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Abstract and Figures

Significant research has been undertaken focusing on the application of evolutionary algorithms for design exploration at conceptual design stages. However, standard evolutionary algorithms are typically not well-suited to supporting such optimization-based design exploration due to the lack of design diversity in the optimization result and the poor search efficiency in discovering high-performing design solutions. In order to address the two weaknesses, this paper proposes a hybrid evolutionary algorithm, called steady-stage island evolutionary algorithm (SSIEA). The implementation of SSIEA integrates an island model approach and a steady-state replacement strategy with an evolutionary algorithm. The combination aims to produce optimization results with rich design diversity while achieving significant fitness progress in a reasonable amount of time. Moreover, the use of the island model approach allows for an implicit clustering of the design population during the optimization process, which helps architects explore different alternative design directions. The performance of SSIEA is compared against other optimization algorithms using two case studies. The result shows that, in contrast to the other algorithms, SSIEA is capable of achieving a good compromise between design diversity and search efficiency. The case studies also demonstrate how SSIEA can support conceptual design exploration. For architects, the optimization results with diverse and high-performing solutions stimulate richer reflection and ideation, rendering SSIEA a helpful tool for conceptual design exploration.
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SSIEA – A Hybrid Evolutionary Algorithm for Supporting
Conceptual Architectural Design
Journal:
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Manuscript ID
AIE-2019-073.R4
Manuscript Type:
Research Article
Date Submitted by the
Author:
n/a
Complete List of Authors:
WANG, Likai; Nanjing University, School of Architecture and Urban
Planning
Janssen, Patrick; National University of Singapore, Department of
Architecture
Ji, Guohua; Nanjing University, School of Architecture & Urban Planning
Keyword:
steady-state replacement strategies, island models, Optimisation-based
exploration, Evolutionary algorithm, Conceptual architectural design
Abstract:
Significant research has been undertaken focusing on the application of
evolutionary algorithms for design exploration at conceptual design
stages. However, standard evolutionary algorithms are typically not well-
suited to supporting such optimisation-based design exploration due to
the lack of design diversity in the optimisation result and the poor search
efficiency in discovering high-performing design solutions. In order to
address the two weaknesses, this paper proposes a hybrid evolutionary
algorithm, called SSIEA. The implementation of SSIEA integrates an
island model approach and a steady-state replacement strategy with an
evolutionary algorithm. The combination aims to produce optimisation
results with rich design diversity while achieving significant fitness
progress in a reasonable amount of time. Moreover, the use of the island
model approach allows for an implicit clustering of the design population
during the optimisation process, which helps architects explore different
alternative design directions. The performance of SSIEA is compared
against other optimisation algorithms using two case studies. The result
shows that, in contrast to the other algorithms, SSIEA is capable of
achieving a good compromise between design diversity and search
efficiency. The case studies also demonstrate how SSIEA can support
conceptual design exploration. For architects, the optimisation result
with diverse and high-performing solutions stimulate richer reflection
and ideation, rendering SSIEA a helpful tool for conceptual design
exploration.
Cambridge University Press
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
For Review Only
Title: SSIEA – A Hybrid Evolutionary Algorithm for Supporting Conceptual Architectural Design
Abstract: Significant research has been undertaken focusing on the application of evolutionary algorithms
for design exploration at conceptual design stages. However, standard evolutionary algorithms are typically
not well-suited to supporting such optimisation-based design exploration due to the lack of design diversity
in the optimisation result and the poor search efficiency in discovering high-performing design solutions. In
order to address the two weaknesses, this paper proposes a hybrid evolutionary algorithm, called SSIEA.
The implementation of SSIEA integrates an island model approach and a steady-state replacement strategy
with an evolutionary algorithm. The combination aims to produce optimisation results with rich design
diversity while achieving significant fitness progress in a reasonable amount of time. Moreover, the use of
the island model approach allows for an implicit clustering of the design population during the optimisation
process, which helps architects explore different alternative design directions. The performance of SSIEA is
compared against other optimisation algorithms using two case studies. The result shows that, in contrast to
the other algorithms, SSIEA is capable of achieving a good compromise between design diversity and search
efficiency. The case studies also demonstrate how SSIEA can support conceptual design exploration. For
architects, the optimisation result with diverse and high-performing solutions stimulate richer reflection and
ideation, rendering SSIEA a helpful tool for conceptual design exploration.
Keywords: Evolutionary algorithms, steady-state replacement strategies, island models, optimisation-based
exploration, conceptual architectural design
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Nomenclature and Abbreviation
EA
Evolutionary Algorithm
SSIEA
Steady-stage Island Evolutionary Algorithm
LHS
Latin Hypercube Sampling
GA
Genetic Algorithm
RS
Random Search
RBFOpt
Radial Basis Function Optimisation
HypE
Hypervolume-based Multi-Objective EA
CMA-ES
Covariance Matrix Adaption Evolution Strategy
DIRECT
DIviding RECTangles algorithm
DIVA
A Radiance-based daylight simulation tool in Rhino-Grasshopper environment
FPT
Fitness Progress Trendline
Avg.
Average
Std.
Standard deviation
1 Introduction
As a significant branch of computational design optimisation methods, evolutionary optimisation has long
been regarded as a promising and powerful tool to assist architects in addressing complex design challenges
related to building performance either at individual building scale (Rodrigues, Fernandes, Gomes, Rodrigues,
& Costa, 2019; Toutou, Fikry, & Mohamed, 2018) or at urban scale (Natanian, Aleksandrowicz, & Auer,
2019; Nault, Waibel, Carmeliet, & Andersen, 2018). Based on evolutionary algorithms (EAs), evolutionary
optimisation can technically solve performance-based building design problems by evolving a population of
design solutions. For architectural design, such an evolutionary process can be guided by various energy-
related performance criteria such as daylighting and passive solar energy (Touloupaki & Theodosiou, 2017).
In addition, evolutionary optimisation also allows for an automated exploration of the design space, which
facilitates architects to extract information about the design problem. The latter exercise can be referred to
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as optimisation-based design exploration, and its relevance in enhancing design ideation and overcoming
design fixation at the conceptual design stages has become increasingly appreciated and upheld recently
(Bradner, Iorio, & Davis, 2014; Dino, 2012; Turrin, Von Buelow, & Stouffs, 2011).
Despite many successful cases in the literature, applying evolutionary optimisation in the conceptual
design phases remains challenging. The challenge can be partly attributed to two key weaknesses of EAs.
The first relates to the lack of adequate design diversity in the optimisation result, and the second relates to
poor search efficiency. These weaknesses mean that in many cases, the optimisation process is incapable of
discovering legitimate high-performing solutions within a reasonable timeframe.
In order to address these two weaknesses, this research proposes an implementation of a hybrid
evolutionary algorithm, named Steady-state Island Evolutionary Algorithm (SSIEA). SSIEA is designed to
facilitate architects to undertake an explorative and efficient evolutionary optimisation as a means of
conceptual design exploration. The implementation of SSIEA integrates the island model approach (Whitley,
Rana, & Heckendorn, 1999) into a standard evolutionary algorithm to enhance the genetic diversity in the
optimisation result. At the same time, SSIEA employs the steady-state replacement strategy (Agapie &
Wright, 2014) to improve search efficiency.
To place this research into the context, we first discuss the progress that has been made in the area of
applying EAs for assisting conceptual architectural design. In the main body of the paper, we will describe
SSIEA and present the case studies and associated results. We conclude by discussing the features and the
relative efficacy of the application of SSIEA and point out future research directions.
1.1 Related works
When applying evolutionary optimisation to design exploration at conceptual design stages, the aim is to
achieve progressive fitness improvement while exploring the design space to discover diverse legitimate
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high-performing alternative solutions (Ekici, Cubukcuoglu, Turrin, & Sariyildiz, 2018; Wortmann, 2018).
Diversity plays a key role in revealing trade-offs and compromises characterising the design problem.
Optimisation results consisting of a selection of legitimate high-performing design solutions are also
preferred by architects (Cichocka, Browne, & Ramirez, 2017; Wortmann & Nannicini, 2017). However, the
exploitative nature of standard EAs and certain commonly-used optimisation algorithms means that such
search processes often produce a population of design solutions that are all very similar, covering only a
small area of the design space (Rodrigues, Gaspar, & Gomes, 2013).
In order to enhance the diversity in the optimisation result, a widely-used method is to combine Pareto-
based methods with crowding-based (Makki, Showkatbakhsh, Tabony, & Weistock, 2018) or hypervolume-
based techniques (Vierlinger, 2013). This method has two key drawbacks. On the one hand, an over-
emphasis on diversity enhancement may degrade search efficiency, which can result in under-optimised
design variants (Cao, Huang, Wang, & Lin, 2012; Montgomery & Chen, 2012). On the other hand, although
the method can produce the optimisation process being able to output many diverse design solutions, another
significant hurdle is that the number of solutions may be very large. Analysing such results and extracting
useful information can be overwhelming and tiring for architects due to cognitive overload (Scheibehenne,
Greifeneder, & Todd, 2010). As a result, an additional effort for filtering and clustering the optimisation
result may also be required (Chen, 2015; Wortmann & Schroepfer, 2019; Yousif & Yan, 2018).
