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Decision Chain Encoding: Evolutionary Design Optimization with Complex Constraints

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A novel encoding technique is presented that allows constraints to be easily handled in an intuitive way. The proposed encoding technique structures the genotype-phenotype mapping process as a sequential chain of decision points, where each decision point consists of a choice between alternative options. In order to demonstrate the feasibility of the decision chain encoding technique, a case-study is presented for the evolutionary optimization of the architectural design for a large residential building.
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P. Machado, J. McDermott, A. Carballal (Eds.): EvoMUSART 2013, LNCS 7834, pp. 157–167, 2013.
© Springer-Verlag Berlin Heidelberg 2013
Decision Chain Encoding: Evolutionary Design
Optimization with Complex Constraints
Patrick Janssen and Vignesh Kaushik
Department of Architecture, National University of Singapore
patrick@janssen.name, vigneshkaushik@gmail.com
Abstract. A novel encoding technique is presented that allows constraints to be
easily handled in an intuitive way. The proposed encoding technique structures
the genotype-phenotype mapping process as a sequential chain of decision
points, where each decision point consists of a choice between alternative op-
tions. In order to demonstrate the feasibility of the decision chain encoding
technique, a case-study is presented for the evolutionary optimization of the
architectural design for a large residential building.
Keywords: evolutionary, multi-criteria optimization, constraints, encoding, de-
coding.
1 Introduction
Evolutionary design is an approach that evolves populations of design variants in
order to optimise certain performance measures. Designs are manipulated by a set of
computational procedures, including a development procedure for generating design
variants, one or more evaluation procedures that use simulation and analysis for rank-
ing design variants, and a feedback procedure for closing the loop by linking results
from evaluation to the input of development.
If the designs being evolved have limited variability, then the developmental pro-
cedure can use direct parametric modelling for generating designs. With this ap-
proach, genes are directly linked to parameters within the model. However, in cases
where complex designs have to be evolved, the development procedure may consist
of an indirect rule-based procedure for generating designs Genes are then linked to
parameters in the rules rather than in the model, and as a result only affect the final
form indirectly via the rules (Frazer 1995, Janssen 2004). In the context of evolutio-
nary design, such rule-based developmental procedures have been referred to as com-
putational embryogenies (Kumar and Bentley 2003).
This paper presents a novel rule-based modelling technique that is particularly well
suited for generating complex designs as it allows constraints to be easily handled in
an intuitive way. In order to demonstrate the feasibility of the decision chain encoding
technique, this paper presents a case-study for the multi-objective evolutionary opti-
misation of the design of the Interlace, a large residential project designed by OMA
and currently under construction in Singapore (OMA 2013). The design uses a ‘stag-
gered brick’ pattern, where 31 building blocks are stacked up on top of one another in
158 P. Janssen and V. Kaushik
a brick pattern. Previous research by Janssen and Kaushik (2012) described a simula-
tion driven method for optimizing the design through a series of manual iterations.
This paper now takes this research further by proposing an automated procedure for
design optimisation.
Section 2 describes decision chain encoding in more detail. Section 3 presents the
case study, where decision chain encoding is used in a multi-objective evolutionary
optimisation problem. Section 4 briefly draws conclusions and indicates avenues of
further research.
2 Decision Chain Encoding
The proposed encoding technique structures the genotype-phenotype mapping process
as a sequential chain of decision points. Each decision point involves choosing one
option from the set of all valid options. The set of valid options is created by a set of
rules that generate and filter options. The genotype consists of a list of real-valued
genes in the range {0,1}. For each decision point, a gene will be used to select an
option by mapping it to an integer value in the range {1,n}, where n is equal to the
total number of valid options for that decision point. Note that for each decision, the
total number of valid options may not be known and may depend on the previous
decisions.
2.1 Travelling Salesman Problem
As an example, the Travelling Salesman Problem (TSP) may be used. If we have 8
cities (labeled as A to H), then assuming we start at city A, the decision chain would
consist of 6 decisions (since the last city does not require a decision as there will only
be one city left). For this case, each decision will select one city. For the first deci-
sion, there would be a total of 7 cities to choose from, so the gene would be mapped
to an integer value between 1 and 7 and the chosen city would then be removed from
the list of remaining cities. For the second decision, there would be a total of 6 cities
to choose from, so the gene would be mapped to an integer value between 1 and 6.
Table 1 shows a set of gene values and the sequence of cities that would be chosen,
with the final sequence being A,G,F,H,D,E,B,C.
