A Computational Intelligence Approach
to Alleviate Complexity Issues in Design1
Michael S. Bittermann, I. Sevil Sariyildiz, and Özer Ciftcioglu
Abstract An approach to handle complexity issues in design is presented, where
computation is used to reach the most suitable solutions. The approach is based on a
novel concept of the objects forming a design. This concept is termed intelligent
design objects. Such objects exhibit intelligent behaviour in the sense that they
approach the most desirable solutions for conflicting, vague goals put forward by a
designer. That is, the objects know ‘themselves’ what to do to satisfy the designer’s
goals. This is accomplished by using fuzzy information processing to deal with the
vagueness of objectives, and multi-objective evolutionary algorithm to deal with
the conflicts among the objectives. The result of this approach is that designers
and decision makers have great certainty about the satisfaction of their goals
and are able to concentrate on second order aspects they could not consider
with great awareness prior to the computation. The effectiveness of the approach
is demonstrated through implementation in two applications from the domain
of architecture.
Keywords Architectural design • Computational intelligence • Fuzzy neural tree •
Genetic algorithm • Multi-objective optimization
1
This paper is taken from M.S Bittermann’s PhD thesis: Intelligent Design Objects (IDO) - A
cognitive approach for performance-based design. Department of Building Technology, Delft
University of Technology, Delft, The Netherlands (2009) 235.
M.S. Bittermann (*)
Delft University of Technology, Delft, The Netherlands
e-mail: M.S.Bittermann@tudelft.nl
I. Sariyildiz • Ö. Ciftcioglu
Chair of Design Informatics, Department of Building Technology, Delft University of
Technology, Delft, The Netherlands
J. Portugali et al. (eds.), Complexity Theories of Cities Have Come of Age,
DOI 10.1007/978-3-642-24544-2_19, # Springer-Verlag Berlin Heidelberg 2012
347
348
M.S. Bittermann et al.
1 Introduction
Design is complex. This is because it involves conflicting goals that are often
vague. For example, a design is demanded to be functional, look appealing and
have moderate costs. The vagueness of these objectives makes it problematic to
remain ‘fair’ when comparing alternative solutions during design, and the conflicts
among the objectives make it problematic to reach optimality. The fairness refers to
high precision in performance evaluations. This is particularly challenging to
achieve, when performance aspects like visual perception are involved, due to
their soft nature. Another source of complexity is that the number of possible
solutions is excessively large in general. A design consists of many parameters,
where every parameter may take different values, so that the total amount of
possible combinations forming a solution is enormous. This is referred to as
combinatorial explosion in the parameter domain. It makes it problematic to ensure
one did not miss a superior solution during the design process. A final source of
complexity, which is in fact a consequence of the ones named already, is that prior
to the design it is generally not clear how important goals are relative to each other.
For example it is difficult to tell exactly how important the functionality of a design
is compared to perception aspects prior to knowing what the meaning and implication of such a statement is. That is, before finding the most suitable solutions for the
goals, and thereby becoming aware of the nature of the inevitable trade-offs, it is
premature to commit to a relative importance among the soft goals.
Every one of these complexity issues is a challenging issue in itself and in
combination they are the reason why it is difficult to accomplish scientific means
for design enhancement. The enhancement is meant to support designers, so that
they can be more certain their designs are most suitable for the intended purpose.
There have been a number of works addressing this issue since the emergence of
computers. A number of them are using methods of classical artificial intelligence
(AI) (Eastman 1973; Gero 1987; Flemming and Woodbury 1995; Koile 2004).
The classical AI approach is severely limited, in particular due to unnatural rigidity
in the reasoning mechanism employed that cannot deal with the complexity inherent to design. Therefore this approach did not flourish, in particular for design
purposes. Recent approaches to computational design are based on an emerging
information processing paradigm known as computational intelligence (CI),
consisting of the methodologies known as fuzzy logic, evolutionary computation,
artificial neural networks, and other, bio-inspired, computational systems (Zadeh
1994; Engelbrecht 2005). CI methodologies are superior to the classical AI
methodologies in particular with respect to dealing with vagueness and combinatorial explosion, e.g. see (Caldas 2006; Deb and Srinivasan 2006; Shea et al. 2006;
Bandaru and Deb 2010).