In consideration of the need for diversity in the optimisation result, the niching-based method, such as
island model approaches, may be advantageous. This method splits the population into subpopulations that
focus on different subspaces in the design space (Whitley et al., 1999). This method allows the diversity in
the optimisation result to be controllable by specifying the number of subpopulations. However, applying
the niching-based method can also reduce the search efficiency of the algorithm (Montgomery & Chen,
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2012). Thus, when using this method, it requires more design generations and evaluations to reach a
convergence of optimal or legitimate solutions satisfying the fitness requirement.
Apart from the lack of design diversity in the optimisation result, poor search efficiency of EAs is
another factor accounting for the failure of many evolutionary optimisation tasks. Poor search efficiency can
result in the evolutionary optimisation only producing inferior solutions, which can be highly misleading for
architects. In order to obtain accurate optimisation results, most EAs require a large number of generations
to converge on a set of legitimate satisficing solutions (Wang, Janssen, & Ji, 2018a). However, in the fast-
paced architectural design process, the time and computational resource budgets for the evolutionary
optimisation are typically limited, with the number of generations ranging from tens to hundreds (Nguyen,
Reiter, & Rigo, 2014; Si, Tian, Jin, Zhou, & Shi, 2019). As a result, the focus of the evolutionary optimisation
is on discovering competitive design solutions within a limited search budget rather than striving to find a
global optimum requiring a vastly greater search budget.
For optimisation problems with a limited search budget, poor search efficiency can partly be attributed
to the generational replacement strategy adopted by standard EAs. This replacement strategy requires the
whole population to be evaluated before reproduction can start. As a result, the evolutionary search process
must be repeatedly paused while all individuals in that generation are being evaluated. In order to overcome
this weakness, steady-state replacement strategies may have certain advantages (Agapie & Wright, 2014;
Janssen, 2005). This strategy employs a large generation gap, where only a small number of individuals in
the population are replaced in each generation. Thus, it allows newly-found fitter individuals to be inserted
back into the population more promptly and have an immediate feedback effect on the evolutionary
optimisation process.
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2 Methodology
SSIEA is aimed to enhance design diversity and improve search efficiency. The algorithm achieves this by
using an island model consisting of a series of parallel evolutionary optimisation processes, each focusing
on different non-neighbouring subspaces. For each of the islands, the algorithm uses a steady-state
replacement strategy to exploit the subspace in a “greedier” manner. The difference between the search
behaviour of a standard EA and SSIEA can be described as Figure 1.
The usefulness of SSIEA lies in the character of optimisation problems during conceptual architectural
design. First and foremost, the design space defined by parametric models during conceptual architectural
design is typically vast and multimodal (Wang, Janssen, & Ji, 2018b). In addition, due to the ill-defined
nature of conceptual design problems, there are often many feasible and legitimate design solutions inside
the design space. Such multimodal design search spaces are, in fact, preferable for conceptual design, since
the aim is exploring diverse legitimate high-performing design solutions rather than finding a single global
optimal solution. Such an exploration would be enhanced by multiple parallel searches for various sub-
optimal alternative solutions (Woodbury & Burrow, 2006). With the island model, parallel evolutionary
processes enable the evolutionary optimisation to focus on multiple design subspaces concurrently. This
search approach allows multiple feasible design solutions to be found at the end of the evolutionary
optimisation process, which helps reveal more information about the design problem.
SSIEA is based on an EA optimisation algorithm. As mentioned above, two key weaknesses of EAs are
poor search efficiency and inadequate design diversity. In SSIEA, these weaknesses are addressed by
integrating the steady-state replacement strategy and the island model strategy. The integration of these two
strategies can be mutually supporting because the strength of one strategy can help to overcome certain
negative tendencies within the other strategy.
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On the one hand, as a niching-based strategy, the island model may have a tendency to reduce search
efficiency (Montgomery & Chen, 2012). The steady-state replacement strategy is an efficient search
mechanism that can counteract this tendency. On the other hand, while the steady-state replacement strategy
may have a tendency to increase the evolutionary pressure, it makes the evolutionary process too exploitative.
The use of subpopulations with the island model can counteract this tendency. When a subpopulation gets
trapped by poor local optima, the application of the island model can facilitate the subpopulation to escape
from the entrapment by exchanging genetic material with other subpopulations.
Before explaining the concept and the techniques implemented in SSIEA, we first briefly outline the
overall SSIEA workflow. As shown in Figure 2, the workflow consists of four steps:
Setp 1 The workflow starts with the creation of the initial population by LHS (Latin-hypercube sampling).
After being evaluated by the fitness function, each individual in the initial population is assigned to
one of the subpopulations in turn;
Setp 2 After the initial generation, a small number of individuals in each subpopulation are selected, based
on the “generation gap” setting. These selected individuals go through a standard evolutionary
procedure, including tournament selection, crossover, and mutation, to create offspring. The newly-
created offspring compete against their parents. Any offspring individual with better fitness than the
parents is inserted back into the subpopulation, replacing a weaker parent individual.
Setp 3 Step 2 is repeated until no offspring with better fitness has been found. If no improvement is obtained
for a certain consecutive number of generations, the optimisation process for that subpopulation is
seen as having stagnated. The stagnation triggers a migration process, which exchanges several
individuals in the subpopulation with another subpopulation.
Setp 4 Lastly, step 2 and 3 are repeated until either the termination criteria or the maximum number of
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generations is reached. When the criteria have been reached, the optimisation results are returned.
2.1 Island Model
Conventional EAs with centralised population models treat the entire population as a single breeding unit
and execute evolutionary operations (crossover and mutation) on the whole population. Such EAs are weak
in maintaining desirable design diversity primarily because many subspaces with legitimate design solutions
are often discarded when solutions with only slightly better fitness are found.
In order to avoid this drawback, the island model can be used to restrain the competition between
individuals from different subspaces. Island models split the population into several ‘niche’ subpopulations
that are evolved relatively independently (Whitley et al., 1999). Thus, the individuals found by each
subpopulation can be preserved for a longer time and will not be immediately replaced, even when better
individuals are found in other subpopulations. When multiple legitimate subspaces can be preserved and
covered by the design subpopulations, it allows the evolutionary process of each subpopulation to exploit
the subspace more accurately without intervention by others.
In addition, the island-model will also perform an implicit clustering of the design population. As a
niching-based method, the individuals in each subpopulation tend to become more homogeneous over the
course of the evolutionary process. Thus, if the architects find legitimate solutions among the elite solutions
from a particular subpopulation, they can easily explore other similar alternative design variants in the same
subpopulation without requiring any additional clustering. For the architects, this can streamline the process
of using evolutionary optimisation in design exploration.
2.2 Migration
Natural evolutionary processes often benefit from mating across the boundaries of the subgroups of different
species (Chipperfield & Fleming, 1994). Likewise, the exchange of genetic material among subpopulations
is also encouraged when using island models, and the exchange process is referred to as migration (Alba &
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Troya, 1999). Migration can help a subpopulation escape entrapment within a poor design subspace by
inputting new genetic material from other subpopulations. The mixture of genetic material from two
subpopulations can allow the focus of the subpopulation to be repositioned somewhere between the two
associated subspaces.
For standard island model algorithms, migration is performed synchronously. When triggered, all
subpopulations simultaneously send out and receive individuals with another subpopulation. However, such
a migration operation can be adverse if high-fitness individuals are sent to a subpopulation consisting of
individuals with lower fitness. To avoid this drawback, SSIEA applies an asynchronous migration scheme
(Horii, Miki, Koizumi, & Tsujiuchi, 2002). This scheme triggers migration only when the evolution of a
subpopulation falls into stagnation. Specifically, if a subpopulation has had no new individuals for several
generations, the evolution of this subpopulation will be judged as stagnant. After that, new genetic materials
are allowed to be inputted through migration.
For SSIEA, the migration operation is also aimed to introduce heterogeneous genetic materials to a
stagnating subpopulation in order to increase the genetic differentiation in the subpopulation. Thus, for a
stagnating subpopulation, the migration operation exchange individuals with the subpopulation that has the
largest distance to the stagnating subpopulation. The distance between the two subpopulations is calculated
by averaging the pairwise Euclidean distance of the individuals in the two subpopulations.
2.3 Steady-State Replacement Strategy
With the steady-state replacement strategy, SSIEA executes all other evolutionary operations sequentially
as standard EAs do. In each generation, a fixed number of individuals in each subpopulation are randomly
selected based on the ‘generation gap’ setting. Next, tournament selection is applied to choose the fitter
individuals from these as parents to create offspring. The parents and offspring all compete with one another.
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The higher-ranking offspring individuals are inserted back into the subpopulation, replacing the inferior
parents, while the remaining inferior offspring are discarded. Although the selective nature of the steady-
state replacement strategy renders the evolutionary process exploitative, the risk of over-exploitation or
premature convergence is compensated by the explorative nature of the island model.
2.4 Initial Population Generation
When using EAs, the initial population plays an important role in determining the quality of the obtained
optimisation result as uneven population distributions could lead to early entrapment by particular local
optima (Maaranen, Miettinen, & Penttinen, 2007; Talbi, 2009). Some researchers seek to avoid the negative
impact on the optimisation result due to the uneven distributed initial population by applying techniques
such as Mersenne Twister Fast Random Number Generator (Vierlinger, 2013) and LHS (Latin hypercube
Sampling) (Park, Jeong, & Choi, 2015). For SSIEA, an uneven initial population distribution can also
undermine the goal of achieving adequate design diversity because an uneven initial population can result
in several subpopulations having overlapping design subspaces containing similar design variants.
