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Analysing Populations of Design Variants Using Clustering
and Archetypal Analysis
Kian Wee Chen1, Patrick Janssen2, Arno Schlueter3
1Future Cities Laboratory, Department of Architecture, ETH Zurich, Switzerland
2Department of Architecture, National University of Singapore 3Institute of Tech-
nology in Architecture, Department of Architecture Zurich
1chenkianwee@gmail.com 2patrick@janssen.name
3schlueter@arch.ethz.ch
In order to support exploration in the early stages of the design process,
researchers have proposed the use of population-based multi-objective
optimisation algorithms. This paper focuses on analysing the resulting population
of design variants in order to gain insights into the relationship between
architectural features and design performance. The proposed analysis method
uses a combination of k-means clustering and Archetypal Analysis in order to
partition the population of design variants into clusters and then to extract
exemplars for each cluster. The results of the analysis are then visualised as a set
of charts and as design models. A demonstration of the method is presented that
explores how self-shading geometry, envelope materials, and window area affect
the overall performance of a simplified building type. The demonstration shows
that although it is possible to derive general knowledge linking architectural
features to design performance, the process is still not straightforward. The paper
ends with a discussion on how the method can be further improved.
Keywords: K-means clustering, Archetypal analysis, Design optimisation,
Performance-based design, Computational design
INTRODUCTION
The early architectural design stages tend to be ill-
defined and explorative in nature. Architects will typ-
ically explore the project brief and design propos-
als simultaneously, with the problems and solutions
feeding into each other to define the boundaries of
what is possible (Harfield 2007, Lawson 2004).
In order to support this exploratory process,
researchers have proposed the use of population-
based optimisation algorithms to search for a set of
well-performing design variants (Caldas 2008; Flager
et al. 2009; Janssen et al. 2011; Lin and Gerber,
2014; Turrin et al. 2011). Such algorithms optimise
a population of design variants based on a set of
performance objectives. In an optimisation process,
the design variants are generated from a parametric
model based on different input parameters (Wood-
bury, 2010). Objective functions are then used to cal-
culate the performance scores for each design vari-
ant. Once a population of optimised design vari-
Design Tools - Exploration - Volume 1 - eCAADe 33 |251
ants has been created, architects need to be able to
analyse this population. Ideally, the analysis results
should give architects a better understanding of the
relationship between architectural features and de-
sign performance.
Common techniques used for analysing the op-
timised design variants include sorting, filtering, and
Pareto ranking. Essentially, these techniques filter
the population, in order for architects to select a small
number of design variants for further development.
However, even after the filtering process, there will
typically still be a large number of design variants
that remain. The selection of design variants is not a
straightforward process. As a result, more advanced
techniques such as Multiple Criteria Decision Analy-
sis (MCDA) (Mela et al. 2012; Pohekar and Ramachan-
dran 2004) and Knowledge-Based Design Support
System (KBDSS) (Singhaputtangkul et al. 2013) are
used to support the architects in narrowing down the
selection to a manageable number of design variants
for further design development.
There are also techniques that extract design
principles through analysing the design variants
(Chichakly and Eppstein, 2013; Deb et al., 2014; Deb
and Srinivasan, 2006). With these techniques, de-
sign principles are derived from the relationship be-
tween the input parameters and performance scores.
These techniques are proposed for engineering de-
sign where the input parameters have a direct rela-
tionship with the performances. In early architec-
tural design stages, architects are exploring design
not only in terms of performances, but also qualita-
tive aspects such as aesthetics. Some input param-
eters are modelled for the qualitative aspects of the
design and have an indirect relationship to the per-
formances. Thus, these techniques are not appropri-
ate for the early architectural design stages.
This paper proposes a method for analysing pop-
ulations of design variants through the use of Clus-
ter Analysis and Archetypal Analysis. Cluster Analy-
sis (Everitt and Hothorn 2011; Han et al. 2012) par-
titions a set of data into subsets of data or clusters
such that the individual units of data in each cluster
are similar to each other, while differentfrom those in
the other clusters. It is used to gain insights into the
distribution of a set of data, observes characteristics
unique to each cluster, and helps identify clusters of
interest for further analysis. Archetypal Analysis iden-
tifies extreme values on the boundary of a data set
or archetypes to represent a set of data (Cutler and
Breiman 1994). An overview of the data can be ap-
proximated based on studying the archetypes.