It is particularly interesting to consider the role that fuzzy sets of fuzzy logic are
playing in dealing with complexity. A shortcoming of the classical AI approach in
treating complexity in design stems from a certain simplification that is ramified by
using fuzzy sets. This simplification is that classical AI approaches generally
A Computational Intelligence Approach to Alleviate Complexity Issues in Design
349
involve a logic that is based on premises with sharp ‘truth boundaries’, i.e. they are
based on classification using crisp sets. For example, a design is considered
expensive if its costs are above a certain threshold value, and it is considered not
expensive if the costs are below this value. The sudden shift of the applicability of a
label to its non-applicability at a certain parameter value is a simplification of the
complexity that is naturally inherent to reality, and in particular design. It entails the
omission of a significant amount of information. Therefore the effectiveness of the
classical AI approach is generally limited to situations with minimal vagueness in
requirements. Fuzzy sets allow the use of the information that is otherwise omitted.
This way the natural complexity of design requirements is subject to computational
treatment and the possibilities for reaching suitable designs that match the intended
purpose are subject to exploration with adequate precision, in contrast with the
classical approach.
This paper presents a novel system for computational design that addresses the
complexity issues mentioned above. It is based on a synergistic combination of
several computational intelligence methods. The paper is structured as follows. In
Sect. 2 a model of human vision is described that quantifies the perceptual
properties of environments. In Sect. 3 a model for evaluating designs is described,
in which the outputs of the vision model are used as input. In Sect. 4 multi-objective
evolutionary search is described, to deal with the combinatorial explosion and
generate optimal designs. The latter is combined with the first two components,
yielding an intelligent system with cognitive features. In Sect. 5 the system will be
applied to two design tasks to verify its effectiveness. This is followed by
conclusions.
2 Modelling Visual Perception
2.1
Introduction
Architects and engineers use different computational models to analyze the
properties of a design. For example, computational methods are used for structural
analysis, wind analysis, or cost analysis. The motivation behind the modelling
effort is to obtain precise information for the evaluation of a design.
Perception is an essential aspect of architecture and often a major factor determining the success of a design. It is therefore important to develop means to analyze the
visual perception properties of built environment. Modelling visual perception is
challenging mainly because it involves not only the eye, but also the brain (Levine
and Sheffner 1981; Gibson 1986; Palmer 1999; Foster 2000; Bittermann and
Ciftcioglu 2008). The final “seeing” event occurs due to brain processes. The
biological vision system is complex, involving many involuntary processes such as
eye saccades, retinal sampling, cortical mapping etc. This complexity is responsible
for a common phenomenon we encounter at practically every moment, while it may
remain unnoticed. We overlook items in our environment, although they are visible to
350
M.S. Bittermann et al.
us. This overlooking refers to the inability to remember visual information, although
the information was processed by the visual system (O’Regan et al. 2000). This
phenomenon may also be referred to as uncertainty of human vision or graded objectawareness. It is a characteristic property of human vision, occurring presumably due
to the way the human memory is built up and facilitates consciousness dealing with
ample environmental information. In this respect, the human vision system clearly
differs from an optical system like that of a camera, although the analogy may be
suitable to some extend as well (Marr 1982; Pentland 1987).
2.2
A Probabilistic Approach
In the present approach the components involved in human vision are modelled as a
whole system instead of modelling each component individually, thereby bridging
between the environmental stimulus and its mental realization. At this point the
definition of the concepts involved in vision put forward in this approach is not
elaborated further. This will be established naturally as a result of the vision model,
which is described in the next paragraph. The work concentrates on the influence of
geometry on the human vision process, where an observer builds up an unbiased
understanding of the environment. This means that an observer has no a-priori
preference for an object in the environment. Such a bias may be due to a task the
person is about to accomplish, or a general personal preference, or other conditioning. In many instances we expect some degree of bias in visual perception, which is
problematic to discern without a model of the unbiased case. Explicitly, the model
gives two advantages:
• The perception and related phenomena in early vision are understood in greater
detail, and some common reflections about them are substantiated.