In order to prevent the subpopulations from focusing on overlapping design subspaces, LHS is applied
to generate the initial population for ensuring the individuals are spread uniformly in the design space. The
advantage of using LHS is that, for every individual in the initial population, the value in each parameter
does not coincide with that of any other individual (Shields & Zhang, 2016). Thus, using LHS can reduce
the possibility of individuals with similar parameters, which may introduce biases in the initial population
towards some design subspaces.
2.5 Software and Platform
To facilitate the ease of use for architects and designers, SSIEA is implemented in the Rhino-Grasshopper
environment as a plug-in component. Rhino-Grasshopper is one of the most popular parametric modelling
design platforms in architecture, and there is an increasing number of performance simulators or interfaces
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being integrated into it, such as DIVA and Archsim (Jakubiec & Reinhart, 2011). Thus, the implementation
in this platform can allow architects to establish design optimisation systems by connecting SSIEA to the
parametric model for building design generation and performance simulation tools for fitness evaluation.
3 Case studies
To demonstrate the efficacy of SSIEA, we present two case studies of architectural optimisation problems
(Wang, Janssen, Chen, Tong, & Ji, 2019; Wang et al., 2018b). These two case studies describe optimisation
problems related to building massing design, and each problem incorporates a different fitness evaluation
criterion.
The first case study describes a building design optimisation problem with the fitness evaluated by a
fast, simplified calculation of the building’s economic performance. Thus, the optimisation process based
on this calculation is inexpensive to compute. In this regard, the focus of the first case study is on comparing
SSIEA against other optimisation algorithms.
The second case study aims to show how SSIEA can be used in a conceptual design scenario with a
more realistic design problem. Hence, in addition to comparing the performance of SSIEA against other
optimisation algorithms, the second case study also investigates the utility of SSIEA in supporting conceptual
design.
3.1 Design Setting
3.1.1 Case Study 1
The first case study describes a 40-story high-rise building design with a central vertical atrium and a series
of sky gardens (Wang et al., 2018b). The optimisation objective is to search for design variants that can
optimise the economic performance considering various factors, including potential rental revenue, façade
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cost, and construction cost.
In terms of the building design generation, the parametric model used in this case study defines the
positions of sky gardens by using a 3D cellular voxel approach (Wang et al., 2018b). The building mass is
represented as a series of fixed-size spatial voxels (Figure 3). Except for the voxels representing the structural
cores and the atrium, sky garden voids can be inserted into the building mass by switching voxels from solid
to void. In order to avoid chaotic design variants, a set of predefined floor layouts are used that constrain the
ratio of indoor space to outdoor voids. In addition, a set of repair functions are used to correct infeasible
local features such as over-large voids (Wang et al., 2018b).
In order to reduce the number of parameters that are required, the building is represented as 15 floor
groups. Each group consists of three to five consecutive floor levels, and all these levels have the same floor
layout. Each floor group requires three parameters, defining the number of floor levels within the group, the
orientation of the floor layout, and the plan of the floor layout. Hence, to generate design solutions, the
parametric model requires 45 discrete parameters. Figure 4 shows a random sampling of design variants.
Based on the parametric model, the fitness of the generated building design variants is calculated by
the function described below:
𝑓𝑖𝑡𝑛𝑒𝑠𝑠
=
𝑖
=
1
(
𝑅𝑅
𝑖
𝑃𝑅𝐹
+
𝐹𝐶
𝑖
+
𝑆𝐶
𝑖
+
𝐶𝐶
𝑖
)
where N is the total number of floors, which is equal to 40. indicates the rental revenue each floor,
𝑅𝑅
𝑖
which is calculated by multiplying the rentable floor area each voxel with the unit rental price. is a
𝑃𝑅𝐹
floor rental price regulating factor that gives different preferences to space with better orientations based on
the ratio indicated in Figure 3 and also gives preference to spaces on the upper or lower floors (due to the
better view or accessibility). , , and indicates the construction cost of facades, slabs, and
𝐹𝐶
𝑖
𝑆𝐶
𝑖
𝐶𝐶
𝑖
structural cores of each floor. is calculated by multiplying the façade surface area with a fixed unit
𝐹𝐶
𝑖
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price of façade material. , and , are calculated by multiplying the floor surface area of the voxel with
𝑆𝐶
𝑖
𝐶𝐶
𝑖
different unit construction price raising along with the increase in floor levels because the construction in
higher floor levels is pricier.
Due to the use of the constraints and repair functions, the genotypes-phenotypes mapping is many-to-
one and not very linear, which results in an irregular design search space that is challenging for optimisation
algorithms to search (Wang et al., 2018b). The irregular design search space can mislead the optimisation
process by local optima and may make the process suffer from premature convergence. For architectural
optimisation problems that incorporate rule-based methods or implicit generative methods, this type of
irregular design search space is not unusual. In this respect, this case study intentionally creates such an
irregular design search space to differentiate the capability of each optimisation algorithms in handling the
challenge.
3.1.2 Case Study 2
The second case study (Wang, Janssen, Chen, et al., 2019) describes a high-rise slab-type building located
in an actual urban environment, and daylighting performance is considered the optimisation objective. Figure
5 shows the building plot and its sun path analysis. The building plot is surrounded by several high-rise
buildings, which leads to significant daylight obstructions. This condition makes it challenging for the
building massing to achieve desired daylighting performance.
The daylighting performance is evaluated by the annual lighting energy (LE) consumed by the building.
At the same time, the gross area of the generated building is considered a functional requirement in this
design, which is set to 45,000 m2. The gross area target is defined as a penalty function. The penalty function
proportionally scales up the value of LE to punish the design variants failing to satisfy the gross area
requirement. The fitness function of this case study can be described below:
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𝑓𝑖𝑡𝑛𝑒𝑠𝑠
=
𝐿𝐸
×
(
1
+
|
𝐴
𝑎𝑐𝑡𝑢𝑎𝑙
𝐴
𝑡𝑎𝑟𝑔𝑒𝑡
𝐴
𝑡𝑎𝑟𝑔𝑒𝑡
|
)
where LE indicates the lighting energy consumption, and Aactual and ATarget indicate the actual gross area of
the building massing and the required target gross area.
The parametric model generates the building massing based on the subtractive form generation principle,
which removes different parts from a predefined cubic building block (Wang, Janssen, Chen, et al., 2019).
This principle creates building massings with high topological variability, while it can also schematically
describe many passive energy-saving strategies in the generated building massing design such as stilts,
atriums, and solar envelope. Figure 6 shows building massings generated by random sampling.
In this case-study design, 42 continuous parameters are used to define seven subtracting volumes. Each
subtracting volume requires six parameters, defining its position (x, y, z) and dimensions (length, width,
height). Similar to the first case study, various constraints and repair functions are used related to the
alignment and size of the subtracting volumes. These result in the relationship between genotype and
phenotype also being a many-to-one with various non-linear behaviours. This genotype-phenotype
relationship, in turn, results in an irregular design search space (Wang, Janssen, Chen, et al., 2019), creating
challenges for search and optimisation.
The simulation of LE is carried out on DIVA, a lighting simulator based on Radiance in Rhino-
Grasshopper (Jakubiec & Reinhart, 2011). The simulation is time-consuming, being roughly 60 to 80
seconds for each evaluation, which can make optimisation processes with thousands of iterations take days
to complete. The time taken to run the optimisation process is problematic when considering fast design
cycles that are typical in design offices. However, this can be addressed by other methods beyond the scope
of this research, such as reducing simulation time by offline simulation (Su & Yan, 2015), parallel computing,
and cloud computing (Kyropoulou, Ferrer, & Subramaniam, 2018).
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3.2 Algorithm Setup
We previously examined the performance of SSIEA by comparing it against the genetic algorithm (GA) and
a random search (RS) algorithm based on pseudo-random techniques (Wang, Janssen, & Ji, 2019). While
SSIEA significantly outperforms to these two, in this paper, we extend our examination by considering
another four more advanced evolutionary and non-evolutionary optimisation algorithms – HypE, DIRECT,
CMA-ES, and RBFOpt (Table 1), for comparing against SSIEA in regards to design diversity and search
efficiency.
These four algorithms have been extensively tested in several studies and showed good performance
on average (Waibel, Wortmann, Evins, & Carmeliet, 2019; Wortmann, 2017; Wortmann et al., 2017). In
addition, the application of HypE, RBFOpt, and CMA-ES can also produce different design variants in the
optimisation result, which allows for the comparison of design diversity between these algorithms and
SSIEA.
For SSIEA, the basic algorithm parameters are set as follows. 1) In order to obtain an adequate diversity
in the optimisation result, the number of subpopulations is set to 5, and each subpopulation has 40 individuals.
Thus, the initial population size (including all subpopulations) is 200. 2) After the initial generation, the
generation gap for the steady-state replacement strategy is set to 75%. Thus, 10 out of the 40 (25 %)
individuals in each subpopulation are randomly selected in each generation for evolution. Among the ten
randomly selected individuals, the selection rate for the tournament selection is set to 60%. Thus, the six
highest-ranking individuals are used to create offspring. 3) We consider two different mutation rates, 0.3 and
0.15, to investigate its impact on the design diversity and search efficiency of the optimisation process.
