimization is streamlined. Architects only need to
specify the initialization parameters to restrict the overall geometric feature in the generated building
massings. In this regard, the parametric model based on the algorithm can be viewed as a “meta-
model” of the subtractive form generation principle, from which various task-specific versioning
models for different projects can be readily derived.
Figure 22. Elite individuals of daylighting (south-east aerial view).
Sustainability 2019, 11, x FOR PEER REVIEW 16 of 21
result in two dominant features found among these elite building massings. First, light wells appear
in Elite1 and Elite5, which allow daylight to reach the inner part of the building. Second, there is a
setback in the south wing of the building massing (the blue-colored volume shown in Figure 23),
which allows the floor plan to become thinner and escape from the shadow cast by the south-west
high-rise building. Apart from these two features, horizontal carve-outs appearing in the south wing
of Elite1 and stepped roofs in Elite6 also help to reduce the depth of the floor plan and increases the
facade area exposed to daylight. Similar to the first case study, stilts also appear in Elite1 and Elite4
due to the same reason explained in the first case study.
Figure 22. Elite individuals of daylighting (south-east aerial view).
Figure 23. Set-back in the south wing of the building massing (south-east aerial view).
In summary, the elite building massing achieves an average 95.6% improvement in the overall
performance compared with the benchmark building massing. Concerning the features, thin plans
stand out in this case study as deep-plan buildings are naturally inferior in daylighting performance.
In contrast, courtyards, as a commonly adopted strategy for daylighting, do not appear in this case
study, which is mostly because a courtyard often occupies a large amount of building floor area, and
its contribution is not sufficiently significant to offset its disadvantage of a loss of floor area. Last, but
not least, Elite1 shows a mixture of different passive energy-saving strategies, including self-shading,
stilts, and light wells. It suggests that synergizing these strategies allows for significant progressive
improvement. Such mixtures of strategies are challenging to conceive by human architects and
unlikely to be found when the optimization is confined to building massing with limited topological
variability.
4. Discussion
The two case studies allowed the efficacy of the proposed algorithm to be investigated under
different design settings, in terms of surrounding buildings and building design objects.
Strengthened by the explorative character of the proposed evolutionary algorithm, the optimization
process successfully explored and evaluated different building massing variants and identified
multiple high-performing solutions for each design scenario. Due to the extensive topological
variability, the building massings retrieved from the optimization present significant design
differentiation. The difference among these elite variants helps to reveal performance trade-offs and
compromises. At the same time, without the need to perform any actual parametric modelling, the
process of carrying out performance-based optimization is streamlined. Architects only need to
specify the initialization parameters to restrict the overall geometric feature in the generated building
massings. In this regard, the parametric model based on the algorithm can be viewed as a “meta-
model” of the subtractive form generation principle, from which various task-specific versioning
models for different projects can be readily derived.
Figure 23. Set-back in the south wing of the building massing (south-east aerial view).
4. Discussion
The two case studies allowed the ecacy of the proposed algorithm to be investigated under
dierent design settings, in terms of surrounding buildings and building design objects. Strengthened by
the explorative character of the proposed evolutionary algorithm, the optimization process successfully
explored and evaluated dierent building massing variants and identified multiple high-performing
solutions for each design scenario. Due to the extensive topological variability, the building massings
retrieved from the optimization present significant design dierentiation. The dierence among these
elite variants helps to reveal performance trade-os and compromises. At the same time, without
the need to perform any actual parametric modelling, the process of carrying out performance-based
optimization is streamlined. Architects only need to specify the initialization parameters to restrict the
overall geometric feature in the generated building massings. In this regard, the parametric model
based on the algorithm can be viewed as a “meta-model” of the subtractive form generation principle,
from which various task-specific versioning models for dierent projects can be readily derived.
While the proposed algorithm addresses the two challenges identified in the first section, there are
three key issues and limitations to be highlighted. First, the generated building massings are all created
from orthogonal geometries. In this regard, the optimization-based exploration with the proposed
algorithm can be seen as an initial exploration of diverse building massings but without in-depth
exploitation of the accurate solution under each specific building massing configuration. In other
words, the result of the optimization can be further improved if higher geometric freedom is provided
by incorporating transformation approaches, such as twist, rotation, and slant [
22
,
23
,
41
]. Incorporating
these in the algorithm requires additional variables to define transformation operations. Since the
algorithm already has a relatively large number of optimization parameters, adding extra parameters
may be ineective since the increase in the size of the design solution space often impedes the discovery
of high-performing solutions [
28
]. Instead, it is more advisable to separate the optimization process
into two stages. In the first stage, the coarse building massing can be explored while, in the second
stage, a small number of massings reflecting the specific architectural implications can be selected, and
transformation operations can then be applied to evolve more in-depth solutions.
