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ACCELERATING THE MULTI-OBJECTIVE OPTIMISATION OF A SEMI-

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TRANSPARENT BUILDING INTEGRATED PHOTOVOLTAIC FACADE

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THROUGH THE USE OF ANT COLONY ALGORITHM

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John MacModeller1, Jane MacSimulator2, and Another MacAuthor2

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1BS0-2014 Secretariat, UCL, London, UK

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2Another Institution, University of Origin, Some City, Some Country

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The names and affiliations SHOULD NOT be included in the draft submitted for review.

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The header consists of 10 lines with exactly 14 points spacing.

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The line numbers are for information only. The last line below should be left blank.

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(The note below is for Reviewers. It will not be part

of the paper)

Dear Reviewers,

Pls note that the title has been modified to reflect

more closely to the content of the abstract submitted

on 20 September 2013 and this full paper. Sorry for

any inconvenience.

Best Regards, Authors of paper submission 136

ABSTRACT

Evolutionary algorithms have popularly been used

for the past ten years in building performance

optimisation (Attia 2013). The long runtime of a

performance-based multi-objective optimisation can

be reduced by using faster proxy simulations (Choo

et al 2013). Beside using proxy simulations, the

optimisation process can be improved by selecting

other types of multi-objective algorithms. This paper

will present the use of multi-objective ant colony

algorithm as a possible alternative to multi-objective

evolutionary algorithm. The multi-objective

optimisation of a semi-transparent building integrated

photovoltaic (BIPV) facade is used for the proof of

concept. The design of semi-transparent BIPV

facades has an impact on a wider range of factors,

including solar heat gain and daylight penetration

into the rooms of the building. Results from the

experiments conducted show that multi-objective ant

colony algorithm can speed up the multi-objective

optimisation process but does not perform as well as

the multi-objective evolutionary algorithm.

INTRODUCTION

Long runtimes are common in performance-based

multi-objective optimisations of building parameters.

This is because detailed building performance

simulation tools, which have relatively long

runtimes, are typically coupled with a multi-objective

optimisation evolutionary algorithm. Choo et al

(2013) has shown that the runtime of a performance-

based multi-objective optimisation can be reduced by

using faster proxy simulations.

Commonly used multi-objective algorithm like

evolutionary algorithm (EA) have been widely used

in building related multiobjective optimisation

(Caldas 2008, Charron and Athienitis 2006, Wang et

al 2005). Attia et al (2013) highlighted that EA has

been very popular for the past ten years in building

performance optimisation. They have even been

integrated into software packages for the designers’

convenience. An example of such integration is

Galapagos, an optimisation component in

Grasshopper (Rutten 2011), a visual data modelling

system that allows designers who are not trained in

scripting to quickly generate parametric models.

Designers usually use the existing optimisation tool

provided in the software packages and do not try and

implement other types of multi-objective

optimisation algorithms. Such algorithms are not

restricted to just multi-objective evolutionary

algorithm (MOEA). There are also swarm

intelligence-based optimisation algorithms like multi-

objective ant colony (MOAC) which are much newer

than EA and are therefore not commonly used for

building related applications.

Hence, this paper will present the use of MOAC for

improving the speed and performance of multi-

objective optimisation. A comparison between

MOAC and MOEA will show if MOAC can be a

better alternative.

The multi-objective optimisation of a semi-

transparent building integrated photovoltaic (BIPV)

facade is used for the proof of concept. Unlike

typical roof-mounted photovoltaic systems, where

performance is predominantly focused on the amount

of electricity generated, the design of semi-

transparent BIPV facades has an impact on a wider

range of factors, including solar heat gain and

daylight penetration into the rooms of the building.

Hence, a semi-transparent BIPV façade is used here

because its conflicting performance criteria presents

a good design senario for multi-objective

optimisation.

The paper is structured as follows: in the next

section we will give a detailed description of

parametric model and facade performance metrics

used in the experiments. It is followed by an

overview of both MOAC and MOEA. Thereafter we

will present the methodology used to conduct the

experiments. Lastly, the results will be analysed and

discussed.

EXPERIMENTS

To compare the performance of both MOAC (multi-

objective ant colony) and MOEA (multi-objective

evolutionary algorithm), a design problem which

involves the multi-objective performance

optimisation of a semi-transparent BIPV facade is

first defined.