The other four algorithms are all implemented in the Rhino-Grasshopper platform. DIRECT is
implemented in Goat (Rechenraum GmbH, 2019), HypE in Octopus (Vierlinger, 2019), and RBFOpt and
CMA-ES in Opossum (Wortmann, 2018). In this case study, default setups are applied to these algorithms,
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while it should be noted that the parameter setup can have a significant impact on the performance of
optimisation algorithms.
For the second case study, we apply the same algorithm parameter setup of SSIEA and other
optimisation algorithms as in the first case study. However, the inferior mutation rate (0.30) of SSIEA found
in the first case study is no longer used in this case study.
3.3 Optimisation Process Setup
For the optimisation process, 2000 iterations of design generations and fitness evaluations are set as the
termination criteria for both case studies. This limit took into consideration the complexity of the problem
and the need for reasonably fast feedback during conceptual architectural design processes.
For SSIEA, the initial population size is 200, and each generation has 30 design generations and fitness
evaluations. Hence, it requires the generation number of 60 to make the optimisation process reach 2000
iterations. For HypE, the default initial population is also 200, and each generation has 100 design
generations and fitness evaluations as the default, which requires 18 generations to reach the termination
criteria. For DIRECT, RBFOpt, and CMA-ES, it generates one design each iteration, and, therefore, the
number of iterations is 2000.
For the first case study, the fast fitness evaluation also allows for the repetition of the optimisation
process to ensure the statistical significance of the results obtained. As a result, except for DIRECT, we
repeat the optimisation process based on each algorithm five times to avoid stochastic deviation. The reason
why DIRECT is excluded was that, as a non-stochastic algorithm, DIRECT produces the same optimization
results each time. For the second case study, each optimisation process based on daylighting simulation
roughly lasts two days. As a result, we only carry out the optimisation process based on each algorithm once.
3.4 Algorithm Performance Measurement
For both case studies, we consider several metrics to evaluate the performance of the algorithm in terms of
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design diversity and search efficiency. For design diversity, genetic diversity (diversity in parameters) is
used as the primary indicator for evaluating diversity in the optimisation result. Genetic diversity is
calculated based on a subset of the final evolved population, referred to as the elite set.
For SSIEA, the elite set is created by selecting the highest-ranking design variant in each of the five
subpopulations. For the other algorithms, the elite set is created by a process that selects representative high-
fitness design variants from the population. These representative design variants are selected using a three-
step process. First, a group of high-fitness design variants is created by selecting the best 200 design variants
from each optimisation process. This group is the same size as the population in SSIEA. Second, these 200
design variants are clustered into five subgroups according to the genotypic similarity. Five subgroups is
chosen in order to keep the size of the elite set equal to that of SSIEA. The clustering is performed by a K-
means algorithm implemented in the LunchBox plug-in in Grasshopper. Last, the elite set is created by
selecting the highest-ranking design variant in each of the five subgroups. In addition, we also use this
approach to processing the evolved population of SSIEA to compare the results produced by the explicit
clustering approach with the K-means algorithm and the implicit clustering approach with the island-model
approach.
With the elite set, we measure the genetic diversity by averaging the genetic difference value of all
design variants in the elite set. The genetic difference value of each design variant is calculated by averaging
the genetic distance between the design variant and all other design variants in the elite set. The genetic
distance between two design variants is measured by the normalised Euclidean distance between the
parameters (genotypes) of the two design variants. The genetic diversity is calculated as follow:
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foreach design variant:
calculate “genetic_distance” to four other design variants:
gd1, gd2, gd3, gd4
calculate the “genetic_difference”:
GD = (gd1 + gd2 + gd3 + gd4) / 4,
then take the five “genetic_difference” and calculate “genetic_diversity”:
genetic_diversity = (GD1 + GD2 + GD3 + GD4 + GD5) / 5
As mentioned in Section 1, the relevance of diversity in the optimisation result also depends on the
fitness of the design variants. Thus, the fitness of the five design variants in the elite set is also taken into
account. Moreover, the building design (phenotypic diversity) of these selected design variants is also
presented to show the design diversity at the phenotypic level, which helps to explain how differences of the
optimization result among these algorithms may affect the information extraction.
In terms of search efficiency, we consider the best fitness achieved by each optimisation process within
the predefined time frame (2000 iterations). To visualise the search efficiency, we draw fitness progress
trendlines (FPT) to show more detailed search behaviours among different algorithms. The drawing of FPTs
is based on the best solutions found over time.
Last, in the first case study, the optimisation process is run multiple times. Multiple executions allow
us to investigate the robustness of the algorithm. Robustness is an important indicator evaluating the
performance of optimisation algorithms. The ability to repeatedly obtain similar results is important for
architects to develop trust in the optimisation algorithm. We investigate the ability of each algorithm to
achieve stable optimisation results in terms of design diversity and search efficiency. For the second case
study, since the optimisation process based on each algorithm is executed only once, the robustness of the
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algorithm cannot be considered.
4 Results
4.1 Case Study 1
For the first case study, the optimisation goal is to maximise the economic performance of the building. Each
algorithm (excluding DIRECT) is executed five times to avoid stochastic deviation. Table 2 and Figure 7
summarise the results for the design diversity and fitness ranges of the five selected elite design variants.
Table 3 summarises the best fitness (the highest value) obtained by each of the five optimization runs. Figure
9 shows the fitness progress trendlines (FPTs) for each algorithm, as an average of the five runs. To
differentiate the optimisation process based on the two mutation rates of SSIEA, we label the one with a 0.3
mutation rate as SSIEA_1 and the one with a 0.15 mutation rate as SSIEA_2.
4.1.1 Design Diversity
Design diversity is measured as the average genetic difference among selected design variants in the elite
set, and the average difference value ranges from 0.0 to 1.0. For design diversity, DIRECT is excluded as it
fails to solve the design problem (the best fitness obtained is -35295.51). The significant inferior fitness
obtained renders the solutions found by DIRECT to be of no use to solve the design problem. Hence, in this
case, we do not consider DIRECT.
When only considering the average genetic difference, SSIEA underperforms relative to all other tested
algorithms (Table 2). This result suggests that these other algorithms are able to achieve more explorative
search than SSIEA. These algorithms typically explore many design subspaces during the optimisation
process, thereby preventing the optimisation from converging into a single design subspace. However, a
closer examination of the design variants in the elite set reveals that this diversity primarily result from the
inclusion of relatively low-fitness design variants in the optimisation result. This is also reflected in the
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overall low average fitness for the elite set.
When comparing the average fitness of the elite set, SSIEA_1 and SSIEA_2 stand out and achieve a
markedly better fitness as compared with the other algorithms. Even though the other algorithms are able to
obtain a higher genetic diversity score than SSIEA, the design variants in the elite set are less competitive.
This tendency can be further clarified by Figure 7, which shows that the fitness range of the elite set produced
by the other algorithms is markedly wider than those produced by SSIEA. In contrast, the design variants in
the SSIEA elite sets tend to have similar competitive fitness. Moreover, the narrow fitness range can also
account for the relatively lower genetic diversity obtained by SSIEA, as high-fitness design variants are
likely to resemble global optima.
When comparing SSIEA_1 and SSIEA_2, we find that a lower mutation rate can make the discovery
of better design variants more likely. At the same time, it does not result in any significant compromise when
it comes to genetic diversity. In addition, the comparison of the SSIEA clustering approaches reveals that
implicit clustering typically results in lower average genetic difference but higher average fitness than
explicit clustering.
The elite sets produced by the two clustering approaches are largely in agreement with one another. In
most cases, the best three or four design variants are typically shared by both elite sets. The explicit clustering
approach typically achieves higher genetic diversity by including one or two relatively low-fitness but more
heterogeneous design variants into the elite set. The higher genetic diversity produced by the explicit
clustering approach reveals the fact that the optimisation process of SSIEA is more explorative as shown in
the result produced by the implicit clutersing.
The result shows that SSIEA produce elite sets that are more optimised than the elite sets of the other
algorithms. The design variants in the SSIEA elite set are closer to global optima compared with other
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algorithms, which is critical for information extraction as under-optimised results can be very misleading.
In order to demonstrate this more clearly, Figure 8 shows the design variants in the elite set with the median
best fitness among the elite sets produced by the five optimisation runs.
As shown in Figure 8, the elite sets (either achieved by the implicit or explicit clustering approach)
found by SSIEA_1 and SSIEA_2 contain design variants sharing similar configurations in terms of the
number of sky gardens and their vertical positions. The diversity among these variants mainly reflects the
varying size and orientation of the sky garden. This result implies there is a specific configuration that is
essential in achieving the desirable good economic performance on the one hand. On the other hand, changes
in the size and orientation of the sky garden are relatively insignificant to the overall performance.
On the contrary, the elite sets found by the other algorithms primarily show the diversity in the number
of sky gardens, which reflects a trade-off between the economic performance and the number of sky gardens.
These design variants mostly have average fitness. For the architects, the trade-off primarily conveys that
controlling the number of sky gardens is essential in avoiding undesirable solutions with poor economic
performance. However, the critical information for the architect about how to achieve further improvements
in performance – for example, where to place the sky garden to get the desired good performance - remains
unclear.