• The model can be effectively introduced into architectural design, since perception is quantified by a probability.
We start modelling the perception process using a simple, yet fundamental,
geometry. This is shown in Fig. 1. For the sake of simplicity of explanation we
consider perception in a two-dimensional space. That is, the vision of an observer is
considered in the x-y plane in Fig. 1.
In Fig. 1 an observer is facing and viewing a vertical plane from the point denoted
by P. Through vision, the observer is able to receive visual information from all
directions within his/her vision scope. In the present case we model unbiased human
vision. This means the observer has no preference for any direction in the scope. In
other words he/she pays attention equally in all directions. In mathematical terms
this is modelled by associating an equal probability with any differential angle
portion in the visual scope as given by Eq. 1 (Ciftcioglu et al. 2006).
A Computational Intelligence Approach to Alleviate Complexity Issues in Design
351
Fig. 1 Plan view of the basic geometric situation of perception (a). Perspective view of the same
situation (b)
fy ¼
1
p=2
(1)
where fy is the probability density (pdf) associated to the vision angle, where the
vision scope is taken to range from p/4 y p/4. The probability density
function models the visual attention an observer pays to the vision angle in early
vision and any differential angle dy receives equal attention, reflecting the unbiased
case. Any point of an environment existing in the visual scope receives a particular
degree of the visual attention. In case of the basic geometry shown in Fig. 1, this
degree is given by Eq. 2 for the interval lo x lo (Ciftcioglu et al. 2006).
The pdf fx(x) in Eq. 2 models visual attention along the x dimension.
fx ðxÞ ¼
2
lo
;
p ðl2o þ x2 Þ
(2)
Integration of visual attention in a finite small interval, where fx(x) is approximately constant, gives unbiased perception as probability P
ð
P¼
Dx
fx ðxÞ dx ffi fx ðxÞ Dx;
(3)
The implications of these results are seen in Fig. 2. Namely, when the distance
between observer and object is short, the visual attention is strongly focused on a
relatively small area in the frontal part of the object, and strongly diminishes
towards the side parts of the wall, whereas when the distance is far, the attention
is ‘smeared out’ almost homogenously over the object, so that the peak attention is
also less. This means that for the nearby wall an unbiased observer will be strongly
aware of the details in frontal direction and hardly aware of the side parts of the
352
M.S. Bittermann et al.
Fig. 2 Unbiased attention for an object at a near distance (a). At a far distance (b)
wall. Another result is that the integral of pdf fx(x) along the wall object is greater in
Fig. 2a than in 2b. This means that when the wall is nearer it yields a higher
perception, i.e. an unbiased observer will be more aware of the wall than in the
distant case.
These results coincide with our common experience of vision, indicating the
validity of the model. The benefit of the computations is the precise quantification
of perception. This way a systematic search for optimal architectural designs,
satisfying requirements that are expressed in terms of perception, may be executed.
This will be explained in the following sections.
One exemplary application of the probabilistic model for spatial analysis is
shown in Fig. 3, where it is used to measure unbiased perception during a walk
through a retail environment. Figure 4 shows the resulting perception of every
object as a virtual observer is moving through the space, where the distance is given
as the number of 30 cm intervals from the starting location. During the first part of
the walk, until interval 20, the observer is most aware of Object O1, which is the
cart of yellow shopping bags. During the second part, from interval 20 until 36, the
observer becomes most aware of objects O8, which are the exhibited furniture
A Computational Intelligence Approach to Alleviate Complexity Issues in Design
353
Fig. 3 Perceptual analysis along a trajectory in the space
Fig. 4 Resulting perception of the respective objects along the trajectory
pieces. This second part is less strongly dominated, so that relatively more attention
is paid to the other objects than at the beginning of the trajectory. The final part of
the trajectory increasingly accentuates the escalators (object O6). In the meanwhile
O7, the advertisement signage indicating prices at the restaurant of the store, is also
receiving significant attention. In the intervals 42–47 the unbiased observer is even
slightly more aware of the signage than of the escalators. Relocation of the objects
in the scene would clearly change the observer’s experience.