Parametric Model.

A parametric model of a typical office space with a

semi-transparent BIPV facade is created with

Houdini, a procedural modelling software from

Sidefx (2013). A typical north oriented office space

for an occupancy of one person with 4 m (width) x 4

m (depth) x 3 m (height) is modelled for the

experiment, as shown in Figure 1 (top). The facade is

separated into three panels: BIPV panels 1, 2, 3, each

of them is independent from one another. For each

panel, three design variables, cell width cell height,

and cell spacing are defined in the parametric model

as shown in Figure 1 (bottom). These design

variables , define the PV cell pattern for each

independent panel, where subscript ,

represents the panels and subscript

represents the three design variables (cell width, cell

height and cell spacing) in each façade panels. Cell

width and height vary from 5 – 15.5 cm at 0.5 cm

steps but are independent from each other. Cell

spacing varies from 0.5 – 5 cm at 0.5 cm steps. All

the cells of the semi-transparent BIPV facades will

be similar in shape. The pattern occupies a facade

with a height of 3 m and width of 4 m.

Façade Performance Metrics

The multi-objective optimisation of a semi-

transparent BIPV façade will involve maximising

electricity generation, minimising the ETTV

(envelope thermal transfer value) and maximising the

working plane area, 0.85m height from the floor, that

has a minimum illuminance of 300lx. These three

performance metrics are used as fitness functions for

the optimisation because of their relatively fast speed

of computation. The competing goals of each metric

presents a good setup for the multi-objective

optimisation algorithms to balance the trade-offs.

Electricity Generation

The fitness function for annual electricity generation

is based on the following mathematical equation:

(1)

where is the electrical energy produced by the

photovoltaic system (kWh·a-1), is the gross area

of the semi-transparent BIPV facade (m2),

is the

fraction of surface area with active solar cells, is

the total annual solar radiation energy incident on the

BIPV façade (which is computed at 561 kWh·m-2·a-1

by Radiance), is the semi-transparent BIPV

module efficiency (which is set at 12%) and is

the average inverter efficiency (which is set at 90%).

Envelope Thermal Transfer Value

ETTV is used as the second fitness function for the

optimisation. ETTV is an easy-to-use mathematical

equation to calculate the heat transfer through the

façade (BCA 2004). It was developed as a measure

of the thermal performance of the building envelope.

The equation of ETTV is shown below:

(2)

where is the window-to-wall ratio, is the

thermal transmittance of an opaque wall which is 0

W·m-2·K-1 because the modelled facade is a full

height curtain wall, is the thermal transmittance of

the fenestration, which is assumed to be 5.8 W·m-2·K-1

in the experiments, is the correction factor for solar

heat gain through the fenestration and is the

shading coefficient of the fenestration.

Figure 1. Top: Typical office used in the simulation

model with illuminance sensor points (in red) on a 10

x 10 grid. Bottom: Schematic of cell arrangement for

the modelled semi-transparent BIPV façade

, where is the BIPV panel number.

Floor Area with Minimum Illuminance

The last fitness function is the working plane area,

0.85m height from the floor, which has a minimum

illuminance for the office of 300 lx. The illuminance

level is calculated using the Radiance software (Ward

and Shakespeare 1998). Sensor points on a 10 x 10

grid at 0.85m height from the floor are used for the

illuminance simulation (refer to Figure 1, top). The

illuminance level is calculated with an overcast sky

for the June solstice at 1200h where the sun faces the

north façade of the typical office space. An overcast

sky is assumed here for the worst daylight scenario.

The following settings were used in Radiance: ab =

2, ad = 1000, as = 20, ar = 300 and aa = 0.1, where ab

is ambient bounce, ad is ambient resolution, ar is

ambient resolution and aa is ambient accuracy. The

detailed explanation of the settings is beyond this

paper. They can be referred to in the Radiance

manual. (Ward and Shakespeare 1998)

OVERVIEW OF ALGORITHMS

Algorithm for MOAC Optimisation

Dorigo (1992) was the first to introduce ant colony

optimisation. Its concept mimics the food foraging

behaviours of ant colonies to find the shortest path

between the food sources and their nests. Ants

randomly explore their surrounding and leave a

pheromone trail on the ground. Ants probabilistically

choose the paths marked by strong concentration of

pheromone levels. When an ant finds a food source,

it will evaluate the quantity and quality of the food.

