1. NEURAL SELF-ORGANISING MAPS
AND
GENETIC ALGORITHM:
EVOLVING 3D CELLULAR AUTOMATA
ARCHITECTURAL MODEL
A.BAKUNOWICZ
MSc
2013

2. AMIINA BAKUNOWICZ
A thesis submitted in partial fulfilment of the requirements of the School of
Architecture, Computing and Engineering, University of East London for the
degree of Master of Science
September 2013
2

3. Table of Contents:
Chapter 1. Abstract
Chapter 2. Introduction
2.1 The New Aesthetics and the Ecology of Design
2.2 Coding vs Traditional Design Methods
Chapter 3. The Concept of the Architectural Problem
3.1 Architectural Scenario
3.2 Proposed Solution to the Architectural Problem
3.3 Other Ways of Solving Similar Problems?
3.3.1. Electrical Graph Approach
3.3.2. Physically based modelling
Chapter 4. Classic Genetic Algorithm
4.1 Traditional Genetic Algorithm
4.1.1. Brief Description
4.1.2. Evolutionary Embryogenies.
4.2 Classic GA for the Current Architectural Scenario
4.2.1 Description of the Code
4.2.1.1. Original CA Model and Body-Plan
4.2.1.2. The First Generation
4.2.1.3. The Fitness Function
4.2.1.4. The Process of Selection
4.2.1.5. Crossover and Mutation
4.2.2 Outcome of the Algorithm
4.3 Examples of GA Applications in Architecture
Chapter 5. Self-Organising Maps and Genetic Algorithm
5.1 Artificial Neural Networks and Self-Organising Maps
5.2 Introducing SOM to the Classic GA
5.2.1 Why Combining GA with SOM?
5.2.2 Managing the Expanded Choice
5.2.3 The Evaluation of the Aesthetics
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4. 5.3. The Evolution of the Proposed Code
5.3.1. Stage 1.Classic GA for the Current Architectural Scenario
5.3.2. Stage 2. Adding Golden Ratio to the Fitness Criteria
5.3.3. Stage 3. Introducing Self-Organising Maps to the Genetic Algorithm
5.3.4. Stage 4. Turning Chromosomes into Neurons and Back
5.3.5. Stage 5. Co-evolving Threshold of the Fitness Factor Components
5.3.6. Stage6. Optional Selection Method
5.4. The Final Algorithm
5.4.1.The Structure of the Algorithm
5.4.1.1. Original CA Model and Body-Plan
5.4.1.2. The First Generation
5.4.1.3. Introducing Self-Organising Maps
5.4.1.4. The Fitness Function
5.4.1.5. Selection Options
5.4.1.5.1. The final decision-making rules of the proposed algorithm
5.4.1.5.2. Selection Option 1: Optimised Random Selection by Clusters
5.4.1.5.3. Selection Option 2: Artificial Selection and Evaluation of Aesthetics
5.4.1.5.4. Selection Option 3: Goldberg Roulette
5.4.1.6. Crossover
5.4.1.7. Mutation
5.4.1.8. The following Generations
5.4.1.9. Visualisation of the Search Space by Clustering and Evolution of Colour
5.4.2. Main Results and Observations
5.5. Advantages and Disadvantages of GA-SOM
5.6. Further Research
5.6.1 Parameterisation of the Body-Plan
5.6.2 Swarms and SOM Pattern Recognition
5.6.3 Discovering the Potential of Clusters
5.6.4. Co-Evolution Instead of Fitness Criteria
5.6.5. Exploring Other Ways in Which CA Can Generate Body-Plans
5.6.6. Other Visualisation Techniques of the Search Space
5.6.7. Adapting Genetic Operators to Evolve the Evolvability
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5. Chapter 6. Conclusion
Chapter 7. References
Chapter 8. Further Reading
Chapter 9. Appendixes
Appendix 1. Traditional Genetic Algorithm: a Brief Description
Appendix 2. Comparing the Types of the Evolutionary Embryogenies
Appendix 3. Example of a SOM Algorithm Application in 3D Modelling and Its Applications
Appendix 4. Piasecki and Sean's Wundt Curve Experiment
Appendix 5. First Ever SOM for Multi-Objective Evolutionary Algorithm
Appendix 6. Brudaru's Cellular Genetic Algorithm with Communicating Grids and SOM
Appendix 7. Kita's Real-Coded Genetic Algorithm (RCGA) and SOM
Appendix 8. Optional Body-Plans for the Proposed Algorithm
Appendix 9. Proposed Algorithm (Python)
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6. “... Game did not display perfection to the outward eye.
Rather, it guided the player…”
Herman Hesse, 1943
“The Glass Bead Game”
6