354
M.S. Bittermann et al.
3 Evaluating Design Performance
The model presented in the previous section delivers, as its output, information on
the perceptual properties of a space. Such a piece of information is one of many
characterizing a design, such as sizes of spaces, distances among objects, stress
resistance of elements, etc. However, in design it is not only necessary to observe
the direct physical features of the objects, but to interpret these with respect to the
goals pursued. For example, in a space the stairs may be desired to be hardly
perceived, for instance in order to organize the people flow efficiently, although
sufficiently perceived to be easily located if needed. It is noted that this requirement
entails a certain low amount of perception for the stairs, and deviation from this
amount means that the requirement will not be totally fulfilled. Many requirements
have this character, i.e. they do not pinpoint a single acceptable parameter value for
a solution, but a range of values that are more or less satisfactory. Design also
involves conflicting requirements, so many requirements are bound to be only
partially fulfilled.
Such requirements are characterized as soft, and they can be modelled using
fuzzy sets and fuzzy logic (Zadeh 1975). These concepts were introduced by Zadeh
as generalizations of classical crisp sets and traditional logic. In contrast to a crisp
set, a fuzzy set has no sharp set boundary, instead the boundary is ‘smeared out’
over a range in the universe of discourse. A fuzzy set is characterized through a
function called membership function. That is, whereas classic sets permit an object
only to belong to a set or not belong to it, through a fuzzy set an object is associated
to the set by means of a membership degree m, which can be any rational number
between zero and one. This allows the modelling of partial truth. In our case this
refers the partial truth that a design object possesses a desired feature. This means
that we interpret the membership degree as a degree of satisfaction of a requirement, the latter being expressed through a membership function. Two examples of
fuzzy sets used to model elemental design requirements are shown in Fig. 5.
From the figure we note that a hall with a certain size a0 partly satisfies the
requirement R1: large hall by 65%. Stairs with a perception of degree p0 satisfy the
requirement R2: low perception of the stairs, but not too low by 86%.
Fig. 5 Two fuzzy sets expressing two elemental design requirements
A Computational Intelligence Approach to Alleviate Complexity Issues in Design
355
Fig. 6 The structure of a neural tree
By means of fuzzy membership functions a physical property of a design is
interpreted as a degree of satisfaction of an elemental requirement. The requirements considered here are relatively simple, whereas the ultimate requirement for a
design, namely a high design performance, is complex. The latter is influenced by
satisfaction of a number of such elemental requirements at the same time. For
instance, several requirements should be highly satisfied for a high design
performance.
In this work, the performance is computed using a fuzzy neural tree (Ciftcioglu
et al. 2007a). This is particularly suitable for dealing with a complex linguistic
concept like design performance. A neural tree is composed of one or several model
output units, referred to as root nodes, that are connected to input units called
terminal nodes, and the connections are via logic processors termed internal nodes.
An example of a neural tree is shown in Fig. 6. The neural tree is used for
performance evaluation by structuring the relationships between aspects of performance. The root node takes the meaning of high design performance and the inner
nodes one level below are the aspects of the performance. The meaning of each of
these aspects may vary from design project to design project and it is determined by
experts. The model inputs shown as squares in Fig. 6 are fuzzy sets, such as those
given in Fig. 5.
Figure 7 shows details of the nodal connections of a neural tree, like the one
shown in Fig. 6. In Fig. 7 wij is the weight assigned to the connection between
terminal node i and inner node j. The weights are given by domain experts, and
express the relative significance of the nodes. The centres of the basis functions are
set to be the same as the weights of the connections arriving at that node.
Therefore, for a terminal node connected to an inner node, the inner node output
denoted by Oj, is obtained by the equation
356
M.S. Bittermann et al.