4.1.2 Search Efficiency
The results in Table 3 indicate that, on average, SSIEA stands out amongst all tested algorithms. Between
SSIEA_1 and SSIEA_2, the lower mutation rate further improves the search efficiency but makes the
optimisation results less stable. In reverse, the higher mutation rate of SSIEA_1 (0.3) improves the early
optimisation phase. In particular, it speeds up the rate at which the optimisation process discovers highly
improved solutions at the outset. By comparing the FPTs shown in Figure 9, it can be seen that during the
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first 1000 iterations, SSIEA_1 makes greater fitness progress. It suggests that, during the early optimisation
phases, the higher mutation rate may heighten the tendency of the optimisation process to continue exploring
new design subspaces. This tendency can, in turn, lead to the discovery of better solutions.
On the contrary, the low mutation rate of SSIEA_2 (0.15) restrains it from exploring too many other
subspaces. This tendency forces the optimisation process to exploit the design subspace that it is already
exploring, which can be corroborated by the number of migrations, shown in Table 4. With the lower
mutation rate of SSIEA_2, the exploitation of design subspaces means that each subpopulation is more likely
to continue discovering new improved solutions by mating (crossover) individuals within the design
subspace. This tendency reduces the likelihood of the optimisation process falling into stagnation, which, in
turn, suppresses the migration between subpopulations during the optimisation process. Hence, despite being
slow in achieving significant fitness progress at the outset, the lower mutation rate allows SSIEA_2 to
discover more optimised solutions at the later optimisation phases.
For the other algorithms, the optimisation results of HypE and CMA-ES show marked decreases in
search performance as compared with SSIEA, while RBFOpt can achieve comparable fitness progress to
SSIEA in certain optimisation processes. In addition, all these algorithms outperform the performance of
GA and RS.
4.1.3 Robustness
Robustness is evaluated with respect to both design diversity and search efficiency. For robustness of design
diversity, we investigate the fitness range of the elite set for each algorithm, shown in Figure 7. The fitness
range obtained by using SSIEA_1 and SSIEA_2 is, in most cases, quite narrow, but also more stable than
those obtained by the other three algorithms. One exception is an optimisation process of SSIEA_2 that
outputs an elite set with large fitness differences. The overall tendency can also be corroborated with the
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standard deviation of the average difference demonstrated in Table 2, where the values of SSIEA_1 and
SSIEA_2 are markedly lower than that of other algorithms. A stable result can ensure that the information
extracted is consistent across different optimisation processes without significant deviations.
For the robustness of search efficiency, we focus on two aspects for each algorithm: the standard
deviation of the best fitness (the highest value) for the five optimisation runs and the ability to achieve similar
progress for all five runs. In terms of the first aspect, SSIEA_1 and SSIEA_2 are more stable than RBFOpt,
while less stable than HypE and CMA-ES (Table 3).
In terms of the second aspect, CMA-ES and HypE are the most consistent. For all five runs, the fitness
progress is quite similar (Figure 10). For these two algorithms, the fitness deviation of the five optimisation
runs across 2000 iterations is in general lower than most of the other algorithms. This result can be further
corroborated by Figure 11, which shows that all FPTs for these two algorithms achieve roughly equivalent
fitness progress at the same iteration number. In contrast, marked fitness leaps can occur during the
optimisation process based on SSIEA_1 and SSIEA_2 (Figure 11). Nonetheless, as shown in Figure 10, the
fitness deviation trendlines of SSIEA_1 start falling after 600 iterations, and the trendlines of SSIEA_2 only
show high variation from 1000 to 1800 iterations. These may suggest that SSIEA_1 and SSIEA_2 can
achieve better robustness if the optimisation process can be prolonged, whereas, if the optimisation process
is too short, the optimisation result can be prejudiced due to stochastic variation.
4.2 Case Study 2
For the second case study, the optimisation goal is to minimise the annual lighting energy (LE) consumed
by the building, while the building is required to have a minimum gross area difference to the target value.
In this case study, each algorithm is only run one time. The results are, therefore, more prone to stochastic
deviation. Table 5 and Figure 12 summarise the results for the design diversity and fitness ranges of the
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selected elite design variants for each algorithm (including DIRECT). Figure 13 shows the design variants
in the elite set obtained by the five algorithms. Figure 14 shows the FPTs for each algorithm.
4.2.1 Design Diversity
For genetic diversity, the result in this case study is similar to that of the first case study (Table 5). On the
one hand, the genetic diversity of the SSIEA elite set is generally lower than most other algorithms. Using
implicit clustering, SSIEA only manages to outperform DIRECT. When using explicit clustering, SSIEA
outputerforms both DIRECT and CMA-ES. On the other hand, SSIEA obtains an elite set (using either
implicit or explicit clustering) with the markedly better average fitness compared with the elite sets obtained
by the other algorithms. In addition, Figure 12 also shows that the SSIEA elite sets contain design variants
that tend to have similar competitive fitness. In contrast, the elite set obtained by the other algorithms often
contain certain undesirable design variants with relatively low-fitness.
Figure 13 shows the design variants in the elite sets obtained by the five algorithms. The first row in
Figure 13 shows the elite set produced by SSIEA using implicit clustering approach. In this set, the design
variants all have distinct architectural features. The second rows in Figure 13 shows the elite set produced
using explicit clustering. This clustering approach has improved design diversity to some extent.
The third to the fifth rows in Figure 13 show the elite sets for HypE, RBFOpt, and CMA-ES respectively.
The design differentiation among these design variants is higher than that in the SSIEA elite set. However,
it should also be noted that, the SSIEA elite set with explicit clustering provides three major alternative
solutions – single or two high-rise towers or one slab-type building. In contrast, the elite sets produced by
HypE, RBFOpt, and CMA-ES typically include only two of the three solutions found in the SSIEA elite set.
The last row in Figure 13 shows the elite set for DIRECT. This elite set displays the least diversity. The
division and subdivision of the design space into multidimensional hyper-rectangles produces chaotic design
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variants as many parameters have identical values.
In this case study, HypE and RBFOpt also show good performance. Both HypE and RBFOpt elite sets
contain high-fitness solutions and have higher genetic diversity than that of the SSIEA elite set. However,
the design variants in the elite sets differ significantly in fitness, which suggests that not all the design
variants in the elite set have competitive fitness. In comparison, SSIEA obtains an elite set where all design
variants have competitive fitness while also maintaining the design diversity at an acceptable level. At the
same time, the subjective analysis of the phenotypes suggests that the elite set obtained by SSIEA allows
architects to extract a more balanced understanding of possible design strategies as compared with the other
four algorithms.
4.2.2 Search Efficiency
In terms of search efficiency, Figure 14 shows the FPTs of the optimisation process obtained by each
algorithm. RBFOpt and CMA-ES discover good solutions at the beginning of the optimisation process.
However, for CMA-ES, achieving further progress after 500 iterations seems difficult. In contrast, SSIEA
and HypE, both adopting evolutionary mechanisms, show similar search behaviours in this case study. The
optimisation processes based on the two algorithms reach convergence at around 1000 iterations while still
making some progress in the later stages. Lastly, DIRECT achieves more marked fitness improvement as
compared with the first case study, but it still underperforms to most other algorithms. Overall, in the 2000-
iteration optimisation process, SSIEA, HypE, and RBFOpt can achieve competitive fitness progress, but at
a different convergent rate.
4.2.3 Information Extraction and Design Process
In this case study, we further demonstrate how the application of SSIEA can facilitate information extraction
for conceptual architectural design. From the design variants in the SSIEA elite set (Figure 13), we can find
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different passive energy-saving strategies and combinations of these strategies appearing among these elite
building massing design variants. For example, stilts, tower-type buildings, and jagged floor plans. The
diversity among the elite design variants reveals how to achieve competitive daylighting performance using
different design strategies in the design setting. For example, one strategy for improving daylighting seems
to be the raising of the building massing. Detailed analysis of the architectural implication of these strategies
can be found in the previous study (Wang, Janssen, Chen, et al., 2019).
Beyond the diversity of the design variants directly provided in the optimisation result, another
advantage of using SSIEA is that it helps to cluster the optimisation result during the optimisation process.
With the clustering of the design population, the optimisation result allows architects to explore other similar
design variants in the same subpopulation with ease. As an example, we may assume that the architect might
consider selecting the slab-type building massing incorporating stilts, as shown in the first and fifth design
variants in Figure 13, for further design development. Figure 15 illustrates several high-ranking design
variants remaining in the same subpopulations containing the two elite design variants. Due to the genetic
homogeneity, these design variants share a similar but not identical topological configuration to the two elite
design variants, which remains a slab-type building massing incorporating stilts. These design variants
provide a broader range of design alternatives and facilitate the uncovering of more in-depth trade-offs
between the position and size of the subtracted void and its impact on daylighting performance under this
specific type of building massing design. This information can better support the architects’ decision-making
process.