7. Chapter 1. Abstract
Since the dawn of Computer Aided Design for a long time architects were coming up with
digitally modelled projects that were very radical, but impossible to build. Later on with the
development of the fabrication techniques a lot of the designs have materialised. Currently,
architects started using computational methods to re-evaluate designs. In addition to that there
always has been the urge for architectural significance and designs became very economic and
performance- orientated. Thus the exploration of the alternative computational ways of the
architectural morphogenesis was left behind.
I would like to propose a possible solution to the form-finding challenge in a given architectural
context by scripting. This paper describes a design process that mostly uses code that
combines Genetic Algorithm and Self-Organising Maps and evolves a predetermined Cellular
Automata model. A computer forms a team with an architect to develop a design, where the
solution is formed gradually during the process of running the algorithm. Together, the designer
and the machine go through the architectural design procedure starting from the phase at which
the appraisal is carried out, concepts are finalised and the basic mass study is done until both
are satisfied with the algorithm's outcome. The eventual model can be then given back to the
architect for final adjustments and detailing.
The proposed algorithm has two tasks. Firstly, based on the information available after the
completed initial design stages, to develop a schematic body-plan of the architectural model
and parameterised it. Secondly, applying the principles of the processes of natural evolution
and biological neural networks, use the genetic algorithms (GA) and neural Self-Organising
Maps (SOM) to evolve optimal solutions.
This paper will concentrate mostly on the second stage of the algorithm, where the selforganising mapping will be applied to each generation of the alternated body-plan in order to
widen, classify, structure and exploit the search space of the GA. I believe that the algorithm
can create and amplify the synthetic intuition and give a designer yet another powerful tool and
a new skill to be applied in the process of the forming the matter around the architectural
concept. Also by structuring and optimising the possibilities space I would like to test if SOM
could help to speed up the process of finding the optimal solution and avoid premature
convergence.
At the same time the proposed algorithm attempts to deal with the challenge of “...moving from
the creation of inventive articulated patterns, and the small-scale installations to the full scale
architectural projects where scripting can unleash the entire universe of opportunities for
architectural space” (Matias Del Campo)
Also certain relevant theoretical problems will be looked at, such as the paradox of the
expanded choice, coding compared to traditional methods of design, philosophical meaning of
“the sympathy of things”, the challenges of the evaluation of aesthetics and many other.
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8. Chapter 2. Introduction
2.1. The New Aesthetics and the Ecology of the Design
In 1917 D’Arcy Wentworth Thompson introduced an idea that form is never a given, but an
emerged product influenced by dynamic forces that are shaped by flows of energy and stages
of growth. Later on with the birth of the mathematical and scientific hypotheses known as
“Complexity Theory” in 1995 Kauffman gave another dimension to Thompson’s ideas. He
argued that the form can replicate an organic life and become an example of “organised
complexity”. The meaning behind its geometry is not necessarily the accidental “form follows
function”, but it could be viewed as a complex system that has “self-organising” properties and
being able to evolve and be sustainable in the absence of any external influence (Kauffman
1995).
Applying this concept to the design process, in order to give the system maximum possible
autonomy it is essential to determine a distinction between behaviour which emerges as a
result of self-organizing processes, and behaviour which was deliberately prefigured in the
design of that organism, or organisms. Also certain behaviours can emerge from an initial set of
simple rules written for locally interacting units that was neither implied nor foreseen to happen.
As independent behaviours emerge, here comes a possible solution to a problem of
programming the certain level of “creativity” or “individuality”.
All above leads back to the perceptual morphogenesis. Perception itself, As beauty is "intrinsic"
and it cannot emerge ex nibilo ("out of nothing") or be applied, the design acquires the aesthetic
properties from the aspiration to make something beautifully and keeping it throughout the
entire design process has been studied by Gestalt psychology and philosophical systems since
the beginning of 19th century (Wertheimer). The perception of complex systems is mostly
generated not so much by its individual elements (for example, human neurons) as by their
dynamic interrelation representing the collective behaviour – a phenomena that can be found
easily in Artificial Neural Networks, where data generalisation, pattern classification or
forecasting abilities are the key features (Ramos 2012).
Another way to approach morphogenesis was analysed by Lars Spuybroek. He took the brave
role to reinterpret the notion of beauty: "Everything feels to some degree, and the feelings we
have towards the object are of the same nature as the ones that have made it or are still
making it...the feelings are of the same nature in the sense of resonating or sympathizing".
Spuybroek claims that “a feeling, a resonance, a sympathy” is a characteristic or parameter of
the design by which we perceive it, that exists in another dimension, that cannot be measured
or valued. The forces that were driving the process of creation stay present and active even
after the object is finished.
The notion of design in a complex system can be viewed as "self-assemblage" or "self-design".
The thought is contradictory in its essence as no self exists prior to the process... Against the
logic, Spuybroek believes in design without a designer. He repeated Paley just leaving God out:
"Things are beautiful because they are made" and then corrected himself through Ruskin:
"Things are beautiful because they are made beautifully". As beauty is "intrinsic" and it cannot
emerge ex nibilo ("out of nothing") or be applied, the design acquires the aesthetic properties
from the aspiration to make something beautifully and keeping it throughout the entire design
process.
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9. The associative or interior aspect of perception is based on immediate feeling or seeing that
extends the experience. That happens when the exterior is internalised, when the objects share
the exterior quality, like flatness of the table top and the glass bottom. Internalised means "felt”,
as when lifted off the table, glass longs for it (Manuel DeLanda). As a result feelings make
things act: take or change shape, in accordance with others.
Carl Jung had similar views. His famous saying "The meeting of two personalities is like the
contact of two chemical substances. If there is any reaction, both are transformed" can be also
viewed in an architectural context.
Henri Bergson refers to the “interior aspect of perception” as intuition: "An absolute can only be
given in an intuition, while all the rest has to do with analysis. We call intuition here the
sympathy by which one is transported into the interior of an object in order to coincide with what
there is unique and consequently inexpressible in it. Analysis, on the contrary, is the operation
which reduces the object to elements already known." This thought puts a big question mark
over the suggestion that computers CAN actually be creative as at this point in time they are
merely analytical tools.
Hopefully one day we will learn to recognise, comprehend and share “feelings” as a main
source of information. Even at this point we perceive everything as a sensation of various
degrees of sympathy and make our decisions based on the resonance to this "felt" assessment.
Then, the process of creating will be the ONE with the result, especially if the complexity of the
potential architectural project could be understood not analytically, but intuitively (Bergson) or
“emotionally” (Spuybroek). Then the context can be parameterised to shape the new interlinked
functional spaces, and then, to close the circle - it updates and adapts the existing, ready to be
changed again. This way an ever-adapting sustainable architectural complex system will be
emerging.
2.2 Coding versus Traditional Design Methods
The evolution of computer-aided design (CAD) demonstrates the search for the ways of how
technology can either fulfil certain pre-allocated roles or how it can carry out the most
appropriate role or combination of roles. Nowadays they mostly serve either as design tools or
as means of communication or as design assistants or as design environments or even as
habitable physical environments and virtual environments (Kalay 2004).
The process of design, which has been practiced over hundreds years and formalised in the
1960s (Minsky 1968) consists of four interconnected phases: problem analysis, solution
synthesis, evaluation and communication. The process of design carried out either with the
traditional methods or by scripting remains the same and consists of these four stages. The
advantage that computers give to the evolution of design during the first three stages is that
they are powerful enough to turn a design into a complex system, evolve it automatically
passing on its qualities to the design:
- Flexibility (being able to cope with incorrect, ambiguous or distorted information or even to
deal with unforeseen or new situations without showing abrupt performance breakdown)
- Versatility (Dorigo and Colorni)
- Robustness that insures the functionality of the system even when some parts are locally
damaged - Damásio)
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10. Such computational systems have “competition-cooperation duality”. Cooperation reflects in a
global behaviours of agents, that interact by communicating information, or hints (usually
concerning regions to avoid or likely to contain solutions) to each other while solving a problem
(Langton). An example of cooperative problem solving is the use of the Genetic Algorithm to
find states of high fitness in some abstract space. In Artificial Neural Networks, we can also find
similar features, where the output of one neuron affects the behaviour or state (Cellular
Automata theory) of the neuron receiving it, and so on (Ramos 2012).
Also there are various design methods that join together the stages of the design process. At
present the design methods can be categorised into four types: trial-and-error searches,
constraint-satisfaction methods, rule-based design and precedent-based methods (Kalay 2004).
Scripting gives bigger flexibility and broader exploration of all design methods and even more
valuably, develops the new or combines the existing ones. Also it permits a broad processing of
information work as it has no intrinsic size. “The computer is the tool for the manipulation of
information, whether that manipulation is a consequence of our actions or a consequence of the
actions of the information structure themselves” (Ramos 2012).
Of course, it’s all well said that computers provide great advantages during the design process.
However, the methods that were discussed earlier on in this chapter were developed by a
human designer, for human designers and were formed based on human design experience.
Only very small new adaptations to these methods were made taking into account the new
design partner - the computer. Consequently, the question arises, could the new synthesised
design methods be evolved that do not depend on both positive and negative human influence?
Also, of course, the ultimate puzzling and unsettling questions, can the procedural methods be
“creative” and yield novel design solutions?
If we apply the criteria of unexpectedness to the results, then the logical (still arguable) answer
is yes. They can, very occasionally generate unexpected results only because of the unique
ability to produce and analyse vast amount of solutions, a skill that humans do not possess.
Some may agree that we can program “creativity” and “individuality” into the code by ensuring
that:
- The bottom-up methodological design is followed by allowing only autonomous implicitly
programmed mechanisms to be embedded in any artificial organism;
- The role of intrinsic co-evolution between parts of the artificial system, on how it can be
implemented, and on his intrinsic scientific properties for each particular project is well
analysed and understood (Ramos 2012);
- The rules of self-organization are implemented;
- A member of a complex system goes through various virtual design encounters. As the more
one’s past experience differs from the others, the more “individual” its behaviour becomes.
However novelty and unexpectedness are not the only criteria for creativity. What about
designer’s personal uncontainable desire to express his/her experience and intuition? What
about the mental intention to create and innovate? What about the search for inspiration and
actual state of being inspired? I don’t think these aspects can ever be programmed into any
algorithm. At the same time by being excellent at mimicking the results of human creativity
(implemented by analogical methods) or evolve shape based on pre-evaluated knowledge
(used by expert systems and grammars) no computer can qualify to be truly creative.
Actually it really does not matter if computers can or cannot be creative. There is a highly
valuable skill that they can contribute to the design methods, they are able to generate and
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11. recognise configurations that were not obvious or even present to begin with. This property is
called emergence. There are certain projects that demonstrate the computational methods as
an irreplaceable collaborator in the design process. One of them is a project that was a
response to the first tender of the Khalifa-bin-Zayed Al Nehayan Foundation competition. The
Computational Design and Research group divided the brief into three areas of applications:
roof – circle packing and connectivity graph, elevations – barycentre coordinate systems for
mesh population, residential units – polyomino tiling for 3D Tetris with evolutionary optimisation
(Aedas Computational Design and Research group 2013).
The deliberate lack of foreseeing the final cladding, roof and residential patterns resulted from
the design of algorithmic and heuristic search methods:
Figure 1. Roof circle packing based on underlying schedule
Figure 2. Geometrical studies for apartment units
Figure 3. Designs for all facades based on underlying uses
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12. Figure 4.Final design: exploded axonometric projection
Having taken into account everything said above I propose a code that combines Genetic
Algorithm and Self-Organising Maps aiming to suggest another way to give a solution to certain
spatial and morphogenetic architectural problems. The approach to the introduced design
process follows computer-aided “bottom-up” principle to ensure that the evolving system
emerges maintaining the autonomic qualities. The following chapters will describe the proposed
design process in full detail.
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13. Chapter 3. The Concept of the Architectural Problem
3.1 Architectural Scenario
The task of the proposed algorithm is to give a shape to the building according to the
predetermined functional and spatial arrangement of the spaces. It must be achieved in a way
that the required layout remains unchanged and the form emerges from the behaviours
between the agents of the complex system of the building. To simplify the task the evolution of
a single family house was chosen as a base for the project. The house has three functional
areas: living, resting and working.
3.2 Proposed Solution to the Architectural Problem
To find a potential solution or solutions to the problem described above a vast search of all the
solutions called a search space will need to be performed. In order to make the design process
feasible the search space has to be narrowed down by creating a group of random solutions,
measuring their relevance or fitness level against the set criteria, crossing over the fittest ones
in order to generate new, hopefully fitter solutions. Genetic Algorithm (GA) will be responsible
for this part of the code.
However GA has its drawbacks and it minimises the search space too much, resulting in the
problem known as “local optima”. Meaning that the algorithm tends to find an optimal solution in
a small part of a search space and finds it very difficult, in most cases almost impossible to be
able to move on to another part of the space for the search of the possible solutions. In order to
try to handle this challenge alongside with other smaller ones (which will be described later on
in this paper) an Artificial Neural Networks algorithm called Self-Organising Maps is introduced.
It expands the search space by producing possible “in-between” solutions of each generation
and classifies them in topological maps, thus allowing for a bigger diversity of the potential fit
models that are arranged in clusters to choose from.
3.3 Other Ways of Solving Similar Problems
3.3.1. Electrical Graph Approach
Philip Stedman was first to propose applying the principles behind the electrical networks to
guide the computational synthesis of architectural form (March, Steadman 1974). He proposed
to use the similarity between a graph representation of architectural floor plans and the physics
of electricity, as expressed by Kirchhoff’s laws of electrical flow.
The idea behind the conventional graph representation is the use of a network of nodes and
edges, which represent architectural elements and relationships between them:
Steadman expressed horizontal walls as nodes of the graph. Each edge in the graph represents
the relationship between the two horizontal walls of the same room. Each edge is labelled with
the length of the wall and each node has a label that shows the distance between the node and
the bottom-most wall in the floor plan.
13