Fig. 7 Details of a neural
tree structure showing the
different type of node
connections
Oj ¼ expð
n wij ðwi 1Þ 2
1 X
Þ
2 i
sj
(4)
where j is the number of the node; i denotes consecutive numbers associated to each
input of the inner node; n denotes the highest number of the inputs arriving at node
j; wi denotes the degree of membership being the output of the i-th terminal node;
wij is the weight associated with the connection between the i-th terminal node and
the inner node j; and sj denotes the width of the Gaussian of node j (Ciftcioglu et al.
2007b). One notes that the fuzzy logic operation performed at each node is an AND
operation among the input components Xi coming to the node. This means for
instance that if all the elemental requirements are fulfilled, then the design performance is high. For any other pattern of satisfaction on the elemental level, the
performance is computed and obtained at the root node output. It is also noted that
the model requires the establishment of the width parameter sj at every node. This
is accomplished by imposing a consistency condition on the model. This condition
ensures that when all inputs take a certain value, the model output yields the very
same value (Ciftcioglu et al. 2007b). The consistency is ensured by means of
gradient adaptive optimization identifying optimal sj values for each node.
4 Generating Solutions with Maximal Performance
The information obtained from the performance evaluation is useful to search for
designs that have superior performance. However, this process is not straight
forward. Assuming we know that the performance of our design is moderate
overall, how to increase its performance remains a difficult question. As a design
consists of many design objects, such as several spaces, walls, floors, ceilings, etc.,
and each object has several parameters characterizing it, the amount of possible
solutions to consider is enormous. This is termed combinatorial explosion.
To deal with combinatorial explosion, advanced search methodologies emerged
in the last decades in order to identify the most suitable solutions among the
excessive amount of possible ones. The most prominent methodology is
A Computational Intelligence Approach to Alleviate Complexity Issues in Design
357
evolutionary computation (EC), due to its established effectiveness (Goldberg
1989; Coello 1999). Evolutionary computation has an inherent mechanism leading
it towards suitable solutions that is inspired by biological evolution. This mechanism breeds better solutions through the combination of successful individuals.
That is, the method generates a number of random possible solutions, evaluates
their fitness, and then exchanges portions of the ‘genetic code’ that characterizes
these between fit solutions. This is schematically shown in Fig. 8.
Evolutionary computation is especially convenient for addressing problems
where multiple objectives should be satisfied at the same time, like minimal cost
and maximal functionality. In the multi-objective case the grading of fitness of
solutions is based on a criterion referred to as Pareto non-dominance. A solution is
termed Pareto non-dominated when there is no other solution that outperforms it for
every objective involved. In other words, when compared to any other solution, a
non-dominated solution is superior for at least one criterion.
Evolutionary computation has been used for optimization in many engineering
applications (Deb 2001). However, for use in design there are still two major
drawbacks to using EC. The first is that EC conventionally uses crisp functions to
evaluate the fitness of solutions. However, as pointed out in Sect. 3, many design
requirements are soft, so that EC needs to be combined with other methods to
handle this issue. The second issue concerns the effectiveness of EC in addressing
problems with multiple objectives. Its effectiveness diminishes drastically if the
amount of objectives exceeds about four or five. Therefore the solutions found may
be of inferior quality and the diversity among solutions is too low for confident
decision-making. This is a topical concern in evolutionary multi-objective optimization (Zitzler et al. 2003; Hughes 2005).
Fig. 8 Flowchart of a genetic algorithm
358
M.S. Bittermann et al.
4.1
An Approach Based on Synergy Among Different CI Methods
In this work both bottlenecks are addressed. The first issue concerning the softness
of criteria is handled by coupling the neuro-fuzzy performance evaluation model
described in Sect. 3 with a multi-objective evolutionary algorithm. The resulting
system is shown in Fig. 9. In this case the fuzzy model plays the role of the fitness
function. This means that the search process makes use of human-like reasoning as
it strives for optimality. The second issue, concerning the effectiveness of multiobjectivity, is alleviated by applying a relaxed Pareto ranking concept during the
search (Bittermann and Ciftcioglu 2009).
