ACCELERATING THE MULTI-OBJECTIVE OPTIMISATION OF A SEMI-
TRANSPARENT BUILDING INTEGRATED PHOTOVOLTAIC FACADE
THROUGH THE USE OF ANT COLONY ALGORITHM
John MacModeller1, Jane MacSimulator2, and Another MacAuthor2
1BS0-2014 Secretariat, UCL, London, UK
2Another Institution, University of Origin, Some City, Some Country
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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.
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
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
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
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
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.
The fitness function for annual electricity generation
is based on the following mathematical equation:
where is the electrical energy produced by the
photovoltaic system (kWh·a-1), is the gross area
of the semi-transparent BIPV facade (m2),
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:
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
. 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
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:
are the averaged normalised
fitness functions of all the design variants in the
Pheromone value of each link:
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:
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),
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
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
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
Population – a population is a set of
individuals in the evolution process of the
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
Figure 3. Graphical representation of crossovers.
Top and middle: where parent x’ and x”are
recombined to create two offsprings. Bottom:
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 ,
for each generation
randomly select number parents,
rank all selected parents,
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
until maximum number of generations, .
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
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
Table 2: Variants of MOEA
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
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.
Table 4: Comparison of best-performing MOAC and
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
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
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.
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.
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
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