Table 1. The process of selecting cities using the decision chain encoding method
Decision point 1 2 3 4 5 6
Gene value 0.77 0.69 0.94 0.63 0.84 0.48
Remaining cities 7 6 5 4 3 2
Integer mapping 6 5 5 3 3 1
Chosen city G F H D E B
For the typical TSP problem, there is little advantage to this approach over other
approaches. However, the decision chain encoding method can easily handle addi-
tional constraints. For example, if direct travel between cities F and H is disallowed,
Decision Chain Encoding 159
then the rules for generating and filtering options could easily be modified. The se-
quence of cities for the genes in Table 1 would become A,G,F,E,D,H,B,C.
In general, the proposed decision chain encoding technique is seen to be useful for
highly constrained problems. Researchers have identifed four main approaches to
handling constraints in evolutionary algorithms: 1) penalty functions that reduce the
fitness of invalid solutions, 2) repair functions that modify invalid solutions, 3)
specialised reproduction opeators that avoid invalid solutions, and 4) specilaised
genotype to phenotype decoder functions that avoid invalid solutions (Eiben and
Smith 2003, pp 210-211). The the fourth approach has the advantage of permitting the
use of standard variation operators. Handling constraints through decision chain
encoding falls into the fourth category.
2.2 Evolutionary Design Method
Within the current research, the decision chain encoding technique is used as a way of
handling constraints in evolutionary design optimisation. Design optimisation typi-
cally requires design solutions that are highly constrained, and therefore decision
chain encoding is seen as being an appropriate technique.
The research aims to develop optimisation tools that can be used by designers. It is
assumed that the designers using such tools will have limited programming skills, and
will therefore need to be able to define the key problem-specific procedures without
having to write computer code. The development procedure and one or more evalua-
tion procedures are therefore defined using Visual Dataflow Modelling (VDM) tools
(Janssen and Chen 2011).
Visual Dataflow Modelling has becoming increasingly popular within the design
community, as it can accelerate the iterative design process, thereby allowing larger
numbers of design possibilities to be explored. Modelling in a VDM system consists
of creating dataflow networks using nodes and links, where nodes can be thought of
as functions that perform actions, and links connect the output of one function to the
input of another function. VDM is now also becoming an important tool in perform-
ance-based design approaches (Shea et. al. 2005, Coenders 2007, Lagios et. al 2010,
Toth et. al. 2011, Janssen et. al. 2011).
In this research, an advanced procedural modelling system called SideFX Houdini
is used for both development and evaluation procedures. For the development proce-
dure, VDM networks are created in Houdini to generate the three-dimensional models
of design variants. These networks use the decision chain encoding technique for
constructing models. At each decision point in the modelling process, a set of rules is
used to generate, filter, and select valid options for the next stage of the modelling
process, as shown in figure 1. The generate step uses the rules to create a set of op-
tions. The filter step discards invalid options that contravene constraints. The select
step chooses one of the valid options. In order to minimise the complexity of the
modelling process, options are generated in skeletal form with a minimum amount of
detail. The full detailed model is then generated only at the end, once the decision
chain has finished completing.
160 P. Janssen and V. Kaushik
Fig. 1. Key steps executed at each decision point in the developmental procedure
3 Case-Study
The case study experiment is based on the design of the Interlace by OMA. The de-
sign consists of thirty-one apartment blocks, each six stories tall. The blocks are
stacked in an interlocking brick pattern, with voids between the blocks. Each stack of
blocks is rotated around a set of vertical axes, thereby creating a complex interlocking
configuration. An example is shown in figure 2, where 6 blocks are stacked and ro-
tated to form a hexagonal configuration.
Fig. 2. The staggered brick pattern. The diagram on the left shows 6 blocks arranged in a
straight line, while the diagram on the right shows the same six blocks folded into a hexagonal
pattern.
Each block is approximately 70 meters long by 16.5 meters wide, with two vertical
axes of rotation spaces 45 meters apart. The axes of rotation coincide with the loca-
tion of the vertical cores of the building, thereby allowing for a single vertical core to
connect blocks at different levels. The blocks are almost totally glazed, with large
windows on all four facades. In addition, blocks also have a series of balconies, both
projecting out from the facade and inset into the facade.
The initial configuration, shown in figure 3, is based on the original design by
OMA. The blocks are arranged into 22 stacks of varying height, and the stacks are
then rotated into a hexagonal pattern constrained within the site boundaries. At the
highest point, the blocks are stacked four high.
For the case study, new configurations of these 31 blocks were sought that optimise
certain performance measures. For the new configurations, the size and number of
blocks will remain the same, but the way that they are stacked and rotated can differ.
Decision Chain Encoding 161
Fig. 3. The initial configuration based on the original design, consisting of 31 blocks in 22
stacks of varying heights
3.1 Development
The developmental procedure is defined using decision chain encoding. In this proce-
dure, the placement of each of the 31 blocks is defined as a decision point. The proc-
ess places one block at the time, starting with the first block on the empty site. At
each decision point, a set of rules is used to generate, filter, and select possible posi-
tions for the next block. Each genotype has 32 genes, and all are real values in the
range {0,1}.