From Fig. 9 we note that the computational design system starts its processing by
generating a population of random solutions within the boundaries put forward by
the designer in advance and instantiates them in virtual reality. Several properties of
these solutions are then measured, such as sizes, distances, and perceptual
properties. These are interpreted with respect to the elemental design requirements
at the input layer of a fuzzy neural tree. This information is propagated through the
tree, yielding the degree of satisfaction of the solution at the penultimate level right
below the root node. That is, the evaluation using the fuzzy model is able to express
the features of a solution in abstract, linguistic terms. For example it provides the
performance regarding functionality, perception and cost effectiveness. These
outputs are then used to compare the randomly generated solutions regarding
their respective Pareto non-dominance. Relatively non-dominated solutions are
then favoured for reproduction and the genetic operations, so that the next generation is more likely to contain non-dominated solutions.
This generation-evaluation-loop is executed for a number of generations, finally
resulting in a set of solutions that are all non-dominated. This set approximates a
surface in objective space that is referred to as Pareto optimal front. A designer or
decision-maker is then able to compare these solutions in order to select his
favourite design among the apparently equally valid solutions. If the favourite
solution completely satisfies the designer’s preferences, the design solution is
Fig. 9 System based on evolutionary computation, perception and fuzzy modelling
A Computational Intelligence Approach to Alleviate Complexity Issues in Design
359
Fig. 10 Cognitive design approach based on the CI system intelligent
found. Otherwise the designer may change the criteria of the computational design
process and re-run the algorithm. This process iterates as shown in Fig. 10, where
the box containing the term IDO represents the system shown in Fig. 9.
4.2
Cognitive Features of the System
The solutions on the Pareto front are not completely equivalent.
As they should be, they are all non-dominated; however some solutions still have
an advantage over the others in the following sense:
At the root node of the neural tree, the performance score is computed by the
defuzzification process given by
w1 ð1Þf1 þ w2 ð1Þf2 þ ::: þ wn ð1Þfn ¼ p;
(5)
where w1+w2+. . .+wn ¼ 1; f1fn are the outputs at the penultimate nodes; p is the
design performance, which is naturally requested to be maximized. The vector
w containing the weights on the penultimate level is termed priority vector. The
node outputs f1fn can be considered as the design feature vector f. The reflection
of these features in the design performance is maximized if the weights w1wn
define the same direction as that of the feature vector.
Normalising the components and equating them to the weights yields
f1
;
f1 þ f2 þ ::: þ fn
fn
¼
f1 þ f2 þ ::: þ fn
w1 ¼
w2 ¼
f2
;
f1 þ f2 þ ::: þ fn
Due to Eq. 6 the performance given by Eq. 5 becomes
::: ; wn
(6)
360
M.S. Bittermann et al.
pmax ¼
f12 þ f22 þ :::: þ fn2
f1 þ f2 þ :::: þ fn
(7)
Every solution on the Pareto front has an associated pmax value that characterizes
it. This value gives the maximum design performance the solution attains, when
there is no a-priori preference regarding the objectives. Solutions can be compared
regarding their pmax value, and the solution with the highest value is preferable
among the Pareto solutions. This solution has a characteristic priority vector w*.
This vector implies that the computer advises the decision maker which goal he
should make more or less important in the present task, information that was not
known prior to the search process. This means that the machine performs an act
beyond mere optimization or intelligent information processing. This act is an act of
cognition, yielding information about second-order aspects that were not included
in the criteria given by the human decision maker. The artificial cognition alleviates
decision making in the sense that the designer need not explore the entire Pareto
front, but has information on proficient areas on the front. It is noted that the
computational search for the Pareto front yields objects with intelligent behaviour.
That is, the objects need no explicit instruction to satisfy high-level criteria.