The quantity of pheromone that an ant leaves on the

ground depends on the quantity and quality of the

food, which is the behaviour that the ant colony

optimisation model replicates mathematically.

Applying MOAC to a multi-objective optimisation

problem, the graphical representation in Figure 2

describes how the problem is represented in an ant

colony optimisation algorithm.

In Figure 2, each layer is a design variable in

Figure 1. Nodes are the values of each design

variable (layer), where is the layer number and is

the design variable number. There are a total of 9

layers. Each layer shown in Figure 2 has 22 nodes.

The nodes are connected through links with

pheromone value,

. The subscript u is the next

layer where and is the design variable

number of this next layer. An example of a possible

“path” or design variant is shown as a bold (red) line.

The ant colony optimisation algorithm contains the

following components:

Number of artificial ants in a colony, – each

“ant” represents a possible design variant.

Probability of selection, – this is the

probability of selecting a link from node to

as shown in Figure 2.

Initial pheromone trail, – all links in the

solution space of an ant colony optimisation

algorithm is first initialised with a single value:

(3)

Where

are the averaged normalised

fitness functions of all the design variants in the

first iteration.

Pheromone value of each link:

(4)

where is the pheromone evaporation rate.

Pheromone evaporation rate, , is applied to

the existing pheromone value when an artificial

ant, , has taken a path to the food source.

Pheromone deposit, is the pheromone value after

an artificial ant, , has taken the same path back

to the nest. Pheromone deposit is applied to the

links on the path after are calculated:

(5)

where are fitness values of fitness

functions of objective for an artificial ant,

.

Figure 2. Graphical representation of a discrete

variable problem with 9 design variables as

described in the text.

The following describes the multi-objective ant

colony optimisation algorithm:

randomly select paths (feasible design variants) for

number of ants,

calculate values of fitness functions,

initialise all links with pheromone,

update pheromone value,

, on each link of the

selected path as described in equation (4),

Repeat

calculate probability of each link ,

select each link to form a path (feasible design

variant) for number of ants based on probability

,

for each of the selected path,

evaporate pheromone value with evaporation

rate ,

calculate the performance metrics, , and ,

update pheromone value,

, on each link of

the selected path as described in equation (5),

until maximum number of iterations, .

For a more detailed description on ant colony

optimisation, Dorigo and Stutzle’s book on Ant

Colony Optimization (Dorigo and Stutzle 2004)

provides thorough and in-depth explanations.

Algorithm for MOEA

MOEA is an optimisation algorithm based on natural

evolution (Eiben 2007). The algorithm contains the

following components:

Representation – a set of design variables,

, which are typically called the

genotypes, are used to define possible

design variations, typically called

phenotypes or individuals, . Individual,

, represents the design variant in a

solution space.

Population – a population is a set of

individuals in the evolution process of the

algorithm.

Parent selection – this involves randomly

selecting a set of individuals for

recombination and mutation.

Crossover and mutation – this is a process

where selected parent individuals are

recombined to create new “off-springs” or

variants which inherit the better “genes”

from their “parent individuals”. This is

shown in Figure 3 (top and middle). To

prevent premature convergence in the

optimisation, mutation is used to randomly

change the “gene” sequence of a design

variant. It is based on a probability rate

called the mutation rate which is shown in

Figure 3 (bottom).

Fitness function – this is used to evaluate

the individuals in the population. It

evaluates and selects for each generation,

the individuals for recombination and

mutation.

Figure 3. Graphical representation of crossovers.

Top and middle: where parent x’ and x”are

recombined to create two offsprings. Bottom:

and

are “genes” that are mutated.

The following evolutionary algorithm code was used

in the experiments. It demonstrates how the

components mentioned above are correlated:

randomly generate first individuals,

calculate the fitness values of fitness function ,

Repeat

for each generation

randomly select number parents,

rank all selected parents,

select first

of parents to recombine off-

springs and eliminate selected parents,

randomly change genotype of off-spring

with mutation rate, ,

calculate the performance metrics for the

new off-springs,

until maximum number of generations, .