In the generation step, possible positions for the next block will be created using a
few simple rules. First, locations are identified, and second orientations for each loca-
tion are identified. The locations are always defined relative to the existing blocks
already placed, and could be either on top of or underneath those blocks. The orienta-
tions are then generated in 15° increments in a 180° sweep perpendicular to either end
of the existing block. In the filtering step, constraints relating to proximity between
blocks and proximity to the site boundary are applied, thereby ensuring that only the
valid positions remain. In the selection step, the decision gene in the genotype
chooses one of the valid block positions.
When generating a new design variant, the first decision point involves selecting a
starting point on the site from a set of possible starting points. These starting points
are generated by overlaying a grid over the site and then filtering out all points that lie
outside the boundary of the site. The next four decisions points are show in figure 4.
In the diagrams, the numbered lines are used to indicate possible valid block posi-
tions, so that the next block could be placed on any of those lines. The selected option
for that decision point is shown as a thicker line.
For decision point 2, the first block needs to be placed on the starting point. The
generative rules create 12 possible positions for the block, orientated around the
starting point, labelled 0 to 11. The gene selects position number 2.
For decision point 3, the second block has to be placed on either end of the first
block. The generative rules find two locations where blocks can be placed, and
they create 7 positions at each location, resulting in total of 14 possible positions.
The gene selects position number 1. Note that this block now has one end unsup-
ported.
162 P. Janssen and V. Kaushik
Decision
point 5
Decision
point 2
Decision
point 3
Decision
point 4
Plan view 3D view
10
5
4
3
14
8
9
0
11
12
13
6
7
2
1
0
1
2
3
4
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0
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34
5
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13
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89
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Fig. 4. Four decision points in the process of mapping the genotype to the phenotype
Decision Chain Encoding 163
For decision point 4, the third block has to be placed. In this case, the generative
rules give preference to the location that will result in a support for the previous
block. This results in 7 positions, all underneath the previous block. The gene se-
lects position number 4.
For decision point 5, the fourth block has to be placed. The generative rules find
four locations, all on top of the three already placed blocks. The rules create 28
possible positions. However, a number of these positions violate constraints, and
are therefore discarded by the filtering rules. Figure 5 shows the filtering stages for
decision point 5. Overall, 7 positions are discarded as they would result in blocks
that would be too close to the three existing blocks, and 6 positions are discarded
as they would result in blocks that extend outside the site boundary. This results in
15 remaining positions, from which the gene selects position number 7.
The process shown in figure 4 is continued until all 31 blocks are placed. The deve-
lopmental procedure using the decision chain encoding technique ensures a match
between the space of all possible genotypes and the space of all valid phenotypes.
This results in two critical features: first, it guarantees that any genotype will map to a
valid phenotype; second, it guarantees that the all valid phenotypes can be generated
from a genotype. It is typically very difficult to create genotype-phenotype decoding
procedures that appropriately control the variability of three-dimensional design ob-
jects with complex relationships and constraints. Decision chain encoding has enabled
the variability problem (Janssen 2004) to be overcome.
As a final stage of the developmental procedure, cores and facades are added to the
blocks. The cores (which would contain the lifts, service shafts, and escape stairs) are
added to the interior of all blocks, and in some cases also inserted below blocks in
those instances where a void remains below the block (in order to provide support for
the block, and to ensure that the flats are accessible from the ground floor). For the
façades, the windows on each of the blocks are analyzed, and both sunshades and glaz-
ing systems are created. The size of the shades and the glazing system types both de-
pend on the amount of solar radiation incident on the windows throughout the year.
This is calculated in a two-step process, using the Radiance simulation program (Jans-
sen and Kaushik 2012). In step 1, the solar radiation incident on the windows without
(a) (b) (c)
Fig. 5. Filtering of positions that violate constraints for decision point 5. (a) All 28 possible
positions; (b) 21 positions after block-based filtering; (c) 15 positions after site-based filtering
164 P. Janssen and V. Kaushik
shading is simulated, and shades are then generated so that windows with more sun
will get larger shades. In step 2, the solar radiation incident on the windows with shad-
ing is simulated, and windows which are still receiving too much solar radiation are
then assigned more expensive glazing systems which are able to limit the amount of
solar radiation.
3.2 Evaluation
For the multi-objective evaluation, three procedures are defined for evaluating per-
formance of the building. The building is located in the tropics in Singapore, and two
key requirements are to maximize the amount of daylight and to minimize the amount
of solar radiation entering the windows (which is seen as the worst case scenario - see
Janssen and Kaushik (2012) for more details). Both these factors are affected by the
orientation of the blocks relative to the north direction, and relative to one another
(due to inter-block shading).