5 Two Applications of the System
5.1
Application 1
In this application, the design of an ensemble of residential housing units is
considered. The problem is taken from an actual design case. The task is to find
suitable locations of a number of housing units on their respective lots. The site
belongs to one of the largest areas in the Netherlands subject to development,
named Leidsche Rijn. The site has a size of about 3,600 m2. The streets and lots
are provided in advance in this case. The site is shown in Fig. 11. In the figure, 20
houses are shown. Three of them are existing, namely E1, E2, and E3, so that 17
houses are subject to optimal positioning. In this task two main objectives are
pursued. The first one is to maximize the visual privacy of the buildings, in
particular that of their south facades, where the living rooms are situated. The
second one is to maximize the size of the gardens.
The visual privacy is computed using the perception model described in Sect. 2.
The visual privacy of a façade is considered to be the reciprocal of the sum of
attention “impinging” on the facade. In other words it quantifies how low the
integral degree of perception of a façade is. Explicitly, we calculate the visual
privacy of an object O as
A Computational Intelligence Approach to Alleviate Complexity Issues in Design
361
Fig. 11 The neighbourhood subject to design
Fig. 12 Visual privacy computation based on the probabilistic perception model
Ppriv ðOÞ ¼ P
n
1
(8)
PðO; Vn Þ
1
where P(O,Vn) is the degree of perception of object O from the n-th viewpoint.
Figure 12 illustrates the implementation of the visual privacy computation for the
362
M.S. Bittermann et al.
houses of the housing complex, where elemental perceptions in the form of vision
rays are shown.
As to the second criterion in this task, the maximum size of the garden facing
south is restricted by the placement boundaries both north and south and the width
of the house. This is illustrated in Fig. 13 using house H1 as an example. In the
figure, the boundary of the lot is shown as a solid line and the placement boundary is
shown as a dashed line. Explicitly, the garden performance G is given by g/gmax.
This means the garden performance belonging to a house is calculated by dividing
the extent of a garden towards the south by the maximum extent the garden can
have, considering the boundary of the house’s plot.
Figure 14 shows the requirement of high visual privacy for the various houses. It
is noted that as the terminal node output increases with increasing privacy.
The fuzzy neural tree used in this application is shown in Fig. 15.
The resulting Pareto optimal front after 20 generations is shown in Fig. 16.
Pareto optimal solutions 1 and 4 in Fig. 16 are shown in Figs. 17 and 18 for
comparison. It is noted that solution 1 outperforms solution 4 as its maximal
performance p from Eq. 7 is larger, namely .89 versus .85. This is seen in Fig. 16.
In fact, solution 1 is the solution with the greatest maximal performance p among
the Pareto solutions. This means that for the present task the computations indicate
that privacy is a more significant factor in the design than garden size. This result
could not be foreseen prior to executing the computational search process; it is an
act of machine cognition. In terms of the parameters of the solutions, both designs
differ significantly only in two places, namely house H6 and houses Gb1–Gb4 are
located further north in design nr. 4. This is also an interesting result that could not
be foreseen, namely that all Pareto solutions have a common optimal location
pattern for most of the houses.
5.2
Application 2
This design task concerns the design of an interior space. The space is based on the
main hall of the World Trade Centre in Rotterdam in the Netherlands. Figure 19
shows the main entrance hall of the building as seen from its entrance.
In the figure, a virtual human observer can be seen viewing the interior space of
the entrance hall. The perception of the virtual observer plays a role in the treatment
of a number of perception based requirements for the design. An example is that the
stairs should not be very noticeable from the entrance of the space. Another
example is that the building core should be positioned in such a way that the
entrance hall is spacious, while the elevators should be easily perceived at the
same time. The task is therefore to optimally place the design objects to satisfy a
number of perception and functionality requirements. The objects are a vertical
building core containing the elevators, a mezzanine, stairs, and two vertical ducts.
A Computational Intelligence Approach to Alleviate Complexity Issues in Design
363
Fig. 13 Calculation of the garden performance
Fig. 14 Elemental requirements of visual privacy expressed via fuzzy membership functions
Fig. 15 Fuzzy neural tree for performance evaluation
364
M.S. Bittermann et al.