METHODOLOGY

Performance Measures to Compare Algorithms

To compare the performance of MOAC with MOEA,

a performance metric called the C measure, defined

by Zitzler (1999) is used. C measure is the ratio of

design solutions on one Pareto front that dominates

another. Given two sets of solution and from

the multi-objective optimisations, the C measure is

defined as:

(6)

where . If the value of

, it means that all points in are dominated by or

equal to points in . Whereas, if , it

means no points in are covered by . Both

and are considered because

may not be equal to .

Three variants of MOAC and MOEA as shown in

Table 1 and 2 were created (for derivation see

“Settings for Multi-objective Optimisation” below)

and the best of each type were selected after using

the C measure to analyse their performance. 10

optimisation runs were conducted for each variant of

MOAC and MOEA. The C measures for ten sets of

runs are later shown in Table 3 and 4.

To compare the speed of MOEA with MOAC, the

best MOAC and MOEA, selected using the C

measure as stated above, are ran on a computer with

a Dual-Core CPU of 3GHz and 4GB RAM. The

average time of the optimisation runs for MOEA and

MOAC are used for comparison. The results of the

runtime are later shown in Table 5.

To compare the average time taken to complete each

optimisation run, the total cumulative number of ants,

for all iterations, used in each MOAC run and the

total cumulative individuals, for all generations, used

in each MOEA run are kept at 5,000.

Settings for Multi-objective Optimisation

For MOAC, Arora (2011) recommended the number

of artificial ants or design variants to be to

, where is the number of design variables or

layers as shown in Figure 2. Arora (2011) also

recommended a pheromone evaporation rate,,

between 0.4 and 0.8. These values were considered in

the settings for the design variants.

Given an optimization run with a total of 5,000

individuals in total, MOAC 0 is first given the

following settings where , and

. To find out the effects of , MOAC 1 is given a

value of , and . To find out

the effects of m, MOAC 2 is given the following

settings where , and . Table

1 summaries these three MOAC variants.

Table 1: Variants of MOAC

Variants

MOAC 0

100

50

0.4

MOAC 1

100

50

0.8

MOAC 2

50

100

0.8

Table 2: Variants of MOEA

Variants

MOEA 0

99

100

0.50

0.01

MOEA 1

62

100

0.80

0.01

MOEA 2

31

200

0.80

0.01

For MOEA, both Zitzler (1999) and Deb (2001) have

used a crossover of k=0.8 and a mutation rate of 0.01.

Hence, MOEA 0 is given the following settings

where , , and . To

find out the effects of the crossover, , MOEA is

given the following settings where , ,

and m=0.01. To find out the effects of the

initial population size, n, MOEA is given the

following settings where , ,

and . Table 2 summaries these three

MOEA variants.

All comparisons between variants of MOAC and

MOEA were done using the C measure (Zitzler

1999). After comparing variants of MOAC and

MOEA individually as shown in Table 3, the best

performing MOAC and MOEA are compared using

the C measures (see Table 4).

Both variants of MOAC and MOEA are applied to

minimise ETTV, maximise electricity generation and

maximise area with minimum daylight of 300 lx.

RESULTS AND DISCUSSION

Comparing the performance of the three variants:

MOAC 0, MOAC 1 and MOAC 2, Table 3 shows

that MOAC 1 is the best-performing variant followed

by MOAC 0. From this comparison, we can see that

for MOAC, a bigger number of artificial ants

improves the results of the Pareto front. In addition, a

higher pheromone evaporation rate of 0.8 also

improves the results of the Pareto front.

Table 3: Comparison of all variants of MOAC and

MOEA. The min (minimum), avg (average) and max

(maximum) of the C measure for the set of 10 runs

for the MOAC and MOEA variants are presented.

Comparison

of variants

C Measure

min

avg

max

MOAC 0,

MOAC 1

0.066

0.267

0.467

MOAC 1,

MOAC 0

0.226

0.421

0.566

MOAC 0,

MOAC 2

0.469

0.875

1.000

MOAC 2,

MOAC 0

0.000

0.152

0.583

MOAC 1,

MOAC 2

0.773

0.489

0.981

MOAC 2,

MOAC 1

0.000

0.049

0.131

MOEA 0,

MOEA 1

0.189

0.304

0.436

MOEA 1,

MOEA 0

0.327

0.469

0.613

MOEA 0,

MOEA 2

0.084

0.229

0.338

MOEA 2,

MOEA 0

0.360

0.506

0.762

MOEA 1,

MOEA 2

0.223

0.313

0.464

MOEA 2,

MOEA 1

0.307

0.391

0.432

Table 4: Comparison of best-performing MOAC and

MOEA.