Second, in the context of evolutionary optimization, the arbitrary placement of subtractors creates
a many-to-one relationship between the optimization parameters lists and the corresponding output.
This relationship defines the genotype–phenotype mapping. For example, although two design
variants (phenotypes) have similar topological configurations, the two variants could be generated
from two entirely dierent optimization parameter lists (genotypes). This is because the two dierent
parameter lists contain the segment (chromosomes) at dierent positions with similar or identical
values, and this segment results in a subtractor in similar spatial positions and with similar dimensions.
Sustainability 2019,11, 6965 17 of 20
Figure 24 shows the parallel coordinate visualizing the parameter lists of the elite design variants.
Compared with the similarity among the formal representations (phenotypic representation), as shown
in Figures 20 and 22, the parameter lists (genotypic representation) do not show equivalent similarity.
This many-to-one mapping could be problematic for evolutionary optimization as it may result in early
entrapment into a local optimum [
28
]. However, in this research, the many-to-one mapping may help
to clarify dominant features when these features repeatedly appear in many subpopulations.
Sustainability 2019, 11, x FOR PEER REVIEW 17 of 21
While the proposed algorithm addresses the two challenges identified in the first section, there
are three key issues and limitations to be highlighted. First, the generated building massings are all
created from orthogonal geometries. In this regard, the optimization-based exploration with the
proposed algorithm can be seen as an initial exploration of diverse building massings but without in-
depth exploitation of the accurate solution under each specific building massing configuration. In
other words, the result of the optimization can be further improved if higher geometric freedom is
provided by incorporating transformation approaches, such as twist, rotation, and slant [22,23,41].
Incorporating these in the algorithm requires additional variables to define transformation
operations. Since the algorithm already has a relatively large number of optimization parameters,
adding extra parameters may be ineffective since the increase in the size of the design solution space
often impedes the discovery of high-performing solutions [28]. Instead, it is more advisable to
separate the optimization process into two stages. In the first stage, the coarse building massing can
be explored while, in the second stage, a small number of massings can be selected, and
transformation operations can then be applied to evolve more in-depth solutions.
Second, in the context of evolutionary optimization, the arbitrary placement of subtractors
creates a many-to-one relationship between the optimization parameters lists and the corresponding
output. This relationship defines the genotype–phenotype mapping. For example, although two
design variants (phenotypes) have similar topological configurations, the two variants could be
generated from two entirely different optimization parameter lists (genotypes). This is because the
two different parameter lists contain the segment (chromosomes) at different positions with similar
or identical values, and this segment results in a subtractor in similar spatial positions and with
similar dimensions. Figure 24 shows the parallel coordinate visualizing the parameter lists of the elite
design variants. Compared with the similarity among the formal representations (phenotypic
representation), as shown in Figure 20 and Figure 22, the parameter lists (genotypic representation)
do not show equivalent similarity. This many-to-one mapping could be problematic for evolutionary
optimization as it may result in early entrapment into a local optimum [28]. However, in this research,
the many-to-one mapping may help to clarify dominant features when these features repeatedly
appear in many subpopulations.
Figure 24. Parallel coordinate visualizing the parameters of elite design variants.
Third, instead of considering one objective as in the case studies, architects can alternatively use
multi-objective approaches, such as Pareto optimization, to include multiple objectives. Using multi-
objective optimization can show trade-offs and compromises among conflicting objectives. While
using multi-objective optimization has become popular in the literature, it should be noted that it
may result in a reduction in the search efficiency of the evolutionary optimization process [42]. In
addition, the result of multi-objective optimization blends features related to conflicting objectives,
which could make it difficult to identify the dominant feature related to each objective as clearly as
shown in the case studies of this research.
Last, apart from the issues and limitations mentioned above, there are two other directions
related to the algorithm itself that can be considered in future research. First, when considering the
Figure 24. Parallel coordinate visualizing the parameters of elite design variants.
Third, instead of considering one objective as in the case studies, architects can alternatively
use multi-objective approaches, such as Pareto optimization, to include multiple objectives.
Using multi-objective optimization can show trade-os and compromises among conflicting objectives.
While using multi-objective optimization has become popular in the literature, it should be noted
that it may result in a reduction in the search eciency of the evolutionary optimization process [
42
].
In addition, the result of multi-objective optimization blends features related to conflicting objectives,
which could make it dicult to identify the dominant feature related to each objective as clearly as
shown in the case studies of this research.