14. Steadman adapted the graph by applying Kirchhoff’s first law of electrical flow, which states that
electricity flows from a higher voltage node to a lower voltage node, giving the graph
directionality. Applying the second law, which states that the total current entering a node is
equivalent to the current leaving it, permitted Steadman to turn the graph into a floor plan
generator. The method allows generating the process to determine the height of the rooms as
well:
Figure 5. Applying the principles of the electrical networks to guide the computational synthesis
of architectural form.
A different electrical-flow analogy was used by Schwartz to develop his Automated Building
Design (ABD) floor plan generator (Schwatrz, Berry, Shaviv 1994).
3.3.2. Physically Based Modelling
Physically based modelling is a technique that applies the principles of dynamic motion and
geometrical deformations to rigid and non-rigid objects for the purpose of simulating realistic
behaviours and visual effects (Witkin, Baraff 1997). The method was adopted by Arvin and
House for the purpose of generation of floor plans that correspond to a wide range of
constraints (Arvin, House 2002)
They apply the principles of physical notion of mechanical strings to connect spaces. These
strings draw or repel the spaces according to their spatial arrangement and the length of each
string that connects the spaces. The idea of the system is quite simple at its core: as the
masses move further away from each other, the spring tries to move them closer, and as they
approach each other the spring tries to separate them. The motion of the masses is dampened
by producing the forces proportional to their relative velocity along the trajectory of their
movement:
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15. Figure 6. The principles of physical notion of mechanical strings to connect spaces
The essential characteristic of this particular method is that topological design objectives, such
as desired proximity between spaces, are represented as forces that operate on point nodes at
the centres of the spaces. Geometrical objectives, such as the sizes, proportions, alignment or
offset of the spaces, are represented by forces on line nodes. A global “gravity” objective
stimulates spaces to grow together without gaps. The system first resolves the topological
problems until it is in equilibrium:
Figure 7. Resolving the topological problems.
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16. Figure 8. The system works out the geometric objectives
Figure 9. The topological actualisation stage, the spaces are simulated as circles to allow them
to “slide” over each other.
The methods described above provide with a wide range of solutions. However, the methods at
the same time are too deterministic as the boundaries and sizes are well defined from the
beginning. Both algorithms are responsible solely for an adjustment of the possible layouts. The
principle that is proposed in this paper attempts to leave more transparent boundaries between
spaces of a model allowing for better continuity of space and possible future adjustment by the
end user.
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17. Chapter 4. Classic Genetic Algorithm
4.1 Traditional Genetic Algorithm
4.1.1. Brief Description
Genetic Algorithm (GA) has an essence of evolution in its domain: the Darwinian process of
generating a vast amount of random “solutions”, appropriate in terms of fitness between form,
function and context. The solutions that are defined “unfit” are abandoned; the survivors are
copied and modified generating the pool of newly created individuals ready for the next leap of
the same evolutionary process of mating and mutation, until one or more solutions exhibit a
greater degree of “fit”. The fit normally is not absolute and can be controlled by modifying the
number of individuals and generations that adapt them.
Synthetic genetic algorithms closely resemble the natural model of evolution. Artificial
Chromosomes are represented as string structure made of “genes”.
The detailed description of the traditional Genetic Algorithm and its embryogenies are described
in the Appendix 1.
4.1.2. Evolutionary Embryogenies.
Out of the four main types of evolutionary algorithms only GA evolves the computational models
motivated by genotype-phenotype mappings in biological systems. In other words it performs
artificial development, also known as artificial embryogeny. There are three main types: implicit,
explicit and external.
a. Implicit embryogeny.
The growth process is implicitly specified by a set of rules or instructions, similar to a ’recipe’
that govern the growth of a shape.
Examples of implicit criteria:
-
amount of novelty
survival ratio
similarity with the neighbours (for data-mining)
mass customization, or the degree of possible customization of the product
ratio of similarity of FC's components to each other, i.e. if the fitness value of each
component is within a range and/or close to each other
Through emergence during evolution, these implicit embryogenies incorporate all concepts of
conditional iteration, subroutines, and parallel processing which must be manually introduced
into explicit GP embryogenies (Bentley, Kumar 1999).
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18. b. Explicit embryogeny
It specifies each step of the growth process in the form of explicit instructions. In computer
science, an explicit embryogeny can be viewed as a tree containing a single growth instruction
at each node. Typically, the genotype and the embryogeny are combined and both are allowed
to evolve simultaneously. The advantage of using this type is that there no need to design
embryogenies. However, it is difficult to evolve their representations and often specialised
genetic operators are required to ensure disruption is minimised (Koza et al, 1999).
Examples of explicit criteria:
-
intersection of the objects
proximity of the objects
sensitivity to light
c. External embryogeny
It is “hand-designed” and is defined globally and externally to genotypes and a designer retains
higher control over the resulting evolved solutions. It can be manipulated by carefully changing
the design of the embryogeny. Also it produces the fewest harmful effects for evolution, and
require no specialised genetic operators". The biggest drawback of the type is that
embryogenies do not evolve during the evolution of genotypes. The challenge is "to ensure that
this complex mapping process will always perform the desired function" (Koza et al, 1999).
Examples of external criteria:
-
total floor area or volume of the building
height of the building
area of the southern facade (to make it more sustainable)
Ratio of floor area to volume (to make it more sustainable) - proximity of the proportion
of the elements to the golden ratio - etc.
Examples of researches and experiments in the area of artificial embryogenies are explained in
Appendix 2.
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19. 4.2 Classic GA for the Current Architectural Scenario
4.2.1. Description of the Code
The architectural problem described in section 3.1 Architectural Scenario is proposed to be
solved by evolving the predetermined Cellular Automata (CA) model using the conventional GA,
where decoded values of the chromosomes are used to parameterise the original CA model
thus creating the first generation of its variations. Then the parents are chosen for crossover
using the Goldberg Roulette selection method. Offsprings are mutated and replace their
parents, thus creating the new generation. The process repeats for a certain number of loops.
4.2.1.1. Original CA Model and Body-Plan
Cellular Automata (CA) model at this point created randomly. It represents a building with the
three functional areas:
BLUE – working
RED – living
GREEN - resting
Figure 10. Cellular Automata model of one floor.
Figure 11. Cellular Automata model of many floors.
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20. Parameterisation of the body-plan:
Each CA unit is parameterised according to its own state being either "working", or "living" or
"resting". At this point the parameters are purely geometrical and GA genes are programmed to
define the sizes and positions of the units.
Figure 12. CA unit's width and length depending on its state being "working", "living" or
"resting" (3 + 3 genes)
Figure 13. CA unit's position in relation to the unit's original location on the grid and at the same
time keeping the original spatial arrangement provided by the CA model
4.2.1.2. The First Generation
The first generation is created out of the individuals that represent the geometrical variations of
the original CA model:
Figure 14. The first generation of GA individuals
20

21. 4.2.1.3. The Fitness Function
The Fitness Criteria is still very simple and aimed to maintain the spatial arrangement of the
units of the original CA model:
- Intersecting volumes are kept to minimum (fig.14);
- The distances between non-edge unit and its Moore neighbours kept to minimum (Fig.16 a,b);
- Non-edge unit and its Moore neighbours should intersect;
- The proportion of the width and the length of each unit should be close to the Golden Ratio
(Fig. 15);
- The “Living” area must be bigger than “Working”, and “Working” – bigger than “Resting”.
Figure 15. Intersecting volumes
Figure 16(a).
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22. Figure 16(b).
Figure 17. The Golden Ratio programmed into the Fitness Function
22

23. 4.2.1.4. The Process of Selection
Selection method applied is Goldberg's Roulette Wheel, or pie chart (Mitchell 1998). The
principle is that the fittest individual has more chances to be chosen as a parent, compared to
the individual with the smaller fitness value:
Figure 18. The principle behind the Goldberg Wheel selection method.
4.2.1.5. Crossover and Mutation
Mutation Rate was set to be 0.5, meaning that an individual has 50/50 chance to be
mutated. The mutation rate is relatively high, just to make sure that the algorithm does work
and evolves fitter individuals over the generations and also to gives better diversity to the
phenotypes.
Crossover Rate: 1.0, meaning that every single couple of chosen parents is crossed-over.
Crossover Type: One Point, where a single crossover point on both parents' organism strings is
selected. All data beyond that point in either organism string is swapped between the two
parent organisms. The resulting organisms are the children:
Both general processes of mutation and a one point crossover were explained in detail in the
section 4.2.1. A Brief Description of Genetic Algorithm.
4.2.2 Outcome of the Algorithm
10 individuals evolved over 50 generations showing the emergence of the model that maintain a
certain spatial arrangement of the different types of units and keeping them next to each other
with the slight intersection of the masses.
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24. Figure 19. 1st generation (colourful individual is the fittest with the Fitness Factor being 8.4).
Figure 20. 50th generation (colourful individual is the fittest with the Fitness Factor being 9.4).
Figure 21. Example of the fittest model of one level (Fitness Factor of 10.4).
Figure 22. Example of the fittest model of three floors (Fitness Factor of 7.4).
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25. The models can evolve more sophisticated shapes as more creative forms are programmed
into the CA units instead of simple boxes, the search space becomes more structured and the
selection methods improve.
Figure 23. Part of the search space
4.3.3 The Drawbacks of the Algorithm
The most obvious and crucial drawback is algorithm’s lack of produced solution diversity as a
result of a problem known as “local optima” and extremely narrow search space. The others
are:
- the intensification process is not accurate
- genetic drift
- the production of a vast amount of data during an optimization process without actually using
much of it
- high convergence rate
4.3 Examples of GA Applications in Architecture
Genetic Algorithms have been applied to a variety architectural problems, mostly spatial,
structural or performance optimisation and also to floor plan generation. Only recently GAs
started to take on board morphogenetic tasks, however still most of them tend to be a result of
any sort of performance analysis and development. For example, SOM architects programmed
a Genetic Algorithm revealed surprising structurally-efficient shape of the tower - a teardrop:
Figure 24. A teardrop tower by SOM architects
25

26. Another example where GA is used for a shape-optimisation purpose based on analysis of the
lines of principal stress is the TransBay Transit Centre by SOM architects:
Figure 25. Trans Bay Transit Centre by SOM architects.
Not many are working on giving GA’s field of application another dimension: shape evolution
that emerges from the behaviours of other agents of building’s complex system. Among them
are Aedas|R&D and Davis Brody Bond who have designed The National September 11
Memorial Museum in New York. They built a suite of software that allows architects as well as
exhibition designers to simulate the cognitive effect of geometry on visitors as they view and
move through the building. By calculating expanse of views, maps of intuitive orientation are
produced that help designers to understand transitions between spaces where no obvious
delineation exits (Aedas Computational Design and Research group 2013)
Figure 26. The models of movement and volumetric visual perception
26