5 Discussion
In the two case studies, we compare the performance of SSIEA against RBFOpt, HypE, CMA-ES, and
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DIRECT. The comparison focuses on two aspects: design diversity and search efficiency. In certain cases,
the other algorithms were able to outperform SSIEA in either design diversity or search efficiency. However,
the strength of SSIEA was its ability to perform reasonably well in both design diversity and search
efficiency at the same time. SSIEA can achieve acceptable diversity in the optimisation results while being
able to discover high-fitness individuals with good search efficiency when there is a reasonable amount of
search budget. Last, considering all five algorithms, we find that evolutionary-based algorithms (SSIEA,
CMA-ES, and HypE) generally tend to be more explorative than non-evolutionary ones (RBFOpt and
DIRECT). In contrast, it is also noted that certain non-evolutionary algorithms, such as RBFOpt, are capable
of discovering good solutions faster than evolutionary-based algorithms.
In the second case study, we also demonstrate how SSIEA can support conceptual design. The diversity
in the elite design variants helps architects discover the architectural implications related to daylighting
performance in a challenging design setting. Furthermore, the use of SSIEA not only provides several
competitive design alternatives for architects to choose from, but it also clusters the design variants during
the optimisation process. Thus, it facilitates the architect to readily continue exploring other homogeneous
design variants remaining in the design subpopulations. In contrast, using other algorithms typically requires
an additional working step to achieve such exploration.
The design problem of the second case study also helps to amplify the strength of using SSIEA. With
a parametric model capable of generating higher topological variability, the optimisation result also shows
higher design diversity at the phenotypic level compared with that of the first case study. It indicates that
SSIEA is of greater utility if the design space defined by the parametric model encompasses a broader range
of design variants with significant design differentiation. In other words, to exploit the potential of
performance-based optimisation in early-stage design exploration, both optimisation algorithms and
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parametric models play an indispensable role.
Based on the result of this study, we can also compare the search behaviours of the different
optimisation algorithms. SSIEA focuses on discovering a small number of design solutions with competitive
fitness while ensuring that these design solutions have sufficient design diversity for information extraction.
This tendency differs from the Pareto-based optimisation approach, such as HypE, which can produce a very
large number of Pareto-optimal design variants. Although this can result in a more comprehensive range of
possibilities, it can also be overwhelming for the architect. Moreover, many of the design variants may not
be able to satisfy the optimisation objective. In contrast, SSIEA can be used to retrieve the most relevant
information, in the form of a selected set of high-fitness solutions, while filtering out other less relevant
solutions with inferior fitness. It facilitates architects to understand the essence of the design problem quickly
without having to analyse large numbers of design solutions, as is common with the Pareto-based
optimisation approach (Yousif & Yan, 2018).
Figure 16 summarises the underlying concepts of different types of optimisation algorithms considered
in the research. First, standard optimisation algorithms, such as GA and DIRECT, tend to focus on searching
for a near-optimal within single design subspace. As a result, these algorithms typically compromise on
design diversity to differing extents (Figure 16-a). Moreover, simple algorithms, such as GAs, may actually
perform quite poorly when it comes to discovering near-optimal solutions (Wang, Janssen, & Ji, 2019). In
contrast, the second type of optimisation algorithms, such as the Pareto-based optimisation (HypE), model-
based algorithms (RBFOpt), and distribution-based algorithms (CMA-ES), tend to explore many design
subspaces during the optimisation process. This tendency can reduce search efficiency, and as a result, many
feasible local-optimal or near-optimal solutions may not be found (Figure 16-b).
Lastly, SSIEA focuses on several non-neighbouring design subspaces while managing to find a set of
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legitimate and high-fitness solutions within these design subspaces, which are helpful for accurately
characterising and representing these design subspaces (Figure 16-c). Although the design diversity for
SSIEA is lower than the other algorithms, the average fitness is higher. SSIEA is capable of providing
essential information about the design problem.
5.1 Future Research
The results of the research raise three potential avenues for further investigation. First, the application of the
island model may provide an intuitive method for controlling the trade-off between exploitation and
exploration. Architects can easily and directly control this trade-off by setting the total number of
subpopulations to be maintained by the algorithm. The impact of such a change is also more easily
understood than other approaches, such as modifying selection pressure or step sizes.
Figure 17 illustrates the hypothesis of the trade-off between the number of subpopulations and the
search efficiency of the optimisation. An increase in the number of subpopulations is likely to result in higher
design diversity. In contrast, a decrease results in the discovery of higher-fitness solutions from within each
design subspace as more search budget can be assigned to each subpopulation. However, the search
behaviours of SSIEA under different subpopulation numbers and subpopulation sizes needs further
investigation.
Second, the difference in the search performance and behaviour between SSIEA_1 and SSIEA_2
highlights that different mutation rates may have various advantages and disadvantages to the optimisation
process. In this regard, adaptive mutation rate control schemes (Thierens, 2002) can potentially synergise
the conflicting advantages of high and low mutation rates by varying the mutation rate as evolution
progresses.
The last question is to identify the range of design problems for which SSIEA is suitable. The research
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has demonstrated the success of SSIEA on the two case-study design problems. Based on the No-free-lunch
theorem (Wolpert & Macready, 1997), it is clear that search algorithms only tend to perform well on certain
classes of problems. For SSIEA, this class of problem is likely to focus on those that have a large design
space with many promising subspaces, while the search budget should be assumed to be limited. However,
further research is required to describe this class of problems more precisely.
6 Conclusion
To conclude, the research proposes an implementation of a new optimisation algorithm – SSIEA – which is
aimed at enhancing design diversity, while minimizing any degradation in search efficiency. The
development of SSIEA focuses on conceptual architectural design, where the role of computational
optimisation is not merely a design problem solver, but rather a means of design exploration. The conducted
case-study experiments systematically investigate the efficacy of SSIEA by comparing against other
optimisation algorithms. The results of the two case studies demonstrate SSIEA can achieve a good
compromise between design diversity and search efficiency. Furthermore, the implicit clustering of the
design population also helps architects explore the design space with ease. These features make SSIEA an
ideal algorithm for architects using evolutionary optimisation in design space exploration, which will, in
turn, lead to richer design reflection and ideations. As such, the application of SSIEA allows the performance
feedback to become a catalyst for the ongoing synthesis process in conceptual architectural design.
Acknowledgement
This research is partly supported by the National Natural Science Foundation of China (51378248) and the
China Scholarship Council (201706190203). The authors are also thankful to the comments from the
anonymous reviewers and editors.
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Tables
Table 1. The algorithms for comparison with SSIEA.
Algorithm
Description
Implementation
RS
RS (random search method) is a simple algorithm that generates random
genotypes using a pseudo-random number generator. Implemented using the
C# component in Grasshopper.
C# component
GA
GA (Genetic Algorithm) is a standard genetic algorithm incorporating a
niching/speciation operator (inbreeding) that controls the reproduction
operation (crossover) according to the genetic distance between two
individuals.
Galapagos
HypE
HypE (Hypervolume-based Multi-objective Evolutionary Algorithm) is a
Pareto-based optimization algorithm supporting multiple objectives and uses
Hypervolume as an optimisation indicator. When it is fed with a single
objective, the second objective is to increase the diversity of the design
population found by HypE.
Octopus
RBFOpt
RBFOpt (Radial Basis Function Optimisation) is a global model-based
optimization algorithm using a machine-learning method to approximate the
unknown fitness landscape. The algorithm is aimed to speed up the
identification of promising areas in the design space.
Opossum
CMA-ES
CMA-ES (Covariance Matrix Adaptation Evolution Strategy) is a second-
order optimization algorithm estimating a positive definite matrix within an
iterative procedure. The matrix represents the distribution of the design
population in the design space. The matrix is iteratively updated to move closer
to promising areas in the design space.
Opossum
DIRECT
DIRECT (DIviding RECTangle) is a global deterministic search method that
recursively subdivides the fitness landscape into multidimensional hyper-
rectangle. In each search step, the algorithm chooses the rectangle with the
solution having the best fitness for further subdividing.
Goat
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Table 2 The statistical analysis of design diversity in the optimisation result (EXPL: SSIEA elite set produced by
explicit clustering, hereinafter).
Run #1
Run #2
Run #3
Run #4
Run #5
Avg.
Std.
Avg. Fitness
4865.41
4531.08
5202.07
5165.61
5632.40
5079.31
270.35
Fitness Std.
497.73
566.15
828.80
838.69
664.93
679.26
-
SSIEA_1
Avg. Distance
0.380
0.402
0.418
0.357
0.396
0.391
0.023
Avg. Fitness
4784.70
4352.66
4951.78
4772.08
5455.13
4863.27
221.06
Fitness Std.
554.08
743.28
1188.71
1334.14
741.31
912.31
-
SSIEA_1
(EXPL)
Avg. Distance
0.417
0.419
0.425
0.401
0.404
0.413
0.009
Avg. Fitness
5708.91
5292.52
6014.09
6155.07
6322.31
5898.58
330.73
Fitness Std.
405.54
746.52
686.48
746.41
1240.38
765.07
-
SSIEA_2
Avg. Distance
0.371
0.389
0.367
0.398
0.392
0.383
0.013
Avg. Fitness
5671.66
5253.40
5642.35
5508.13
5904.78
5596.06
165.22
Fitness Std.
383.87
778.86
1005.24
1263.96
1337.24
953.83
-
SSIEA_2
(EXPL)
Avg. Distance
0.404
0.405
0.391
0.418
0.413
0.406
0.010
Avg. Fitness
3632.44
3137.59
2970.68
3528.55
3754.58
3404.77
272.20
Fitness Std.