The proposed method aims to enable architects
to discover relationship between architectural fea-
tures and design performance. The next section will
describe the proposed method, and the demonstra-
tion section will present an example in which the
method is applied to a case study. Finally, the con-
clusions section briefly discusses future research.
PROPOSED METHOD
The proposed method consists of two stages: cluster-
ing design variants and extracting exemplars. In the
first stage, the population of design variants is hierar-
chically clustered into groups of design variants with
distinct characteristics. Once the clusters have been
created, exemplars are then extracted for each clus-
ter using both Cluster Analysis and Archetypal Analy-
sis. The design clusters and exemplars are then visu-
alised in order to give architects insights into the re-
lationship between architectural features and design
performance.
Clustering Design Variants
The aim is to partition the population of design vari-
ants into clusters with distinct characteristics. A basic
Euclidian distance-based clustering algorithm is suf-
ficient. For this research, k-means analysis (Hartigan
1975) is used. It is one of the most common Euclidean
distance-based algorithm used in data mining. k-
means analysis starts with a random initial cluster-
ing using random selected centroids and then iter-
ates through the data set searching for the best clus-
ters. At each iteration, the quality of the cluster is
measured using the within-cluster-variance measure.
The smaller this variance, the more compact is a clus-
252 |eCAADe 33 - Design Tools - Exploration - Volume 1
ter. The analysis stops when there is no change in the
within-cluster-variance for a number of iterations.
Clusters are created in two stages. In the first
stage, the population of design variants is clustered
according to performance scores. In the second
stage, these clusters are then sub-clustered accord-
ing to a set of selected architectural features derived
from the design variants. These features can be any
type of metrics that can be calculated to describe
general characteristics of design variants. This two-
stage clustering approach allows architects to un-
derstand different combinations of architectural fea-
tures that can result in similar performances.
For the proposed method, the architect needs to
specify the attributes to be used for clustering and
the total number of resultant clusters. For the lat-
ter, a heuristic called the "elbow method" can be
used (Everitt and Hothorn 2011). This method is
based on the observation that an increase in the
number of clusters is associated with a diminishing
improvement in the quality of those clusters. This is
because by splitting clusters that are already high-
quality into finer clusters will have marginal reduc-
tion in the within-cluster sum of square measure. The
"elbow method" can be used to find the turning point
when additional clusters no longer result in any sig-
nificant improvements in cluster quality.
Extracting Exemplars
Once the design variants are partitioned into clus-
ters, a manageable number of representative design
variants are extracted. This facilitates architects in
qualitatively assessing the relationship between ar-
chitectural features and performance scores. This is
done by analysing the input parameters of the de-
sign variants of each cluster to find a set of parame-
ters that best represent the cluster. Archetypal Anal-
ysis extracts archetypes of the clusters, which are ex-
treme values located at the boundary of the cluster.
k-means analysis extracts the centroids that are lo-
cated in the centre of each cluster. Together, the
archetypes and centroids give a good sampling of the
design variants in the cluster. They form the exem-
plars of the design cluster.
Note that the exemplars are not created by se-
lecting design variants in the cluster. Instead, they
are new design variants that are reconstructed by
analysing the input parameters for all design variants
in the cluster. Thus, they need to be validated by en-
suring that their performances and architectural fea-
tures are within the range of the design cluster. For
example, for a design cluster that has a daylight per-
formance of 500-1000 lux and a shape factor of 0.2-
0.5, the exemplars need to fall within these ranges to
be valid. The proposed analysis method is illustrated
in Figure 1.
DEMONSTRATION
The method is demonstrated on an abstract building
type. The demonstration explores how self-shading
geometry, envelope materials and window area will
affect the overall performance of a simplified build-
ing located in the Singapore climate. The design
schema is illustrated in Figure 2. The schema is based
on two 4x2 grids stacked on top of each other (Figure
2a). There are four options for the location of the ver-
tical core of the building: columns 1 and 5, columns
2 and 6, columns 3 and 7, or columns 4 and 8 (Figure
2b). One grid is chosen from each remaining column
to create the building form (Figure 2c). By staggering
volumes on top of each other it is possible to create
self-shading geometries. There are a total of 256 pos-
sible building forms that can arise. All the external
walls have windows, the heights of which range from
1.2 m to 3.6 m (Figure 2d). The walls and windows are
assigned a material (Figure 2e). The building can be
rotated 360º (Figure 2f). The design schema can gen-
erate 752,640 possible design variants. The example
Figure 1
Procedure of the
proposed analysis
method
Design Tools - Exploration - Volume 1 - eCAADe 33 |253
Figure 2
Design schema of
proposed building
explores various forms, materials and window areas
that can lead to a better performance.