27. Figure 27. Visibility polyhedra along a visitor's path
Figure 28. Volume of space visible from a single point in the exhibition
Figure 29. Strength and direction of visual field
27

28. Chapter 5. Self-Organising Maps and Genetic Algorithm
5.1 Artificial Neural Networks and Self-Organising Maps
Artificial Neural Networks (ANNs) were first introduced in the 1950s, but only in the mid-1980s
their algorithms have become sophisticated enough for general applications. A self-organizing
map (SOM) (Kohonen 1982) produces a low-dimensional structured representation of the high
dimensional input space of the training samples, called a map. The data is represented by
prototypes, called weight vectors. SOM is trained using unsupervised learning, which means
that no human intervention is needed during the learning and that little needs to be known
about the characteristics of the input data.
An example of a SOM Algorithm Application in 3D Modelling, its applications and other types of
SOM algorithms are described in appendix 3.
5.2. Introducing Self-Organising Maps to the Classic Genetic Algorithm
5.2.1 Why Combining Genetic Algorithm with Self-Organising Maps?
Having decided to engage computational methods of design and implement the process of
emergence during the design process the two main challenges have arisen: how to generate
novel, unique and unexpected forms; and how to distinguish “interesting” and meaningful
shapes once they have emerged.
One of the best ways to tackle the first problems known to date is through a technique known
as genetic programming. A possible solution to the second problem could be to involve artificial
neural networking.
Being the only one of four types of Evolutionary Algorithms, the GA treats genotypes separately
from phenotypes, i.e. maps "from genotypes (evolved parameter values), to phenotypes, (to
problems)." (Bentley, Kumar 1999) This quality on its own gives increased advantages like
"better enumeration of search space, permitting two very differently organised spaces to
coexist" (Bentley 1999). On the other hand, SOM represents the quality similar to the
associative type of memory of the brain. The brain naturally associates one thing with another.
It can access information based on contents rather than on sequential addresses as in the
normal digital computer. The associative, or content-addressable, memory accounts for fast
information retrieval and permits partial or approximate matching (Ramos 2012).
Naturally, Genetic Algorithm reduces the search space. As only highly compact genotypes are
permitted to characterise phenotypes, genotypes have fewer parameters than their
corresponding phenotypes. It results in the reduction of the dimensionality of the search space
(Bentley 1999). I believe that SOM could help to reverse the process of a constantly shrinking
possibilities space, allowing higher parameterisation of the genotypes. However, at the same
time the expansion of the search space creates a challenge of how to manage the massively
expanded choice.
28

29. On the other hand, AG belongs to the class of stochastic methods that find solutions to
problems by examining random parts of the search space. SOM permits the thorough
exploration of well-defined parts of the search space. If essential, more control is gained by
using the artificial selection of the potential parents where the designer hand-picks the
individuals for crossover and mutation.
Moreover, traditional GA generates a large number of solutions rather than a single possible
solution at a time, thus exhibiting a sophisticated quality of operational parallelism. Meaning that
GA has a greater chance to find the meaningful solution, but it has a tendency of getting “stuck”
in a local optimum. SOM attacks this challenge by allowing an in-depth search of the expanded
neighbourhood of solutions similar to the ones that caught the attention of the designer. Also if
there are few potential candidate solutions the whole spectrum of the resulting models that lies
in between them can be assessed as well.
Design cannot be carried out without the visualisation of the potential models. In traditional
methods most of the visualisation happens in the imagination of the designer and only the
selected elements are brought to life by sketching or drawing. SOM in a way becomes that
virtual imagination that structures, classifies and records the broader search space of the
traditional GA and enhances the creative intuition of the designer.
Therefore by combining the two approaches, organising the search space with the help of SelfOrganising Maps algorithm, the design of the possibilities space can be classified thus enabling
better optimisation of the search process, providing with a more advanced visualisation of the
solutions.
5.2.2. Managing the Expanded Choice
As mentioned earlier, the expanded search space is an advantage and a drawback at the same
time. Why it is beneficial, was looked at earlier. The reasons why its size has to be controlled is
described below.
Expanded choice can lead to "...less happiness, less satisfaction and can even lead to
paralysis" (Piasecki, Hanna 2000). A designer can experience the same confusion when faced
with a massive solution space offered by a Genetic Algorithm, even more so when it is
expanded at each generation with the SOM.
Being different to machines, human beings have a very powerful filter of information – their
subconscious, when it comes to making a decision. Subconscious is formed by one's
experience, knowledge and inherited genes. However the verdict in most cases is made by the
conscious mind. When having to make a choice between two fairly equal options, most of us
often feel confused and distressed. I believe that this is due to another characteristic of human
beings - a personal attachment. Luckily computers do not possess personal attachment and a
way around the problem can be worked out.
Now, how do I imitate both the sub-consciousness and the consciousness of human beings in a
program to help the computer to make the right choice even with the helping hand of the
designer? What will the fitness factor consist of? Will there be a fitness factor at all? Or will it be
evolving over the duration of the algorithm?
Keller and Stealin suggested that the results of the decision-making process depend on the
correlation between the quality and quantity of information. If the amount of information
increases whilst maintaining its quality, the efficiency of good decision making will decrease,
and visa versa. This concept is represented in Wundt Curve Representation of the Paradox of
Choice:
29

30. Figure 30. Wundt Curve: Graphic representation of the Paradox of Choice.
Self-Organising Map can represent a multidimensional Wundt curve, where each product
attribute is mapped onto a separate dimension. The shape of the curve will vary in each
dimension going from user to user.
When it comes to architectural design an architect faces certain challenges of being able to
successfully define the meaningful attributes of the design:
- The importance of the parameters varies whilst they all have to be read in conjunction with
each other. It can be represented in the weighed complex fitness criteria
- The end user simply may not know what he/she needs. The idea of co-evolution emerges.
- By nature the architectural design due to its complexity is an "ill-defined problem" or a "wicked
problem", in which potential solutions evolve together with the formulation of the problem itself
(Rittel 1973)
Below is the proposed breakdown of the important factors to consider whilst coding the process
of selecting the right individuals for the crossover based on selected thoughts of Piasecki and
Hanna (2000):
1.
Limit the solution space by choosing the individuals based on evaluation of
their mostessential and meaningful parameters, parameters that the designer wishes to work
with or customise.
2.
Let multiple users to experiment with the population and the algorithm to adjust
thedefining selection criteria for a particular problem.
3.
Create an algorithm that learns from users and creates a model of their
preferencesbased on a definition of meaningful solutions. It can be used later on to narrow
down the solution space. Alternatively, use a selection method based on the recognition of the
remaining meaningful choices based on artificial or "manual" selection. Users are not forced to
explicitly define values of all the parameters available to customize. Instead they express
preferences among a couple of different options.
4.
Implement a Recommender System
Appendix 4 shows Piasecki and Sean's experiment that proves that by using GA in rationalising
the "meaningfulness" of choice the Wundt curve relation of users satisfaction and the scope of
choice doesn't apply.
30

31. 5.2.3. The Evaluation of the Aesthetics
The challenge of managing the expanded choice was tackled suggesting that the user
assesses the essential criteria that determine both performance and aesthetical values of the
emerged models. But how the evaluation of aesthetic qualities can be performed? How can
they be controlled in the bottom-up computer-aided design process?
The formal study of aesthetics dates back at least to the ancient Greeks, who were trying to
establish the connection and analogies between architecture and other forms of art like dance
and music. This is why the principles of rhythm, proportion and symmetry were widely applied in
Greek and Roman architecture. Until now architects, critics, artists, psychologists, and
philosophers are persistently trying to develop the objective methods for evaluating aesthetic
qualities of building or even simple objects. Still their efforts did not result in the establishment
of neither agreed-upon aesthetic “standards” nor methods that will compare the objects or
buildings to such standards. The experimental methods do exist and they are described as
“Habitual” or “Computational” (Kalay 2004). They include an “objective” or mathematical
approach, a “subjective” or perceptual approach, shape grammars, computational
approximation of “acquired taste” and so on.
To establish aesthetic criteria is extremely challenging if not impossible, as the relation of the
design formation and the architect can be seen as a process of co-evolution. One way to define
an aesthetic evaluation is as a translation from the evolving over-all perception image of an
architectural model to an automatic set of mathematical selection rules. In the absence of such
mathematical function the final result will remain an exploration of some random sub-spaces of
possible and hypothetical novel solutions. Alternatively, however, the objective and analytical
evaluation of any final design could be misleading if those aesthetical fitness functions were
implemented, mapping genotypes into the “usefulness” of the hypothetical novel forms.
Probably this is mostly because this aesthetical “mapping” uses a compression method, where
the diversity of any multidimensional conceptual world of the design reduced and represented
by its only few aspects. Luis Borges words on these matters are wise: the only true map of the
world is the world itself.
There is however one way to avoid those mathematical mappings. That is of using the human
observer or “artist”, as an “aesthetical mapping machine”, connected in real-time to the artificial
evolutionary process. (Ramos 2012). In other words, the human being selects the images which
are aesthetically pleasing, or otherwise interesting, and these are used to breed the next
generation. For the first time the idea was introduced in 1991 by Karl Sims, where the
computer-graphics program called Primordial Dance uses genetic algorithms to generate new
images, or patterns, from pre-existing images(Sims 1991):
Figure 31. Images evolved during the Primordial Dance uses genetic algorithms.
31