Fig. 16 Resulting Pareto optimal designs in objective space
Fig. 17 Pareto-optimal design marked with number 1 in figure 16
The goals are to maximize the performance of every design object as seen from
the fuzzy neural tree structure in Fig. 20. As examples of the requirements at the
terminal level, two are shown in Fig. 21.
The resulting front of Pareto optimal solutions is shown in Fig. 22. It is noted that
the objective space has four dimensions, one for the performance of every design
A Computational Intelligence Approach to Alleviate Complexity Issues in Design
365
Fig. 18 Pareto-optimal design marked with number 4 in figure 16
Fig. 19 The design objects of the task
Fig. 20 Two requirements are involved, concerning the spaciousness of the entrance hall (a) and
the perception of the stairs (b)
366
M.S. Bittermann et al.
Fig. 21 Neural tree structure for assessment of design performance
Fig. 22 Pareto optimal designs with respect to the four objective dimensions
object. The representation is obtained by first categorizing the solutions according
to which of the four quadrants they belong to, in the two-dimensional objective
space formed by the building core and mezzanine performance, and then
A Computational Intelligence Approach to Alleviate Complexity Issues in Design
367
Fig. 23 Design D2
Fig. 24 Design D4
representing the performance of stairs and ducts with a coordinate system for each
quadrant. This way four dimensions are shown on the two-dimensional page.
Two Pareto optimal designs are shown in Figs. 23 and 24 for comparison. Design
D2 outperforms design D3 with respect to the maximal performance p obtained
using Eq. 7. Namely D2 scores .78, whereas D4 scores .71. Regarding the satisfaction of the individual objectives, the greatest absolute difference between D2 and
D4 is with respect to the performance of the mezzanine. In D2 the mezzanine is
located closer to associated functions, and this turns out to be more important
relative to the fact that D4 yields more daylight on the mezzanine. D2 therefore
scores higher that D4 regarding the mezzanine. Additionally, D2 slightly
outperforms D4 regarding the performance of the ducts. This is because the ducts
do not penetrate the mezzanine in D2, whereas in D4 they do. The latter is
undesirable according to the requirements. Regarding the building core, D2 is
inferior to D4, because D4 is more spacious and also because the elevators are
368
M.S. Bittermann et al.
more centrally located. Regarding the stairs’ performance, the difference between
D2 and D4 is negligible.
It is emphasized that D2 is the solution with the greatest maximal performance
pmax, so that from an unbiased viewpoint it is the most suitable solution to be
selected for construction. This result is an act of machine cognition, as it reveals
that in the present task the stairs and ducts are more important than the building
core. This information was not known prior to the execution of the computational
search process.
6 Conclusions
A novel computational system for architectural design is presented, and its effectiveness is demonstrated through two applications. It generates designs that satisfy
multiple vague criteria that are conflicting. The application results show that the
system is capable of dealing with three complexity issues that are challenging
computational design approaches. The system handles the common vagueness of
requirements induced by visual perception through using a visual perception model
that yields the degree to which an unbiased observer is aware of environmental
objects. The special neural structure with embedded fuzzy logic processors of the
associated performance model is shown to be suitable for handling the vagueness of
requirements, where it deals with both the complexity and vagueness of design
objectives at the same time. Multi-objective evolutionary search is demonstrated to
be an effective framework for addressing the complexity of the design task, in
particular as it is able to take the information provided by the fuzzy model into
account during its search process. This combination is particularly effective as it
permits the evolutionary search to deal with a large amount of requirements. It is
further demonstrated that using the fuzzy model in the evolutionary framework
yields a form of computational cognition, so that a preferable preference vector is
pinpointed from an unbiased viewpoint. This is a demonstration of an act of
computational cognition, as it includes determining second-order preferences that
were not known before executing the design.
From the perspective of architectural practice, the contribution of this approach
is that project solutions can be assessed without any presupposition, increasing
designers’ confidence of finding the best solution. It is noted that the computational
design process is in a symbiotic partnership with the designer. That is, computation
takes care of those aspects of designing which are computationally intensive and
sensitive to imprecision, giving a designer advanced means to exercise his/her
creative ideas with greater effectiveness.