793.15
1408.01
1230.07
1109.96
944.07
1097.05
-
HypE
Avg. Distance
0.470
0.493
0.487
0.464
0.496
0.482
0.012
Avg. Fitness
2593.01
3295.44
3631.50
2861.14
3595.06
3195.23
398.34
Fitness Std.
1346.30
862.26
1116.13
2181.13
2068.95
1514.95
-
RBFOpt
Avg. Distance
0.444
0.480
0.423
0.479
0.395
0.444
0.024
Avg. Fitness
1983.23
2178.37
2190.50
2331.56
1986.70
2134.07
123.97
Fitness Std.
808.94
1486.09
760.59
1296.43
1093.21
1089.05
311.04
CMA-ES
Avg. Distance
0.413
0.448
0.443
0.453
0.440
0.440
0.016
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Table 3 Fitness values of search results and statistical analysis.
Run #1
Run #2
Run #3
Run #4
Run #5
Avg.
Std.
SSIEA_1
5597.11
6511.75
6887.24
5662.56
6467.82
6225.30
508.00
SSIEA_2
7243.15
6172.88
8417.85
6727.55
7137.96
7114.06
826.99
HypE
4755.86
5341.46
4217.67
4577.89
4665.56
4711.69
364.04
RBFOpt
4394.36
3892.56
4752.92
5648.20
6829.38
5103.49
1036.10
CMA-ES
3887.50
3623.67
3213.19
3465.89
3999.52
3637.95
283.99
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Table 4 Number of migrations and statistical analysis based on SSIEA_1 and SSIEA_2.
Run #1
Run #2
Run #3
Run #4
Run #5
Avg.
Best Fitness
5597.11
6511.75
6887.24
5662.56
6467.82
6225.30
SSIEA_1
Migrations
4
1
2
1
2
2.0
Best Fitness
7243.15
6172.88
8417.85
6727.55
7137.96
7114.06
SSIEA_2
Migrations
0
0
0
1
0
0.2
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Table 5 The statistical analysis of design diversity in the optimisation result.
SSIEA
SSIEA(EXPL)
HypE
RBFOpt
CMA-ES
DIRECT
Avg.
23239.68
25810.89
57818.75
46833.91
65544.46
41183.08
Best
19090.95
19090.95
19615.92
26522.31
40491.79
37915.37
Worst
28100.54
35774.38
109125.97
66546.20
122339.57
44971.48
Fitness
Difference
9009.59
16683.43
89510.05
40023.88
81847.78
7056.11
Avg.
0.364
0.422
0.458
0.449
0.410
0.033
Min
0.342
0.392
0.433
0.371
0.388
0.027
Genetic
Difference
Max
0.387
0.460
0.481
0.520
0.451
0.041
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Author Biographies
Likai Wang is a Ph.D. candidate in the School of Architecture and Urban Planning, Nanjing University. His
current doctoral research deals with a generation and optimisation system for performance-based building
massing design. His research interests include: computational design optimisation, design exploration, and
parametric design.
Patrick Janssen is an Associate Professor at the Department of Architecture at the National University of
Singapore and is the Director of the Design Automation Laboratory. He is also Adjunct Associate Professor
in Automation in Urban Planning and Design at the 3D GeoInformation research group at the Department
of Urbanism, Faculty of Architecture and the Built Environment, TU Delft. He received his Ph.D. from Hong
Kong Polytechnic University. He conducts research into computational methods and tools for design
exploration and optimisation at the urban scale.
Guohua Ji is dean and professor of School of Architecture and Urban Planning at Nanjing University. He
received his Ph.D. from ETH-Zurich. He mainly engages in architectural design and methodology, with
particular focus on computer-aided architectural design and digital architecture. He is a member of National
Steering Committee of Architectural Education in China, an executive director of Academic Committee of
Computational Design of Architectural Society of China (ASC) and a member of Digital Construction
Academic Committee of ASC.
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Numbered List of Figures and of Tables
Figure 1. Comparison of search approaches between the standard EAs (left) and SSIEA (right).
Figure 2. The workflow of SSIEA.
Figure 3. Voxels of floor plan.
Figure 4. Random sampling design variants.
Figure 5. The building plot and sun path analysis.
Figure 6. Random sampling design variants.
Figure 7. The box-plotting of the fitness range of the elite set from each optimisation process. (EXPL: SSIEA
elite set produced by explicit clustering, hereinafter)
Figure 8. The design variant found by different algorithms.
Figure 9 Mean fitness progress trendlines of the four search approaches. (For the sake of comprehensive
comparison, we also include the FPTs of a Genetic Algorithm (GA) and a random search approach (RS)
retrieved from (Wang, Janssen, & Ji, 2019). The FPT based on DIRECT is not included because the
solutions found by DIRECT are very poor)
Figure 10 Trendlines of the standard deviation of fitness obtained by the five optimisation runs. (The trendline is
drawn based on the FPTs in Figure 11)
Figure 11 Fitness progress trendlines (FPTs) obtained by different algorithms.
Figure 12. The box-plotting of the fitness range of the elite set from each optimisation process.
Figure 13. The design variant in the elite set found by different algorithms.
Figure 14. Fitness progress trendlines (FPTs) obtained by different algorithms (The drawing of FPTs are based
on the best solutions found over time).
Figure 15. High-ranking design variants remaining in the subpopulation.
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Figure 16. Diagrammatic comparison of the search behaviours of different optimisation algorithms.
Figure 17. Diagrammatic comparison of the relationship between numbers of subpopulations and the
expectation of the quality of the result.
Table 1. The algorithms for comparison with SSIEA.
Table 2. The statistical analysis of design diversity in the optimisation result (EXPL: SSIEA elite set produced by
explicit clustering, hereinafter).
Table 3. Fitness values of search results and statistical analysis.
Table 4. Number of migrations and statistical analysis based on SSIEA_1 and SSIEA_2.
Table 5. The statistical analysis of design diversity in the optimisation result.
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Figure 1 Comparison of search approaches between the standard EAs (left) and SSIEA (right).
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Figure 2 The workflow of SSIEA.
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Figure 3 Voxels of floor plan.
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Figure 4 Random sampling design variants.
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Figure 5 The building plot and sun path analysis.
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Figure 6 Random sampling design variants.
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Figure 7 The box-plotting of the fitness range of the elite set from each optimisation process. (EXPL: SSIEA elite set produced by
explicit clustering, hereinafter)
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Figure 8 The design variant found by different algorithms.
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Figure 9 Mean fitness progress trendlines of the four search approaches. (For the sake of comprehensive comparison, we also include
the FPTs of a Genetic Algorithm (GA) and a random search approach (RS) retrieved from (Wang, Janssen, & Ji, 2019). The FPT
based on DIRECT is not included because the solutions found by DIRECT are very poor)
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Figure 10 Trendlines of the standard deviation of fitness obtained by the five optimisation runs. (The trendline is drawn based on
the FPTs in Figure 11)
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Figure 11 Fitness progress trendlines (FPTs) obtained by different algorithms.
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Figure 12 The box-plotting of the fitness range of the elite set from each optimisation process.
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Figure 13 The design variant in the elite set found by different algorithms.
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Figure 14 Fitness progress trendlines (FPTs) obtained by different algorithms (The drawing of FPTs are based on the best
solutions found over time).
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Figure 15 High-ranking design variants remaining in the subpopulation.
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Figure 16 Diagrammatic comparison of the search behaviours of different optimisation algorithms.
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Figure 17 Diagrammatic comparison of the relationship between numbers of subpopulations and the expectation of the quality of
the result.
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... Based on several studies related to building massing design generation and evolutionary optimization, we have developed a design tool, called EvoMass, in Rhino-Grasshopper. EvoMass integrates two algorithms for building massing design generation 36,37 and a hybrid evolutionary algorithm 38,39 aiming to diversify the design in optimization results. The development of EvoMass streamlines the utilization of performance-based design optimization and provides designers with a codingfree tool for building massing design. ...
... The two objectives are integrated into a single-objective evaluation function using a weighted sum approach. In addition, the embedded evolutionary algorithm, called steady-state island evolutionary algorithm (SSIEA), 38 is used as the optimization solver. The wind speed is simulated using GH_Wind, a fast fluid dynamic solver in Rhino-Grasshopper, while the sunlight accessibility is simulated using Ladybug. ...
Article
Full-text available
The role of using performance-based design optimization in early-stage architectural design to prevent poorly designed buildings has been increasingly recognized by researchers and designers. Recently, a large amount of research has been made focusing on technical advancement, which, however, also reflects the limited research on how this technique can be applied to the design process and how it can aid designers when confronting ill-defined design problems. In this regard, this paper centers on the design approaches assisted by using performance-based design optimization. The paper proposes two optimization-aided design approaches that were identified in the previous applications of a design tool, called EvoMass, and showcases these approaches in case-study designs. The case studies demonstrate how the use of performance-based design optimization can facilitate designers’ reflection and exploration. With the demonstration of the design approaches, we discuss the utility of performance-based design optimization in assisting architects in the early design stages.