32. 5.3. The Evolution of the Proposed Code
5.3.1. Stage 1.Classic GA for the Current Architectural Scenario
The algorithm was described in the section 4.3. Classic GA for the Current Architectural
Scenario.
5.3.2. Stage 2. Adding Golden Ratio to the Fitness Criteria
An arguable aesthetic factor was added to the model's existing Fitness Criteria. The idea was to
encourage the proportions of the width and length of the boxes to be close to Golden Ratio
number 1.618, whilst maintaining the spatial arrangement of the units of the original CA model.
Observations and Conclusion:
The more factors are added to the Fitness Factor the more problematic becomes the problem of
local optima. The algorithm has a tendency to stick to one or two fitness criteria and evolve
them, compensating with their very high ratio the low level fitness of the other criterias, like in
the example shown below. The units' proportions became very close to the ratio of 1.618 thus
achieving very high fitness factor. However the intersection and proximity to each other
requirements are far from being met.
Example of the evolved model with very high total fitness factor that gets its value mostly from
meeting the criteria of the proximity to Golden Ratio, leaving the other fitness factor constituents
un-evolved:
Figure 32. A model with a high fitness value assessed on meeting the Golden Ratio criteria
32

33. The emerging properties of the resulting models of the algorithm were not consistent as the
fitness function was confusing the process of evolution. To attempt to solve the problem the
following code adjustments could be implemented:
to introduce the process of expanding and structuring the search space with the
SelfOrganising Maps. Alternatively
to ensure that only that model is allowed to become a parent if each component of the
fitness criteria is above the certain acceptable level;
to create an elimination criteria. It can also be getting stricter with each generation thus
still encouraging evolution however at the same time promoting diversity and avoiding the
problem of local optima.
Nevertheless the algorithm did work and produced some good results. For example, below is
the comparison of the best individual of the 1st generation and the best individual of the 250th
generation.
Figure 33. The best individual of the 1st generation
Figure 34. The best individual of the 250th generation:
33

34. 5.3.3. Stage 3. Introducing Self-Organising Maps to the Genetic Algorithm
Each Self-Organising Map trains its neurons to become a close match to every individual of
each generation that represent “inputs” of the neural map. The neurons highlighted in RED are
the best match of an individual of the generation or “winners”. The fitness of the neurons within
the map at this stage was not checked therefore they couldn’t become parents yet and fuel the
evolution.
Figure 35. SOM expanding each generation of GA.
34

35. 5.3.4. Stage 4. Turning Chromosomes into Neurons and Back
In order for neurons to participate in the selection process, chromosomes and neurons have to
be compatible in their parameterisation as they represent two classes in the algorithm. One that
produces and works with GA individuals and their chromosomes, and another with SOM
neurons.
At the stage when SOM inputs are generated every individual from the current generations has
to serve as an input neuron. To do that, chromosomes and their values have to be encoded into
the vectors of corresponding neurons. As the chromosome coding and neuron’s vector
parameterisation are exactly the same, their fitness assessment can be performed with the
same function. However, later on, after the SOM is trained and the parents have to be selected,
neurons have to pass their coded vectors’ values to form chromosomes for crossover. In order
to achieve this the resulting vectors of the trained neurons have to be encoded to represent the
binary string of the chromosome.
Turning GA individual into a neuron of SOM
In a standard GA algorithm a decode function does the following. It takes a chromosome list
that contains zeroes and ones. Then it decodes it and turns it into the list of corresponding to
each gene values (please see section 3.2 .Traditional Genetic Algorithm: a Brief Description).
These values are assigned to their corresponding neurons’ vectors.
Turning neuron back to GA individual
In order to SOM neurons have generated lists of values and a "reverse decoding" had to be
performed in order to be able to have chromosome lists ready for crossover and mutation of the
individuals. In other words the task was to create a chromosome list like this:
From values list like that:
Also all neurons' values are decimal numbers (as they were trained by artificial neural networks)
so the values have to be rounded up to the closest even number and not bigger than the max
decode value for the defined gene length
Now neurons have all the information necessary for crossover and they now can become
parents.
35

36. Colour-coding of the models:
PURPLE - individuals of Genetic Algorithm generations
BLACK - Self-Organising Map trained on each
generation RED - the SOM "winners" or a model that is
the closest match to the individuals in their generation.
GREEN - the fittest models among each GA generation
and neurons of SOM.
The Fitness Criteria is unchanged
The Selection Process is carried out among the
individuals of the particular generation and its
corresponding Self-Organising Map using Goldberg's
Roulette Wheel method
Mutation rate 0.2
Crossover: One Point type with 1.0 rate. Siblings replace
random individuals of the current GA generation thus
becoming the population of the next generation.
Self-Organising Maps & their values: Winner learning
strength is 0.98; others learning strength is 0.95;
convergence rate is 0.3.
Figure 36. The example of the resulting evolution of the
SOM-expanded generations.
36

37. Figure 37. Example of the first generation and its Self-Organising Map
Observations:
- All the fittest models are within SOM
- With the evolution there are less winners as the training individuals from the later generations
are getting more and more identical to each other. Therefore one "winner" can be a match to a
few individuals of the GA;
- By the 7th generation the algorithm got stuck on its local optima. The population of each
generation should be refreshed each time by replacing the old individuals with the neurons of
high fitness. Alternatively an age criteria could be incorporated into the fitness value. However
on the other hand, it will not yield good results as complicating fitness criteria leads to losing
some values and concentrating on others. It can be fixed however by introducing the filter that
determines the individuals with equal proportions of fitness criteria components as mentioned
earlier;
- There is a linear correlation between the fitness values of the neurons and their location within
the map if fitness criteria is mostly dependent on the geometry of a model.
37

38. Conclusion:
- Manage the expanded choice by introducing the elimination criteria;
- Introduce the threshold for Fitness Factor components;
- Artificial Selection;
- The population of each generation could be refreshed each time by replacing the old
individuals with the neurons of high fitness
5.3.5. Stage 5. Co-evolving Threshold of the Fitness Factor Components
In order to gain some fitness an individual (or a neuron) must have the components of the
fitness factor defined accepted level. If one of the Fitness Factor constituents is below the
defined threshold, its total fitness is written down to zero. This is introduced for two reasons.
Firstly, so individuals evolve their fitness evenly across all its components. The individuals
whose fitness is zero are not participating in the selection process at all. Secondly, to manage
the problem of expanded choice and structure the search space by narrowing it down and
eliminating the individuals that are not fit across all the components of the fitness factor. Also
the computational time is saved as the neurons with fitness zero, do not go through the
laborious process of encoding their values to binary chromosome code.
Figure 38. Extract from the code: assessing the fitness value
However if the population is too small the chance to have fitness value of zero is bigger and no
crossover can happen. If all individuals are of fitness zero, the algorithm communicates this and
suggests setting up more individuals in the next run.
Much fitter individuals started to appear straight away in the next generation. However the
evolution speed slows down. To keep it up, a co-evolving threshold can be introduced, i.e. the
defined level will be getting higher and higher depending on the growth of the Fitness Factor
components of each individual. In this case, to keep it simple for the sake of the experiment,
each component fitness factor increases by 5% with each generation.
Co-evolving fitness components threshold and composing the next generation from the siblings
after the crossover processes resulted in a surprisingly slow fitness criteria increase. However
the algorithm gave back something much more valuable: from the second generation onward
almost 90% of neurons were over the fitness components threshold structured in a clustering
manner. At the same time the variety was very poor. The algorithm was behaving very similar
to the classic GA - tending to get stuck on the local optima.
38

39. Observations and Conclusions:
-
At this stage filtering out the population with the elimination criteria and applying
artificial selection a designer has a great choice of good quality models, but of poor
diversity. To increase it a Fitness Factor has to contain non-geometrical criteria;
-
as the algorithm structures the search space and only concentrates on the individuals
with higher fitness, the Goldberg's Roulette or even artificial selection was not a very
logical choice. A totally random pick of parents from the group of already selected
individuals could be perfectly adequate, as the selection is already programmed into
the fitness threshold. The problem with Goldbergs Roulette is that it tends to select the
fittest individuals thus creating a perfect environment for the future local optima. By
randomly selecting parents from the cloud of the fit candidates hopefully the results can
be more diverse especially restructured by SelfOrganising Maps;
-
the problem of limited variety of the models' geometry is down to the facts that the
fitness factor is composed of 100% external criteria;
-
by changing the learning factor from 0.3 to 0.5 (the lower the factor the closer neuron's
parameters will be to the individual it is trying to match), bigger diversity was noticed
among neurons and resulting in a very aggressive fitness increase;
-
keeping the learning factor at 0.5, the mutation process was eliminated. Much more
structured space, slightly faster fitness evolution;
-
not many generations the population needs to be evolved over in comparison with the
classc GA;
even if all the individuals in the generation have fitness of zero, a map can produce
couple of neurons with some sort of fitness. It is like driving a car using only clutch;
-
the fitness grows so fast from generation to generation even with the co-evolving
fitness threshold that it is necessary to introduce a fitness assessment function to
determine the reasonable threshold level for each generation;
-
this algorithm gains its effectiveness with the larger populations and neural maps, that
takes a lot of the computational power and time.
5.3.6. Stage 6. Optional Selection Method
As the selection of individuals is already programmed into fitness, the assumption is that there
is no point to even use Goldberg Roulette as a selection method. A random coupling can be
performed and their off-springs can compose the next generation. The experiments showed
that if there are more couples than the number of individuals in each generation and the fitness
threshold is not set very high, than the evolution dies out. At best the fitness remains exactly
the same throughout generations, without even giving much of form diversity. That is due to a
vast variety of certain level fitness values, so it fluctuates from generation to generation without
steadily going up.
39