Comparison

of variants

C Measure

min

avg

max

MOAC 1,

MOEA 2

0.0167

0.131

0.266

MOEA 2,

MOAC 1

0.226

0.557

0.867

Comparing the performance of the three variants of

MOEA, MOEA 0, MOEA 1 and MOEA 2, Table 3

shows that MOEA 2 is the best-performing variant

followed very closely by MOEA 1. With reference to

MOEA 2, we can see that increasing the crossover

value of a MOEA improves the results of the Pareto

front. However, a two-fold increase in the number of

the initial population size from 100 to 200 does not

yield a significant improvement in the Pareto front.

Comparing the best-performing MOAC variant,

MOAC 1 and best-performing MOEA variant,

MOEA 2, Table 4 shows that MOEA 2 dominates

MOAC 1 by an average of 0.557 whereas MOAC 1

dominates MOEA 2 by an average of 0.131. Figure 4

shows a three-dimensional plot with the Pareto fronts

for an instance of MOAC 1 and MOEA 2. MOAC 1

dominates MOEA 2 with a few design variants

(shown in blue) where MOEA 2 dominates MOAC 1.

Figure 4. Pareto fronts of MOAC 1 and MOEA 2

with only a few design variants from MOAC 1

dominating MOEA 2, shown in blue. Design variants

of MOAC 1 are shown in green and design variants

of MOEA 2 are shown in red.

For multi-objective optimisation, the quality of the

solutions along the Pareto front is determined by how

close they get to the theoretical optimum where

, and the area of minimum

illuminance of 300 lx . Hence, if the

average C measure for MOAC 1 is 0.131, it means

that an average of 13.1% of the design variants on the

Pareto front of MOAC 1 are closer to the theoretical

optimum than those using MOEA 2. In addition,

MOEA 2 has an average C measure of 0.557 where

57.7% of design variants on the Pareto front of

MOEA 2 are closer to the theoretical optimum than

MOAC 1.

The parallel plot for MOAC 1 in Figure 5 (top), has

design variants with relative high ETTV

(approximately 41.00 - 39.60 W·m-2). These design

variants have a relatively high working plane area of

minimum of 300 lx (16.0 – 9.5 m2) and a relatively

low electricity generation of (approximately 764 –

700 kWh·a-1). In addition, the parallel plot for

MOAC 1 has design variants with relatively low

ETTV (approximately 37.00 – 39.00 W·m-2),

relatively low working plane area of minimum 300 lx

(approximately 0.0 – 3.2 m2) and a relatively high

electricity generation (approximately 800 – 880

kWh·m-2·a-1). This behaviour shows that a design

with more active cell area, generates more electricity

and reduces ETTV and daylighting because the PV

cells are shading the sunlight which results in lower

heat gain and reduced visible light transmittance.

Figure 5 Top: Parallel plot of MOAC 1 shown in

green. Middle: Parallel plot of MOEA 2 shown in

red. Bottom: superimposed parallel plots of MOAC 1

and MOEA 2

Comparing the parallel plots of both Pareto fronts of

MOAC 1 and MOEA 2, we can see that the design

variants of both MOAC 1 and MOEA 2 occupy high

and low regions of all the three fitness functions.

This is seen in Figure 5, where both MOAC 1 and

MOEA 2 have managed:

to minimise ETTV which results in the

increase in electricity generation and

reduction in the area of minimum

illuminance of 300 lx.

to maximise the electricity generation which

results in the reduction in ETTV and

reduction in the area of minimum

illuminance of 300 lx.

to maximise the area of minimum

illuminance of 300 lx which results in the

increase in ETTV and reduction in

electricity generation.

However, from Figure 5 (bottom), we can observe

that the design variants of MOEA 2 occupies a wider

range for ETTV and electricity generation on the

parallel plots when compared with MOAC 1. This

means that MOEA 2 has managed to optimise the

two individual objectives, ETTV and electricity

generation, better than MOAC 1.

Table 5: Comparison of the runtimes of all variants

of MOAC and MOEA. The min (minimum), avg

(average) and max (maximum) for the set of 10 runs

for the MOAC and MOEA variants are shown.