... The RFBS model which is based on the FBS model is proposed by Christophe et al., when he introduced the concept of knowledge into the conceptual design stage [14]; The FBES model which is the combination of TRIZ and FBS is constructed by Cao et al. when he introduced the additional level of effect between behavior and structure [15]; Liu et al. promoted the conceptual design of automobile body by using MRRM and GA in the conceptual design of automobile [16]; When optimizing the jacket structure size, Sandal et al. found that the research on the structure in the conceptual design stage can be conducive to the subsequent conceptual design [17]; Tyurbeeva et al. modelled and analyzed the problem, and stores the knowledge in the computer to help the subsequent conceptual design [18]. Wang et al. proposed a new concept in the design stage of the algorithm, which can save time [19]. Zhang et al. considered the impact of design specifications on products in the conceptual design stage, and proposed a new conceptual design method, which can effectively help realize the mapping between specifications and conceptual design [20]. ...
Conference Paper
Full-text available
With the rapid development of today’s economy, people’s requirements for products are more diverse, and lightweight requirements are typical of these. Lightweight products play an important role in today’s engineering practice, and many researchers are participating in lightweight research. Schemes generated by conceptual design are used to realize the function, but it is difficult to consider simultaneously the lightweight and the functions’ realization. Especially the structures of the products may conflict with the way of working when the lightweight is considered. Sometimes, choosing which structure to start lightweight design is an important issue for a product; so an innovative design model for lightweight products based on FBS and conflict resolution is offered by the authors which can also take into account the product function while reducing the weight from the structure. The model includes three parts: Firstly, multi requirement analysis and FBS is constructed for the initial scheme. Secondly, if the requirements are not met, the structure in the initial scheme is scored by AHP, and the appropriate structure is selected for preliminary lightweight. Thirdly, the lightweight structure is obtained through conflict resolution, and then the conflict between it and other structures in the initial scheme is solved, to generate a new general structure. This paper takes the vertical frame and brace of a gantry crane as an example to verify the effectiveness of the model.
... Because of the geometrical freedom inherited by these two concepts, the produced designs have a lot of topological variety. In addition to the design generation, EvoMass also includes an optimization algorithm called the steady-state island evolutionary algorithm (SSIEA) (Wang, Janssen, et al., 2020). SSIEA integrates an island-based approach and a steadystate replacement strategy into an evolutionary algorithm. ...
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Computational design optimization has been widely considered a promising technique to help designers address complex design challenges regarding building performance. However, a barrier to applying it to real-world projects is the difficulty in incorporating functional requirements and constraints into the design optimization process. In response, this study presents an optimization-assisted design approach for early-stage architectural design. The approach combines the application of EvoMass, an integrated building mass design generation and optimization tool, and the soft constraint strategy. The combination allows designers to integrate various design requirements and constraints into the optimization, which makes it produce results with higher practical values. To demonstrate the efficacy of the approach, two case studies are presented, which show that the application of optimization facilitates designers to better formulate the design problem and rapidly investigate different design directions for exploration and information extraction. INTRODUCTION Building performance has become a prominent concern in early-stage architectural design in response to the goal of sustainable urban development, and many architects have begun to adopt the performance-based design approach in their design practice. An important responsibility for architects is to explore alternative design possibilities and compare the performance of these solutions in order to obtain more significant performance improvements. However, when this exploration is conducted manually, time restraints in real-world projects often limit the scope of architects' design exploration, which also makes early-stage design exploration both time-consuming and challenging. The capacity of computational design optimization to assist architects in early-stage design exploration has been demonstrated over the last decade by research advancements in the use of computational design optimization in architecture. Computational design optimization can automate the design generation and exploration process by combining parametric modeling, performance simulations, and optimization algorithms, freeing architects from the time-consuming trial-and-error process of finding high-performing solutions.
... Apart from the design generation, EvoMass also includes an evolutionary algorithm, called the steady-state island evolutionary algorithm (SSIEA) (L. Wang, Janssen, et al., 2020). SSIEA combines an island-based approach and a steady-state replacement strategy into the evolutionary algorithm. ...
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Over the past decade, computational design optimization has been increasingly applied to the studies related to early-stage architectural design exploration and information extraction, in which various optimization approaches have been adopted such as single-objective optimization (SOO) and multi-objective optimization (MOO). Despite this, the impact of optimization approaches on information extraction has been relatively under-researched. In this regard, this paper presents a comparison study of different optimization approaches, with a special focus on search efficiency and information extraction. In the comparison study, we investigate the impact of different optimization approaches on information extraction and design cognition and finally, discuss the utility of these approaches to architectural design ideation and synthesis.
... For the design optimization, the embedded optimization algorithm in EvoMass, called Steady-State Island Evolutionary Algorithm (SSIEA), is used as the optimization solver (Wang, Janssen, and Ji 2020). SSIEA is also able to produce optimization results with higher design diversity and differentiation by using the island-based model. ...
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In architectural design, the design processes of building massings and facades are typically separated, which hinders the synergy of the two elements in sustainable building design. In response, this paper proposes an integrated design optimization workflow that can evolve design incorporating building massings with different formal characteristics and various façade schemes. With the proposed workflow, a case study is presented to demonstrate how the two design elements mutually influence one another and how the two-element can complement one another to maximize their potential for performance enhancement. The result indicates that different combinations of building massings and façade schemes can effectively drive the optimization toward different design directions, which significantly impacts the optimization result and the revealed architectural design implications related to performance improvement. As a result, the proposed design workflow can help architects better understand the performance implications of building massing and façade design and make more informed design decisions.
... For the designer, diversity must be maintained in the population. Having many design variants that are either identical or almost identical would not be useful (Wang et al., 2020b). The aim is therefore to ensure that design variants have parameters that differ significantly from one another. ...
Chapter
During the early stages of design exploration, competing design strategies are typically considered. This chapter presents a design method, supported by a novel type of evolutionary algorithm, that maintains a heterogeneous population of design variants based on competing design strategies. Each strategy defines its own search space of design variants, all sharing a common generative concept or idea. A population of design variants is evolved through a process of selection and variation. As evolution progresses, some design strategies will become extinct while others will gradually dominate the population. A demonstration is presented showing how a designer can explore competing strategies by running a series of iterative evolutionary searches. The evolutionary algorithm has been implemented on a cloud platform, thereby allowing populations design variants to be processed in parallel. This results in a significant reduction in computation time, allowing thousands of designs to be evolved in just a few minutes.
Chapter
Benchmark designs can play a critical role in giving performative feedback to the design exploration process. This paper explores the idea of using computational design optimization as a way of generating such site-specific benchmark designs. A case study of the proposed benchmarking approach is presented focusing on public residential precinct design in Singapore. A key feature of this approach is a parametric typology that can generate designs that vary significantly in their overall configuration while at the same time remaining feasible and valid. In addition, an evolutionary optimization system is then used to evolve a set of high-performing site-specific benchmark designs. The case study successfully demonstrates how these benchmarks can be used to give performative feedback to the design exploration process.
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This paper presents a framework for rapid design optimization, which is aimed to support the iterative design optimization process. The framework consists of Rhino-Grasshopper and an evaluation server. In order to speed up the optimization process, three strategies are implemented in the framework, including parallel execution, early abortion, and multi-resolution simulations. To examine the efficacy of the developed framework, a case-study design optimization is conducted, and different combinations of the strategies are tested and compared. The case study investigates the impact of the adopted strategies on the optimization process in terms of search efficiency and effectiveness, and the result of the case study also demonstrates that optimization can be significantly improved by the use of the adopted strategies.
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Chapter
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This study pre­sents a sys­tem­atic re­view and sum­mary of per­for­ma­tive com­pu­ta­tional ar­chi­tec­ture us­ing swarm and evo­lu­tion­ary op­ti­mi­sa­tion. The tax­on­omy for one hun­dred types of stud­ies is pre­sented herein that in­cludes dif­fer­ent sub-cat­e­gories of per­for­ma­tive com­pu­ta­tional ar­chi­tec­ture, such as sus­tain­abil­ity, cost, func­tion­al­ity, and struc­ture. Specif­i­cally, en­ergy, day­light, so­lar ra­di­a­tion, en­vi­ron­men­tal im­pact, ther­mal com­fort, life-cy­cle cost, ini­tial and global costs, en­ergy use cost, space al­lo­ca­tion, lo­gis­tics, struc­tural as­sess­ment, and holis­tic de­sign ap­proaches, are in­ves­ti­gated by con­sid­er­ing their cor­re­spond­ing per­for­mance as­pects. The main find­ings, in­clud­ing op­ti­mi­sa­tion and all the types of pa­ra­me­ters, are pre­sented by fo­cussing on dif­fer­ent as­pects of build­ings. In ad­di­tion, us­age of form-find­ing pa­ra­me­ters of all re­viewed stud­ies and the dis­tri­b­u­tions for each per­for­mance ob­jec­tives are also pre­sented. More­over, us­age of swarm and evo­lu­tion­ary op­ti­mi­sa­tion al­go­rithms in re­viewed stud­ies is sum­marised. Trends in pub­li­ca­tions, pub­lished years, prob­lem scales, and build­ing func­tions, are ex­am­ined. Fi­nally, fu­ture prospects are high­lighted by fo­cussing on dif­fer­ent as­pects of per­for­ma­tive com­pu­ta­tional ar­chi­tec­ture in ac­cor­dance to the ev­i­dence col­lected based on the re­view process.