40. As a solution, off-springs of all couples can compose the next generation and therefore
increase the size of the neural map, so its efficiency is not lost. Coincidentally the phenomenon
of the ever changing size of the population of each generation is very similar to what occurs in
nature. The size of population depends on so many factors and luck itself and is never
constant. The drawback of this method can be excessively large size of the population and their
corresponding maps. To control the situation the fitness threshold must be evaluated properly
and adjusted to represent only the appropriate range for the selection purposes. Only the
parents with the right characteristics should participate in creation of the next generation.
Figure 39. SOM participates in crossover function. The dark and light orange coloured
individuals represent the parents of the next generation.
As a result, the potential parents were filtered leaving only those with the fitness of greater than
half of the best one of the current map. It was done in order to minimise the size of the further
generations and their neural self-organising maps. So the algorithm evolves the fitter
generation from the expanded search space extremely fast. However, the biggest drawback is
that it has to run many times before it can create the first generation where the components of
the fitness criteria are at the right balance. If it doesn't happen then the code just terminates
with the message informing that the fitness of all individuals is of zero value. In a way it is not a
bad thing as it stops the user from wasting a lot of computational time and evolving the wrong
generations. However, even though the algorithm works perfectly well, something can be done
in order to produce a more appropriate first generation as at the moment it is created randomly.
Alternatively, the fitness components threshold can be more intelligent and be set depending on
the fitness values of each component of the current generation. The second option is more
realistic to program. The same goal was achieved by simply lowering the Fitness Components
Threshold and increasing the minimum fitness level for the parents’ selection. Also the
maximum size for the neural maps was set to keep the computing time to realistic limits as
sometimes the map can be so large that it concentrates too long on one generation without any
benefit for the evolution process.
40

41. The resulting maps showed well-defined clustering (due to the fitness factor being geometry
dependent), displaying the concentration of the fittest models on the maps:
Figure 40. Clustering of potential parents.
41

42. 5.4. The Final Algorithm
5.4.1. The Structure of the Algorithm
The algorithm is described in the stages of its performance.
5.4.1.1. Original CA Model and Body-Plan
The initial part of this stage remains unchanged and is described in the section 4.2.1.1. Original
CA Model and Body-Plan. An example of the possible architectural application and
parameterisation of the body-plan is described below.
Once the parameterised CA volumes are built the morphogenetic process of the final
architectural model begins. Firstly the centroids of the edge boxes are located. Then the
centroid of the area between the points is determined.
Figure 41. Locating the centre point between the centroids of all edge CA units
42

43. After that the ellipse is drawn from the centroid of each CA unit as shown on the
Figure. 42 and then its extruded (Fig. 43).
Figure 42. Creating ellipses.
Figure 43. Extruding ellipses.
43

44. Both top and bottom ellipse of each unit is divided into equal amount of segments. The division
points are shown of Fig. 44.
Figure 44. New shape of the CA units and their division points.
Figure 45. Double loft surfaces going through the division points.
44

45. Figure 46. Surfaces of the new model with the bridges between the units
Figure 47. Top view of the model
45

46. All similar types of units are connected with each other by a bridge-platform, providing the
connectivity between the functional zones.
Figure 48. Colour-coded connection bridges between the similar units on each floor.
46

47. Figure 49. Perspectives of the model
47

48. Figure 50. The bridges viewed from the interior of the towers
The alternative models that can be programed into the proposed algorithm are shown in
Appendix 8
The task of this stage is to find the ways to parameterise the defined functional zones so they
can be moulded together in one connected space and let the user choose the method.
Alternatively, mould the spatially allocated masses together by combining all the objects with
different sets of parameters to form one (with the sum of the characteristics of all the separate
parts). Parameters do not necessarily need to represent geometry. Qualities can be both
extensive and intensive.
A different initial model can be chosen for development. For example, a spatial layout as a
result of an automated space planning by Computational Design group at Aedas R could be
used. The concept behind this planning is that the accommodation schedule is loaded, and its
components try to arrange themselves automatically according to an adjacency matrix (Aedas
Computational Design and Research group 2013):
Figure 51. Abu Dhabi Education Council: accommodation schedule
48

49. Figure 52. Abu Dhabi Education Council: massing derived from layout application
Figure 53. Abu Dhabi Education Council: Design principles
49

50. 5.4.1.2. The First Generation
The first generation is composed from the “fit” models hand-picked by the designer from the
number of random “fit” models generated by the algorithm. Each of them is given a unique
colour that will be evolving together with the form of the models. The first generation is created
out of the individuals that represent the geometrical variations of the original CA model. Each
CA unit is parameterised according to its own state being either "working", or "living" or "resting"
and located within chromosome-defined distance from the CA’s origin of each unit:
Figure 54. The first generation hand-picked by the designer.
5.4.1.3. Introducing Self-Organising Maps
The detailed process is described in the section 5.3.4. Stage 4. Introducing Self-Organising
Maps to the Genetic Algorithm
Clustering of the neural map is performed based on the proximity of each neuron to the
winners. Each neuron chooses the closest one and assigns itself to become a part of that
winner’s cluster. At the same time each list of the cluster's individuals contains the
corresponding original individual from the current population. For visualisation purposes each
individual has its own colour and the same colour has individual's best match on the neural
map. Every neuron on the map changes its colour to match the colour of the closest input or
teaching neuron (marked with the circle around it). This way the self-organising map displays
colour-coded clusters:
Figure 55. Colour-coded clusters of the map classifying it according to the similarity of neurons
to each input (or individual of the current generation).
50

51. 5.4.1.4. The Fitness Function
One of the biggest challenges in evolving the optimal design solution with multi-objective criteria
is to balance out the fitness criteria components or overall performance of the solution. The
goal is to overcome the problem when a design proposal excels with regard to some
performance objectives and yet prove insufficient on others. In order to achieve that one of the
most crucial principles of the current algorithm is the condition to assign a sum of all
components to the total fitness of the individual only if a value of each fitness constitute is
above its minimum corresponding threshold level.
The initial fitness constituents were described in the chapter 4.2 Classic GA for the Current
Architectural Scenario, section 4.2.1.3. The Fitness Function. Additional two fitness
components are added:
-
Minimising the total intersection area of the elliptical slabs of the new architectural
model (Fig. 56);
Minimising the length of the centroid curve of the model (Fig. 57 a, b, c).
Figure 56. Intersection areas of the elliptical slabs.
51

52. Figure 57(a). Middle point of all the edge units’ centroids.
Figure 57(b). Centroid curves of the models
Figure 57(c). Centroid curves of various length
52

53. Composition of Fitness Criteria
At this stage the proposed algorithm assumes that all Fitness criteria components are equally
important. However, fitness constituents can be programmed to have their own weightings
within the total fitness value, thus mathematically assigning their importance in the overall
fitness assessment, if after the process of the evaluation it is clear that all design objectives
cannot be equally satisfied. This ensures that GA will not evolve an individual with a high total
fitness value that is represented only by one or two fitness criteria constituent and at the same
time it naturally narrows down SOM-expanded search space. Furthermore, depending on the
selection method a fit neuron is selected from each cluster for crossover and mutation in order
to keep the diversity rate high.
Figure 58. Composition of Fitness Criteria
Fitness Function Explained Mathematically:
max(TFabc) = max(Fa) + max(Fb) + max(Fc); max(TFabc) is the maximum value of total
fitness, where max(Fa), max(Fb), max(Fc) are the maximum possible values of constituents Fa,
Fb, Fc of the actual total fitness TFabc; max(Fa), max(Fb), max(Fc) are calculated at the
beginning of the algorithm;
max(TF) = 100 is a preassigned new maximum total fitness value of 100 so the actual value will
be mapped to have a value between 0 and 100;
β = max(TF)/max(TFabc) = 100/max(TFabc), where β is the mapping index;
TFabc = Fa + Fb + Fc is actual total fitness, where Fa, Fb, Fc are the constituents of the actual
total fitness;
Fthr = 20% is the fitness threshold that represents the minimum value all of the fitness
constituents must have in order for an individual to qualify as a candidate to become a parent; if
any of the fitness components is less that this threshold, then the total fitness of that individual
automatically goes to zero;
Actual min value of the fitness component a: min(Fta) = Fthr * max(Fa)
If Fa > min(Fta) then the value of the fitness constituent a is mapped to be within the range
between 0 and 100: Fa acquires the value of (Fa * β) the new total fitness value will be: TF
= Fa + Fb + Fc and its maximum value will be 1:
53

54. Fitness Topography
As it was mentioned earlier due to the pure geometrical fitness criteria, the fitness values of the
maps and GA individuals are arranged in clusters throughout generations. The Surfaces below
represent the Fitness Topography of the entire evolved population over the generations. This
visualisation is useful for analysis of the performance of each neuron, their maps and datamining. The cooler the colour, the higher the fitness value.
Figure 59. Example 1: The Fitness Topography Surface of the population evolved over six
SOM-expanded generations (a)
54

55. Figure 60. Example 1: The Fitness Topography Surface of the population evolved over six
SOM-expanded generations (b)
Figure 61. Example 1: The Fitness Topography Surface of the best individuals of each SOMexpanded generation
55

56. Figure 62. Example 2: The Fitness Topography Surface of the population evolved over six
SOM-expanded generations (a)
56

57. Figure 63. Example 2: The Fitness Topography Surface of the population evolved over six
SOM-expanded generations (b)
Figure 64. Example 2: The Fitness Topography Surface of the population evolved over six
SOM-expanded generations (c)
57