Variants

Runtime

min

avg

max

MOAC 1

36:28

36:42

37:00

MOEA 2

40:14

40:50

41:47

Table 5 shows that the averaged normalised time

taken to run MOAC 1 is 36:42 hrs and 40:50 hrs for

MOEA 2. This shows an improvement of 10.2% in

the run when MOAC 1 is used.

We can conclude from the results discussed above

that MOAC can be a good alternative, if the speed of

running a multi-objective optimisation is more

critical than the quality of the Pareto front which is

determined by the C measure.

Although MOAC 1 dominates MOEA 2, the trend of

both parallel plots for MOAC 1 and MOEA 2 are

similar. However, MOEA 2 has been shown to find

better design solutions, with 57.7% of its design

solutions dominating those of MOAC 1.

CONCLUSION

This paper has introduced the use of multi-objective

ant colony (MOAC) in the multi-objective

optimisation space of a semi-transparent BIPV

façade. The experiment demonstrated that MOAC

could be an alternative for multi-objective

optimisations. It has shown reasonable improvements

in speeding up the multi-objective optimisation

process for BIPV façade design. However, future

research needs to be conducted, to compare other

variants of MOAC and MOEA to give more insights

into the use of ant colony optimisation for multi-

objective optimisation for building design

optimisation.

REFERENCES

Arora, J. 2011. Introduction to Optimum Design,

Academic Press, Boston, MA.

Attia, S., Hamdy, M., O’Brien, W. and Carlucci, S.

2013, Assessing Gaps and Needs for Integrating

Building Performance Optimization Tools in Net

Zero Energy Building Design, Energy and

Buildings 60, 110-124.

BCA, 2004. Guidelines on Envelope Thermal

Transfer Value for Buildings, Commissioner of

Building Control, Singapore.

Caldas, L. 2008. Generation of Energy-efficient

Architecture Solutions Applying GENE_ARCH:

An evolution based generative design system,

Advanced Engineering Informatics 22:1, 59-70.

Charron, R. and Athientitis, A.K. 2006. The Use of

Genetic Algorithms for a Net-zero Energy Solar

Home Design Optimisation Tool, PLEA 2006

Conference, Geneva.

Choo, T.S Ouyang, J., and Janssen, P. 2013. Multi-

objective Optimisation of Semi-transparent

Building Integrated Photovoltaic Façade,

Proceedings for Sustainable Building

Conference 2013.

Deb, K. 2001. Multi-objective Optimization Using

Evolutionary Algorithms, John Wiley & Sons

Ltd, England.

Dorigo, M. 1992. Optimization, learning and natural

algorithms. PhD thesis, Dipartimento di

Elettronica, Politecnico di Milano, Italy.

Dorigo, M. and Stutzle, T. 2004. Ant Colony

Optimization, MIT Press, Massachusetts.

Eiben, A. E. and Smith, J.E. 2007. Introduction to

Evolutionary Computing, Springer, Heidelberg.

Fung, T.Y.Y. and Yang, H. 2008. Study on Thermal

Performance of Semi-transparent Building-

Integrated Photovoltaic Glazings, Energy and

Buildings 40:3, 341-350.

Robinson, L.E. and Athienitis, A.K. 2009. Design

methodology for optimisation of electricity

generation and daylight utilization for facades

with semi-transparent photovoltaics, Proceedings

Building Simulation 2009.

Rutten, D., 2011, Evolutionary Principles Applied to

Problem Solving, available from

http://ieatbugsforbreakfast.wordpress.com/2011/

03/04/epatps01/, accessed on 1st December 2013.

Sidefx 2013. Houdini 3D Animation Tools, available

from http://www.sidefx.com/, accessed on 1st

December 2013.

Wang, W., Zmeireanu, R. and Rivard, H. 2005.

Applying Multi-objective Genetic Algorithms in

Green Building Design Optimisation, Building

and Environment 40:11, 1512-1525.

Ward, G. L. and Shakespeare, R. A. 1998. Rendering

with Radiance – The Art and Science of Lighting

Visualization, Booksurge LLC, Charleston.

Zitzler, E. 1999. Evolutionary Algorithms for

Multiobjective Optimization: Methods and

Applications. PhD Dissertation, ETH Zurich