The design schema is evaluated in terms of ther-
mal transfer through the envelope, the envelope
cost, and the daylight level. The thermal transfer
measures the solar heat gain through the envelope
in the tropical climate, and is a good performance in-
dicator of the cooling performance of a building. It
is calculated using a simplified method, as the sum
of Envelope Thermal TransferValue (ET TV) (Chua and
Chou, 2010) and Roof Thermal Transfer Value (RTTV)
(BCA, 2013). The envelope cost is calculated by mul-
tiplying the envelope area with the cost per square
metre of the material. The better-insulated materials
are more costly. The daylight level is calculated as the
ratio of the floor area receiving at least 300 lux to the
gross floor area. The overall thermal transfer and the
envelope cost are to be minimised, while the daylight
level is to be maximised.
A Non-Dominated Sorting Genetic Algorithm 2
(NSGA2) (Deb et al. 2000) is used for the optimisa-
tion process. The settings of the algorithm are an ini-
tial population of 100, crossover rate of 0.9, and mu-
tation rate of 0.01. A total of 5000 design variants are
generated from 50 generations.
RESULTS
The population of 5000 design variants are analysed
using the proposed method. In the clustering stage,
two levels of clustering are performed. First, k-means
clustering is used to cluster the population accord-
ing to their performance scores. Three performance-
based design clusters are produced, labelled Perfor-
mance Clusters A, B and C. Cluster A achieves a bal-
ance between all three performance objectives, Clus-
ter B focuses on low overall thermal transfer, and
Cluster C focuses on low cost.
Each performance cluster is then sub-clustered
based on two architectural features: the shape factor
(CEN 2007) and Window Wall Ratio (WWR). The shape
254 |eCAADe 33 - Design Tools - Exploration - Volume 1
Figure 3
Feature clusters A1,
A2 and A3 with its
exemplars
Design Tools - Exploration - Volume 1 - eCAADe 33 |255
factor and WWR describes the building form and
envelope of the design variants, by using these at-
tributes for the second stage of clustering, one will be
able to identify the relationship between the build-
ing form, envelope design and performance scores in
the feature-based clusters. This results in a total of 9
feature clusters.
In the exemplar extraction stage, the exemplars
are extracted by running an Archetypal Analysis and
k-means analysis on the input parameters. The de-
sign clusters are then visualised in two forms. The
performances and architectural features will be vi-
sualised as Parallel Coordinate Plots (PCP) and the
exemplars as 3D models, as shown in in Figures 3
to 5. The exemplars are arranged in three rows,
the centroid is located in the middle row while the
archetypes are at the first and last row. The descrip-
tion on the top of each exemplar indicates its wall and
window material. Figure 2e shows the legend of the
wall and window materials.
Performance Cluster A
Performance cluster A achieves a balance between all
three performance objectives. Cluster A2 and A3 (Fig-
ure 3) are the most balanced design clusters. They
achieve an acceptable overall thermal transfer and
daylight level while maintaining a low cost, relative to
the other design clusters. The design variants in clus-
ter A3 have a lower shape factor, which is illustrated
by its exemplars with their compact forms. These
compact forms have lesser over-hangs and shadings.
Cluster A3 has a smaller daylight performance range
than cluster A2 because of the lesser shadings: the
WWR needs to be low to maintain the overall ther-
mal transfer, and a lesser window area leads to lower
daylight performance. Lastly, the long façades of
the exemplars mainly face north-south to avoid the
east-west sun. Cluster A2 has a high shape factor,
and its exemplars have building forms that self-shade
themselves with over-hangs. Due to the shading, the
exemplars are able to afford higher WWR and thus
achieve a higher maximum daylight level of 40.43%,
compared with the 35.48% of cluster A3.
The design variants in cluster A1 (Figure 3) have a
shape factor higher than that of cluster A3 but lower
than that of cluster A2, and higher WWR than both
design clusters. Cluster A1 is able to achieve similar
overall thermal transfer and daylight performance to
cluster A2, with a higher envelope cost. This higher
cost is due to the high WWR, as better glazing mate-
rial is required to maintain the overall thermal trans-
fer performance with the increased window surface
area.