58. Figure 65. Example 2: The Fitness Topography Surface of the best individuals of each SOMexpanded generation
58

59. 5.4.1.5. Selection Options
5.4.1.5.1. The Final Decision-Making Rules
-
Provide the user with the minimum parameters, only with those that they wish to work
with or customise;
-
Define multiple constraints. Define a separate very simple multiple fitness criteria that
consists of pure functional values that increase feasibility of the building (min/max floor
area, min/max height, structural capacity, etc). Eliminate the least fittest individuals of
each benchmark from the current SOM-expanded generation instead of classic "choose
the fittest". This will stop the algorithm from taking into account the attractive features of
non-suitable individuals during the next few steps;
-
Offer simple visualisation of each architectural solution thus enabling user to access it
quickly and efficiently;
-
Artificial selection of the individuals for the cross-over. The individuals can be assessed
in pairs to increase efficiency of choice and promote the intuitive choice of "good
enough" individuals instead of looking for the optimal ones (Schwartz, B. 2004). This
step can be repeated a few times in order to narrow down the parents to a desirable
number of potential parents;
-
Choose when to choose parents for crossover. Sometimes only mutation needs to be
applied. The choice can be left for a Recommender System to find the patterns (not
part of this thesis);
-
Regardless the chosen selection method the first selection process is performed on the
background during the stage of the fitness assessment. The total fitness is assigned to
the individual only if a value of each fitness constitute is above its min corresponding
threshold level. Otherwise it is set to zero, thus carrying out the first filtration of the
potential parents;
-
The parents are chosen one from each cluster. However, if there are no fit individuals in
the cluster then a brand new individual is created that has fitness above the average of
that particular cluster. This fulfils three purposes. Firstly, it keeps evolution from dying
out by lowering the number of the individuals as the selection criteria are relatively high.
Secondly, it serves as another more effective variation of mutation function and keeps
the diversity levels up. Thirdly, non-intrusively broadens the relevant search space by
bringing occasional individual of a relatively high fitness.
Even the preferred and the most logical method for handling the expanded choice is Artificial
selection, the other two selection methods are introduced for comparison and proved to perform
equally well if not sometimes better when facing various design objectives.
5.4.1.5.2. Selection Option 1: Optimised Random Selection by Clusters
As the neural map is trained classifying the neurons according to their vector parameterisation
and is dividing the map into clusters, the selection process takes place. The initial selection of
individuals is already programmed into the fitness function. Only those individuals are given
fitness whose fitness constituents are above a certain evolvable threshold.
59

60. After the neural map is trained, of all fit individuals in each cluster only those are qualified to go
through this stage if their total fitness is above the average of all the fit neurons within the
cluster .The cut-off level can be set even higher if the purpose is to speed up the evolution
process.
The following rules are applied to the process of the parents’ selection among the neurons that
are fit enough and have a fitness value above certain threshold over the average cluster fitness:
-
If there are two or more fit enough neurons in the cluster, then two random ones are
selected for the crossover;
If there is only one, then it becomes a parent automatically;
If there are no fit enough neurons, then a brand new fit enough individual is created to
become a parent (Fig. 66 on the next page).
This selection method is used when the designer is more confident with the programmed fitness
evaluation rules and wishes to give more control to the machine which is programmed to look
for a potential parent in the certain area of each cluster.
5.4.1.5.3. Selection Option 2: Artificial Selection by Clusters and the
Evaluation of Aesthetics
The proposed selection method gives power to a designer’s experience and intuition in order to
evaluate the aesthetics of the evolving model when the artificial selection method is chosen. At
the same time designer influences the aesthetics by programming low level implicit rules into
the code. Also it helps to avoid the local optima problem.
The individuals are assessed in pairs going from cluster to cluster in order to increase efficiency
of choice and promote the intuitive choice of "good enough" individuals instead of looking for
the optimal ones (Schwartz, B. 2004). This step must be repeated a few times in order to
narrow down the parents to a desirable number of potential parents. The structure of the
algorithm allows the designer to choose a different number of parents for crossover at each
generation. Also at this stage the crossover rate controls which parents to mate, not the
designer. An option for the user to choose which individuals to carry on to the next generation
and which to pair could be suggested as a possible variation to the code.
The following rules are applied to the process of the parents’ selection among the neurons that
are fit enough and have a fitness value above certain threshold over the average cluster fitness:
-
If there are two or more fit enough neurons in the cluster, then the designer chooses
two among them for the crossover;
If there is only one, then it becomes a parent automatically;
If there are no fit enough neurons, then a brand new fit enough individual is created to
become a parent (Fig. 66 on the next page).
The Artificial Selection method can be used when the priorities are the aesthetical qualities of
the model or/and the architect feels essential to personally carry out the assessment of the
offered solutions by him/herself and needs to put his/her hands directly into the design process.
60

61. Figure 66. SOM, its clusters and the selection principle
61

62. 5.4.1.5.4. Selection Option 3: Goldberg Roulette
The mechanics of this selection method were described in the chapter 4.2 Classic GA for the
Current Architectural Scenario, section 4.2.1.4. The Process of Selection.
It was introduced in the proposed algorithm as a comparison to more deterministic methods
described above. Even being the simplest and the closest to a natural selection process it has
its drawbacks. It may lead to biased selection towards high fitness individuals. It can also
possibly miss the best individuals of a population. There is no guarantee that good individuals
will find their way into the next generation.
5.4.1.6. Crossover
Depending on the chosen selection method a list of parents is generated. Then the couples are
formed randomly from the individuals on that list. The same type of one point crossover is
applied. The unique quality of this algorithm is that the size of each generation and therefore
their corresponding neural maps can change, depending on the number of the parents chosen
during the selection stage. It helps to maintain the diversity at the early stages of the design
process. However if the point where the small solution space is defined as relevant and optimal,
then the number of individuals can go down allowing thorough investigation of this particular
area of the search space.
5.4.1.7. Mutation
The mutation rate can be changed depending on the level of the genetic diversity that needs to
be maintained. However if a new individual is created for any of the clusters because there
were no fit ones then mutation doesn’t apply. Mutation as a genetic operator was described
more in detail in the section 4.2.1. Brief Description of Genetic Algorithm.
5.4.1.8. The Following Generations
All chosen parents are mated and the siblings compose the next generation. The same process
performed again for a certain number of generations or until the individual/s with the adequate
characteristics has/have evolved.
5.4.1.9. Visualisation of the Search Space by Clustering and the Evolution
of Colour
The illustration below shows the neural maps in clusters. The colour of each cluster represents
the colour of the corresponding training individual of the current generation. Each neuron
acquires the colour of the closest to it winner (a neuron closest to the training individual of the
current generation). When the parents are chosen their off-springs inherit their averages of R
and G colour indexes spliced in a randomly chosen proportion. B is constant for all individuals
and their off-springs to keep the colours readable. Therefore the colour of the clusters evolves
with generations in parallel with the shape of the models:
62

63. Figure 67. The example of the population evolved over three generations.
63

64. Figure 68. The example of the population with the example of the developed body-plan evolved
over two generations.
Figure 69. The perspective of the same population.
64

65. So far, neurons' vector parameters were 100% geometrical. That gives the map a very welldefined visual clustering. As more implicit types of parameters are programmed into the vector
(or chromosome values) and also into the Fitness Factor, the more diverse will be the
appearance of the search space.
5.4.2. Main Results and Observations
As the algorithm finishes running it produces the summary of the data of each generation
(Fig.__)
Figure 70. The example of the algorithm’s report
The key observations over the process of the algorithm development:
- The evolution of the model is recorded for further reflection as the fittest solution does not
always mean the most appropriate in both functional and aesthetical sense;
- By changing the neural learning factor from 0.3 to 0.5 (the lower the factor the closer neuron's
parameters are to the individual it is trying to match), bigger diversity was noticed among
neurons resulting in a rapid fitness increase and much more structured space;
- Even if all the individuals in the generation have fitness of zero, a map can produce couple of
neurons with some sort of fitness. It is like driving a car using only the clutch.
- By changing the converge rate, “winners” and “non-winners” learning strength the designer
can control which part of the GA's search space will be explored next
- In order to avoid the local optima problem, the best solutions are the artificial selection and
introduction of other non-geometrical fitness criteria components. The relationship between
the units of each model must understood as a notion of “sympathy” and be reflected in the
way they are acquiring their form;
- The majority of the fittest models are located on the neural map;
- With the evolution there are less winners as the training individuals from the later generations
are getting more and more identical to each other. Therefore one "winner" can be a match to a
few individuals of the GA;
- There is a linear correlation between the fitness values of the neurons and their location within
the map if the fitness criteria is mostly dependent on the geometry of a model.
65

66. 5.5. Advantages and Disadvantages of GA-SOM
5.5.1. Advantages
As more and more complicated design tasks are being set in front of the computers, it is
essential to take care of the "representation of the solutions", otherwise the increase in
complexity of the genetic algorithms can cause certain problems such as "disruption of
inheritance and premature convergence to local minima often preventing the generation of fit
solutions altogether" (Bentley & Kumar 1999).
Conventionally architects use sketching technique known as “thinking with diagrams” - a
process where the designer “lets his/her hand do the thinking” (Akin 1978). Sketching is
performed with the context of a specific problem in mind, when the solution to it is not fixed to
begin with. Rather, it emerges as the process unfolds (Habraken 1985). It has been argued that
this process of the emergence of form and the meaning behind it from a representation is the
essence of creative design. SOM provides the designer with such visual feedback of the
possible solutions and a reinforcing system to recognise and understand the possibilities and
implications of the evolving design.
The explored search space of the Genetic Algorithm is mapped only according to the fitness
criteria. The biggest advantage of SOM-GA algorithm is that its search space is also mapped
based on the results of the evolution of the neurons’ vectors or individuals’ chromosomes. The
design process is led towards that part of the possibilities space where the combination of
model’s programmed parameters and fitness are found to be appropriate.
The other ways in which SOM benefits to the current algorithm:
-
Re-structures and expands the possibilities space;
-
Better performance at generating unexpected solutions and thus potentially being able
to compete with human creativity;
-
Introduces clustering property to the search space of GA, a characteristic that is a
direct consequence of the data visualization- and exploration capabilities of the
topographic map - ability to evaluate the solutions in non-procedural ways;
-
Tot as many generations the population needs to be evolved over in comparison with
the classic GA;
-
SOM classifies the search space in order to make the essential choice of regions of the
space should be explored next;
-
Out of all known algorithms only SOM handles the challenge of working with the
models of
Large dimensionality. GA individuals are parameterised following the similar principle
as the neurons in SOM, making GA and SOM compatible;
-
-
Minimises many drawbacks of the traditional GAs, such as inaccuracy of the
intensification process, genetic drift, production of vast amount of the data during an
optimization process without actually using much of it, high convergence rate, limited
diversity, and problem of "local optima", helps to broaden and amplify the synthetic
intuition of the designer.
66