For daylight, an evaluation procedure is defined that executes Radiance in order to
calculate the amount of light reaching the window on a cloudy overcast sky. The
amount of light entering each window is then adjusted according to the visual trans-
mittance of the glazing system for that window. The performance criterion is defined
as the maximization of the total number of windows where the light entering the win-
dow is above a certain threshold level for reasonable visual comfort, referred to as
‘good daylight windows’.
As described in the previous section, the minimization of solar radiation entering
the building is already tackled by the developmental procedure by adding the sun
shades and high performance glazing systems. However, these additional systems
have a significant effect on the cost of the façade, and therefore the performance crite-
ria in this case actually focuses on the cost of the façade. For façade cost, an evalua-
tion procedure is defined that calculates the total cost of all the glazing systems and
shading systems for all 31 blocks. The performance criterion is defined as the mini-
mization of this cost, referred to as ‘façade cost’.
Lastly, one more performance criterion is added, relating to the cores. As discussed
in the previous section, the developmental procedure will generate design variants
where additional cores need to be inserted. These cores will add significant additional
cost, and therefore need to be minimized. The final evaluation procedure therefore
calculates the total length of core for all the blocks. The performance criterion is de-
fined as the minimization of the total vertical core length.
3.3 Results
The evolutionary process was executed using Dexen, a distributed execution envi-
ronment for population based optimisation algorithms (Janssen et. al. 2011). A set of
10 networked PCs was set up consisting of one server and 9 compute nodes (each
with 4 slaves). The execution time to develop and evaluate a single design variant on
one machine was close to two minutes, but when it was run using Dexen with the 9
compute nodes, it was reduced to approximately 18 seconds.
Decision Chain Encoding 165
The population size was set to 200 and a simple asynchronous steady-state evolu-
tionary algorithm was used. Each generation, 50 individuals were randomly selected
from the population and ranked using multi-objective Pareto ranking. The 4 individu-
als with the lowest rank were killed, and the 4 individuals with the highest rank (rank
1) were used as parents for reproduction. Standard crossover and mutation operators
for real-valued genotypes were used, with the mutation probability being set to 0.01.
Reproduction between pairs of parents resulted in 4 new children, thereby ensuring
that the population size remained constant.
The evolutionary algorithm was run for a total of 16,000 births, taking approxi-
mately 80 hours to execute. In order to calculate the progress of the evolutionary algo-
rithm, the Hypervolume metric was used (Zitzler and Thiele 1998). At each 100
births, the non-dominated Pareto set was found. For each Pareto set, the performance
scores were normalized, and the good daylight window score was inverted so that all
scores are being minimized. The Hypervolume was then calculated using the tool
developed by Fonseca et. al. (2006). The graph in figure 6 shows the increase in
Hypervolume as evolution progresses.
Fig. 6. The Hypervolume graph for a run of 16,000 individuals
The final non-dominated Pareto set for the whole population contains a range of
design variants with differing tradeoffs between performance and cost. One of the
design variants from this non-dominated set is shown in figure 7. The performance
scores for the initial design shown in figure 2 are: good daylight windows: 70 %;
façade cost: SGD 44.5 million; and core length 1481 meters. For the design shown in
figure 7, the performance scores are as follows: good daylight windows: 83 %; façade
cost: SGD 42.3 million; and core length 1504 meters. The optimized design is there-
fore cheaper than the original design, but also performs better in terms of daylight
performance.
166 P. Janssen and V. Kaushik
Fig. 7. A selected design on the non-dominated Pareto set
4 Conclusions
Decision chain encoding is an effective way of handling complex sets of constraints.
The case-study demonstration has shown how the decision chain encoding technique
can be applied to the evolution of a complex design. Furthermore, due to the simplici-
ty of the way that constraints are handled, developmental procedures using decision
chain encoding can be implemented using VDM systems. This allows designers with
limited programming skills to engage with evolutionary design methods.
Future research will compare the performance of decision chain encoding tech-
niques to other techniques such random key encoding (Bean 1998). In particular, it is
noted that the decision chain encoding technique results in genotypes that have high
epistasis, in that genes early in the genotype sequence have a significant impact on the
expression of the genes later on in the sequence. Benchmarking experiments will be
performed in which evolutionary algorithms using decision chain encoding are com-
pared to evolutionary algorithms using alternative encoding techniques.
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... These mapper nodes are currently implemented as Python scripts, but part of this research is the development of a graphical application for defining mapper nodes. See Janssen at al. (2013) for more details. ...
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... For the developmental procedure, a generative technique called decision chain encoding is used to generate street patterns (Janssen and Kaushik, 2013). The decision chain encoding technique structures the street pattern generation process as a sequential chain of decision points, where each decision consists of a 'design move' that inserts an urban block into the urban grid. ...
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