Performance Cluster B
Performance cluster B consists of design variants with
low overall thermal transfer but high envelope ma-
terial cost. Cluster B3 (Figure 4) has the best over-
all thermal transfer performance and the worst day-
light performance. The envelope cost is higher than
cluster A2. Most of the exemplars have their long
façade facing north-south, and a low WWR, as with
cluster A3. Most of the exemplars use highly insu-
lated materials, which is reflected in the higher en-
velope cost. The combination of good orientation,
low WWR, and good envelope materials contributed
to the best overall thermal transfer performance. The
trade-offs are a higher envelope cost and the worst
daylight performance among the nine clusters.
Overall thermal transfer and cost performance
similar to cluster B3 can be achieved with an architec-
tural design of lower shape factor and bigger range of
WWR, as shown in cluster B2 (Figure 4). Design vari-
ants in cluster B1 (Figure 4) have a similar shape fac-
tor to that of cluster B3, but a higher WWR range, and
the high WWR requires good insulated window ma-
terials to maintain the overall thermal transfer; as a
result, the design cluster has the worst cost perfor-
mance. The advantage of increasing the WWR is bet-
ter daylight performance, but the daylight improve-
ment is only 0.59-8.71%, compared with cluster B3.
Performance Cluster C
Performance cluster C consists of design variants
with low envelope cost, high daylight level, but high
overall thermal transfer performance. Cluster C2 (Fig-
ure 5) has the best envelope cost performance of the
256 |eCAADe 33 - Design Tools - Exploration - Volume 1
Figure 4
Feature clusters B1,
B2 and B3 with its
exemplars
Design Tools - Exploration - Volume 1 - eCAADe 33 |257
Figure 5
Feature clusters C1,
C2 and C3 with its
exemplars
258 |eCAADe 33 - Design Tools - Exploration - Volume 1
nine design clusters. Its shape fac tor and WWR range
are similar to those of cluster B2. The main difference
between the two design clusters is the envelope ma-
terial cost, as the design variants use envelope con-
structions of lower thermal qualities, as shown by the
cluster's exemplars. It achieves similar daylight per-
formance to that of cluster B2, but due to the low-
quality envelope materials the overall thermal trans-
fer performance is much worse than that of cluster
B2.
Overall thermal transfer and daylight perfor-
mances similar to those of cluster C2 can be achieved
with an architectural design of higher shape factor, as
shown in cluster C1 (Figure 5). The increase in shape
factor increases the surface area of the envelope, and
as a result the cost is 13.3k higher than that of clus-
ter C2. Cluster C3 (Figure 5) has the best-performing
daylight, while having the worst-performing over-
all thermal transfer performance. The exemplars are
characterised as having high shape factor and high
WWR with low-quality glazing materials.
CONCLUSION AND DISCUSSION
The demonstration shows how k-means clustering
and Archetypal Analysis can be used to partition de-
sign variants into clusters and to extract exemplars.
The PCP of the design clusters and 3D geometry of
the exemplars facilitate the analysis of a large num-
ber of design variants generated from the optimisa-
tion process. The clusters are able to provide a visual
summary of the 5000 design variants.
The demonstration shows that although it is pos-
sible to derive general knowledge linking architec-
tural features to design performance, the process is
still not straightforward. It is not easy with which
such knowledge can be derived depends on the spe-
cific clusters being compared. For example, com-
paring feature cluster A2 and A3 reveals how differ-
ent architectural designs can achieve similar perfor-
mances. One can either have a low shape factor with
low WWR, or a high shape factor with a bigger range
of WWR. Other comparisons are much less reveal-
ing. For example, when comparing cluster A1 and
A2, it is difficult to identify any clear relationship be-
tween architectural features and performance scores.
In this case, the two sets of exemplars do not seem to
have any distinct architectural features, which in turn
makes it difficult to conclude anything with regards
to performance.
Future research aims to improve on the current
method by supporting a more interactive approach.
Rather than automating the whole analysis proce-
dure as discussed in this paper, this approach will
allow architects to analyse populations of design
variants by interactively applying various techniques
such as clustering, archetypal analysis, and filtering.
This interactive approach will allow architects to en-
gage in an iterative process in which the analysis
techniques are repeatedly tweaked in order to home
in on specific relationships between architectural fea-
tures and design performance.
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