67. Main characteristics of SOM that are automatically are passed to GA search space that uses
neural maps to expand each generation:
- Unsupervised learning algorithm that reduces the dimensionality of a certain number of units
(Kohonen, 1997);
- The map is able to maintain the topology of a data space by using the neighbourhood
function, thus creating clusters of units that correspond to similar data patterns;
- The uniqueness of SOM is in its ability to handle the problems of large dimensionality;
- Processes information as patterns, rather than executing explicit instructions one at a time
exhibiting the properties of parallelism and pattern recognition;
- Generalisation capability meaning that the network can recognize or characterize inputs it has
never encountered before. A new input is assimilated with the map unit it is mapped to.
5.5.2. Disadvantages
The main disadvantages of the proposed algorithm, excluding the typical ones for each GA and
SOM:
- The algorithm gains its full effectiveness with the larger populations and neural maps, that
takes a lot of the computational power and time;
- there are too many combined factors between GA and SOM (like fitness factor, mutation rate,
selection rate, convergence rate, winner strength, etc.) that proves it very challenging to find
the right equilibrium between them for each design problem;
- The problem of the expanded choice and evaluation of the aesthetics of the models;
5.5.3 Examples of other SOM-GA algorithms and their applications
-
Appendix 5: First ever Self-Organising Maps for Muliti-Objective Evolutionary Algorithm
(SOM-MOEA) by Buche et. al. in 2002
-
Appendix 6: Brudaru's Cellular Genetic Algorithm With Communicating Grids and SOM
-
Appendix 7: Kita's real-coded genetic algorithm (RCGA) and SOM
67

68. 5.6. Further Research and Algorithm Development
The proposed algorithm and the associated research so far were only concentrated on the
SOM/GA part of the potential final code. The chapters below show the other areas of
exploration that could turn the current algorithm into a very productive architectural design tool.
5.6.1. Parameterisation of the Body-Plan
Using the main advantage of using machine in the design process is being able to explore
various parameterisation strategies of the body-plan for shape finding purposes.
While D’Arcy Thompson proposed the idea that natural form may be better understood through
biological process, Christopher Alexander has taken the concept of morphogenesis further,
formulating the principles and applying it to all kinds of natural phenomena. He proposed three
natural processes of form-making. The first one is “smooth unfolding” in nature, the second is
“structure-preserving transformation” and the third is “formation of centers and fields of centers”
(Alexander 2002). Alexander’s work could inspire few different ways of evolving the form that
could be programmed into the proposed algorithm.
Other various form-finding methods can be tested, like for example grammars, expert systems,
case-based methods, mechanical or electrical metaphors, recipe like instructions, attempts to
draw inspiration from divine sources, “rational” methods, “formalistic” methods, and of course
simple trial-and-error methods.
For example, Aedas R&D, developed a concept design for the Taiwan Tower in Gateway Park
of Taichung City in Taiwan (Aedas Computational Design and Research group 2013). The
tower’s shape derived from the form that emerges when a falling object hits the surface of
water. The scheme’s plan takes the geometry of the new Gateway Park and forms a series of
ripples that weave the tower into it surroundings, forming terraces, bridges and the main
structure of the tower itself:
Figure 71. Taiwan Tower: Close-up of the parametric 3D model for the general form, structural
ribbons and walkways
68

69. Figure 72. Taiwan Tower: Site plan with the scheme’s concentric guide arc
Figure 73. Taiwan Tower: Elevation the parametric 3D model for the general form, structural
ribbons and walkways
69

70. 5.6.2. Swarms and SOM Pattern Recognition
Various examples of swarms in nature demonstrate how certain perceptive capabilities can
emerge and evolve from the interaction of many simple local rules. These can be studied and
adapted to become the algorithm’s pattern recognition system/s.
5.6.3. Discovering the Potential of Clusters
The Neural Maps' clusters and their properties can be explored further in order to optimise GA
selection methods.
For example a set of several neural maps can be created for each generation. Each of the
maps can classify the neurons according to different external, explicit or implicit criteria that not
even necessarily were programmed into the fitness function. Thus the designer has better
understanding of the search space that is structured according to different parameters.
The proposed algorithm can also be used in a slightly different context, where clustering of the
search space can be used more efficiently. The large pool of individuals is generated. The ones
are chosen for neural training that possess a high value of only one part of the fitness criteria or
extreme end of one of its parameters. For example, if the fitness criteria consists of four
components or all individuals have four parameters, than four individuals with sharply
distinguished single characteristics are chosen as inputs for the self-organising map. After the
map is trained it presents clusters of neurons categorised by the presence of a single
welldefined parameter or fitness component. The search space is better structured this way and
the process of selection of the parents becomes more systemised and visualised.
The data-mining process can be used that recognises different clusters the SOM and figures
out the suitable candidate to become a parent. This way the SOM-expanded search space of
the GA can be explored, managed and used in evolutionary algorithm even better.
Another principle can be applied to the Optimised Random option. From the remaining
individuals within each cluster choose the neuron that is closest to the winner (or within certain
radius from it) in order to maximise diversity of the parents and consequently the off-springs.
The closer the individuals are to the border between two clusters the more similar phenotype
they have.
Another clustering method application was explored by Aedas R&D as part of Masdar MIST
340. They developed a sketching tool to test variations for one of the concepts for Aedas
Dubai’s proposal. Each apartment type in the area schedule is loaded onto the site and
clustered around a number of cores. The apartments without direct access to a core are raised
onto the next floor. The clustering process is repeated until all the apartments have access
(Aedas Computational Design and Research group 2013).
70

71. Figure 74. Sketch of an apartment within in cluster
Figure 75. Perspective aerial view of the clusters
71

72. Figure 76. Model photograph
5.6.4. Co-Evolution Instead of Fitness Criteria
Benefit of using co-evolution instead of the fixed fitness criteria is that it prevents large portions
of the population become stuck in local optima. The first people to work with co-evolution were
Daniel Hills and Karl SIms.
Daniel Hillis co-evolved sorting networks (Hillis 1991). Also he developed on the algorithm that
co-evolves the artificial parasites. His code works with the two independent gene pools whose
evolution rates are naturally comparable, one representing "prey" and other "parasites". Each of
the populations evolve according to GA's selection /mutation/ recombination sequence. Both
gene pools evolve on the same grid and their interaction is through their fitness functions. The
prey is scored according the failure of parasites at the same grid location. The parasites are
scored based on how well they find flaws in prey's fitness. The fitness functions of the prey and
the parasites are complementary in the sense that a success of one represents a failure of
another and vice versa.
As another example, Karl Sims co-evolved virtual creatures (Sims 1994).
Figure 77.Creatures evolved for walking.

73. Amiina Bakunowicz 2013 | 27
Figure 78.Creatures evolved for jumping.
Sims presents a system for evolving virtual creatures and each creature is tested for their ability
to perform a given task, such the ability to swim in a simulated water environment. Those that
are most successful survive, and their virtual genes containing coded instructions for their
growth, are copied, combined, and mutated to make offspring for a new population. The new
creatures are again tested, and some may be improvements on their parents. As this cycle of
variation and selection continues, creatures with more and more successful behavio urs can
emerge.
5.6.5. Exploring other ways in which CA can generate Body-Plans
One of the many possible methods to test is when CA can be used each time when creating the
next generation. So the genes would simply define the position of the CA seed.
5.6.6. Other visualisation techniques of the search space
The following visual references can be created in order to aid the analysis of the performance of
the algorithm:
- Fitness landscape of both generations and their corresponding neural maps
- Graphs that show the evolution of the fitness and models’ parameters over the generations
- Graphs showing the areas of the search space that is explored by the algorithm - etc.
6.6.7. Adapting Genetic Operators to Evolve the Evolvability
-
Elimination criteria can be used instead of or together with the defined fitness criteria. It
can represent the ratio of similarity of FC's components (same as one of the examples
of implicit FC). EC gets stricter with each generation thus still encouraging evolution
however at the same time avoiding the problem of local optima;
-
Fitness constituents can be programmed to have their own weightings within the total
fitness value, thus mathematically assigning their importance in the overall fitness
assessment;
-
An option for user to choose which individuals to carry on to the next generation and
which to mate;
-
Survival ratio determines the percentage of the population that will survive each
generation. If the initially generated population has fewer individuals with positive
fitness than the number that should survive, another round of seed genotypes is
generated to replace those with zero fitness (Sims 1999);
73

74. -
Modifier genes can be added, whose allelic values control the genetic operators (e.g.
loci controlling recombination or mutation rates and distributions) (Back, Hoffmeister
and Schwefel 1991; Bergman and Feldman 1992; Shaffer and Morishima 1987);
-
Meta-level GA can be running on parameters of the operators, in which each run of the
primary GA produces a performance measure used as the fitness of the operator
parameter (Grefenstette 1986);
-
“Messy GAs”, a form of representation which allows more complex transformations
from parent to offspring (Goldberg, Deb, and Korb 1990);
-
Focusing the probabilities of operator events to those that have had a history of
generating fitter individuals (Davis 1989);
-
Mutation distribution adjustment to maintain certain properties of the fitness distribution,
e.g. the “one-fifth” rule of Evolution Strategies (Back, Hoffmeister and Schwefel 1991);
-
Dynamic parameter encoding (O’Neil and Shaefer 1989; Pitney, Smith, and Greenwood
1990; Schraudolph and Belew 1992; Shaefer 1987; Szarkowicz 1991).
74