Last, apart from the issues and limitations mentioned above, there are two other directions related
to the algorithm itself that can be considered in future research. First, when considering the energy
consumption of air conditioning, the partition on the floor plan of rooms is critical to producing accurate
simulation results. While there is a technique to conduct simple thermal zoning by a straight-skeleton
subdivision [
43
], grammar approaches [
44
] allow for a more realistic approximation of the subdivision
of rooms. These techniques can be integrated into the algorithm. Second, increasing the degree of
customization can allow the algorithm to satisfy more specific design settings. For example:
More complex shapes for the maximal volume beyond box-like masses to make possible
combinations, such as towers and podiums and non-orthogonal geometries.
Provide more practical user-defined constraints to regulate the overall building massing, such as
maximum height, width, and length of the building massing.
Provide additional placement strategies of building cores, such as placing the cores at corners
rather than in the center of the building.
5. Conclusions
The focus of this research was to develop a reusable algorithm that generates building massing
with extensive topological variability to help architects conduct explorative and non-disruptive
performance-based optimization. The underlying intention of the research was to use optimization
as a means of exploiting the potential in building massing design for passive energy savings at the
outset of design processes. This process can narrow down the scope of consideration for architects,
thereby facilitating knowledge extraction for performance-aware design processes. At the same time,
Sustainability 2019,11, 6965 18 of 20
what is indispensable is that such optimization-based exploration should be well integrated into the
architectural design process.
For the algorithm focusing on design exploration rather than providing direct solutions, we
acknowledge that the building massing found by the case-study optimization may not satisfy all
aspects of architectural design [
16
,
45
]. Instead, in the data-poor situation of conceptual design stages,
the solution retrieved from the optimization plays a role as the “medium of reflection” in design
processes and allows architects to draw inspiration from its result [
13
]. In this regard, the use of the
subtractive form generation principle has the advantage that the architectural implication revealed by
the optimization result is intuitive and cognizable, which facilitates architects’ gaining insight from the
optimization results.
Driven by the optimization process, subtractors are manipulated only to remove volume from the
building massing that contributes to the most dominant and profitable eect on the improvement in
the building energy performance. It is evident that compared with the random sampling alternatives
in Figures 17 and 18, irrelevant and unnecessary voids appearing in those sampling alternatives
were mostly discarded and excluded across the optimization process. With minimal redundant
information, architects’ focus can remain on the dominant building massing characters and the
associative architectural implications related to building energy performance. In contrast, ambiguity and
distractions may happen if the geometry of the building massing is too complex. Desired architectural
implications could be misled by other less relevant issues.
In order to maximize the utility of performance-based optimization to assist architects in achieving
compelling energy sustainability, the proposed algorithm provides an unconventional approach to
using such optimization in conceptual design processes. Without parametric modelling, using the
algorithm encourages architects to leverage optimization processes to explore unknown solutions
and collect feedback related to various building energy performance factors at the outset of the
design process. In contrast, conventional performance-based optimization is only carried out after
the stage of design ideation and concept development. However, when the design concept is already
predetermined in building massing design, the room for performance improvements is limited. More
importantly, for those concepts developed in the data-poor situations of early design stages, these
concepts could be problematic and may result in flaws, which “can rarely be compensated at later
design stages and incurs a great redesign expense” [
46
]. In contrast, the proposed algorithm allows for
early interventions of performance-based optimization before and during concept development stages.
Such interventions increase architects’ awareness of building energy performance, thereby reducing
the possibility of a poor decision being made during the building massing design stages. The increased
awareness also allows architects to extrapolate the trajectory beyond the possibilities explored by the
optimization process, thereby driving the design towards a desired environmental-friendly solution.
Author Contributions:
Conceptualization, L.W., P.J. and K.W.C.; methodology, L.W.; software, L.W.; resources,
G.J.; writing—original draft preparation, L.W.; writing—review and editing, K.W.C., P.J. and Z.T.; supervision,
G.J.; funding acquisition, Z.T. and G.J.
Funding:
The work described in this study was sponsored by the projects of the National Natural Science
Foundation of China (NSFC#51578277) and (NSFC#51378248).
Acknowledgments:
The authors would like to thank anonymous reviewers, editors, Zhonggao Chen, and
Hyoung-June Park for their detailed and valued comments and suggestions. A warm acknowledgment is given to
Derek Pung Shuai Shi for his kind help to this research.
Conflicts of Interest: The authors declare no conflict of interest.
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(CC BY) license (http://creativecommons.org/licenses/by/4.0/).
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