Energy and Buildings 42 (2010) 807–814
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Energy and Buildings
journal homepage: www.elsevier.com/locate/enbuild
Optimisation of building form for solar energy utilisation using constrained
evolutionary algorithms
Jérôme Henri Kämpf *, Darren Robinson
Solar Energy and Building Physics Laboratory, Station 18, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
A R T I C L E I N F O
A B S T R A C T
Article history:
Received 30 October 2008
Received in revised form 24 November 2009
Accepted 26 November 2009
In this paper we describe a new methodology for optimising building and urban geometric forms for the
utilisation of solar irradiation, whether by passive or active means. For this we use a new evolutionary
algorithm (a hybrid CMA-ES/HDE algorithm) to search the user-defined parameter space, within defined
constraints. The fitness function, solar irradiation, is predicted using the backwards ray tracing program
RADIANCE in conjunction with a cumulative sky model for fast computation.
Application of this technique to three very different scenarios suggest that the new method
consistently converges towards an optimal solution. Furthermore, with respect to configurations
subjectively chosen to be intuitively well performing, annual irradiation is increased by up to 20%;
sometimes yielding highly non-intuitive but architecturally interesting forms.
ß 2009 Elsevier B.V. All rights reserved.
Keywords:
Optimisation
Building geometry
Geometrical parametrisation
Evolutionary algorithm
Hybrid CMA-ES/HDE
1. Introduction
Half of the global population now lives in urban settlements
which collectively consume three quarters of global resources.
With forecasts that this urban population will increase to three
quarters by 2050 [1] it is imperative that we understand how to
minimise energy consumption in the urban environment. One such
approach is to maximise the utilisation of ambient solar energy –
whether for active conversion using solar thermal and/or
photovoltaic collectors or by passive design, so displacing demands
for heating and lighting. For this, computer modelling of solar
radiation availability can be an invaluable decision support tool for
building and urban designers. But the probability of finding an
optimal solution for the geometric form of even an individual
building by manual trial and error is extremely small. Clearly the
parameter space is yet larger when dealing with many buildings
simultaneously and the probability of finding an optimum
correspondingly smaller. To help to resolve this problem we have
developed a new hybrid evolutionary algorithm [2] and applied
this to the problem of optimising building and urban geometric
form for solar radiation utilisation. To place this work into context
we first discuss progress that has been made to predict urban solar
radiation potential. We then discuss progress that has been made
in the use of computer algorithms to optimise building performance before going on to describe the basis of our proposed
methodology and presenting some scenarios and associated
* Corresponding author. Tel.: +41 21 693 45 47; fax: +41 21 693 27 22.
E-mail address: jerome.kaempf@epfl.ch (J.H. Kämpf).
0378-7788/$ – see front matter ß 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.enbuild.2009.11.019
results. We conclude by discussing the relative effectiveness of
this new approach as well as possibilities for increasing the scope
of its application.
1.1. Optimisation at the urban scale
Two key methods have thus far been employed to predict the
annual irradiation incident on built surfaces, both using the
backwards Monte Carlo ray tracing program RADIANCE [3].
Mardaljevic and Rylatt [4,5] developed a technique of buildingup annual hourly time series irradiance images from simulations of
a statistical sub-set of sun positions and sky types. This is a
powerful technique, but contains a great deal of redundant
information if all we are interested in is the aggregate of these
results to produce annual irradiation distributions over building
surfaces. For this Compagnon and Raydan [6]; Compagnon [7]
developed the alternative technique of computing an annual solar
radiance distribution (Wh m2 sr1), so facilitating prediction of
annual irradiation in a single simulation. Robinson and Stone [8]
later refined this technique, which was based on representing the
sky as discrete light sources (as with an artificial sky), to solve for a
set of joined-up (Tregenza) patches. Annual irradiation simulations
using these cumulative skies have been conducted to investigate a
broad range of problems. Compagnon and Raydan [6] first
investigated the solar utilisation effectiveness of a series of
standard urban morphologies before going on [7] to investigate
the performance of real urban neighbourhoods. Montavon et al. [9]
and Robinson et al. [10] later went on to study the solar potential
of entire city districts. Meanwhile Cheng et al. [11] used this
technique to systematically compare a range of subjectively
J.H. Kämpf, D. Robinson / Energy and Buildings 42 (2010) 807–814
808
selected variants of the height of buildings distributed throughout
a regular grid. However, a relatively small number of variants
(within a very large parameter space) were modelled by this
manual trial and error approach, so that it was not possible to
identify a de facto optimum; or indeed to suggest with confidence
what form this optimum might take.
Meanwhile, various optimisation algorithms have been applied
to successfully optimise a variety of design problems related to
individual buildings [12,13]. For example, in this paper we apply
evolutionary algorithms to the solar irradiation optimisation
problem in the urban context. In this we build on some prior
work on optimising simple roof geometries [14], but this earlier
work did not consider possible constraints such as keeping the
building volume within limits throughout the simulations.
Therefore multi-objective optimisation was introduced as a way
to deal with the volume constraints [15]. However this methodology is rather inefficient as we compute many candidate solutions
that do not satisfy the constraints we set in the beginning. In this
paper we present an add-on to the hybrid evolutionary algorithm
presented in Kämpf and Robinson [2] which can handle constraints
in the parameter space and we apply this to examine a range of
solar radiation optimisation problems of various complexity.
2. Methodology
2.1. Solar potential determination
the point irradiation (in Wh/m2) by the corresponding sub-surface
area (in m2) and summing over all the points. Due to the large
number of sampling points for each of a potentially large number
of simulations, it is desirable to find a compromise between
accuracy and computing time. To this end a sensitivity analysis
was carried out to determine a robust grid spacing and the
RADIANCE simulation parameters.
2.2. Optimisation
The usual way of finding the best urban configuration is to
parameterise the relevant variables describing the buildings and
possibly the spatial relationships between buildings and determine which combination of these parameters maximises the
potential to utilise solar energy. For a few different discrete
variables it may be possible to exhaustively test all possibilities,
but when the parameter space to explore becomes large to very
large, it is desirable to use optimisation algorithms.
With these algorithms, we should be able to find the global
maximum (or maxima) of a function f that depends on n
independant decision variables. Put formally, the algorithm
searches for the supremum (the set of variables that maximises
the function) as in Eq. (1).
f f ð~
xÞj~
x 2 M Rn g
sup
(1)
with:
n2N
f : M!R
M ¼ f~
x 2 Rn jg j ð~
xÞ 0
dimension of the problem
objective function
feasible region
In order to ‘virtually’ measure the solar potential of hypothetical buildings, we have chosen to use the well-known backward ray
tracing program RADIANCE. A virtual scene is defined by a sky,
buildings and a ground. In order to compute the irradiation on
buildings over a period of interest (POI), a cumulative sky (see
Robinson and Stone [8]) is produced for the location. In this study,
we have taken the location to be Basel in Switzerland (47 N,7 E)
and the corresponding meteorological data from the Meteonorm
software. The sky defines 145 Tregenza patches with corresponding cumulative radiance (Wh m2 sr1). The scene, described by
surfaces given by vertices, is compiled using RADIANCE oconv
program to produce an octree file. The rtrace program (the tracing
core of RADIANCE) is given a list of points and associated normal
vectors, along with the octree file to compute the irradiation at the
points position accounting for both direct (solar) and diffuse (sky
and reflections) contributions. The points act like virtual watthourmeters, measuring energy coming from the hemisphere available
to the normal vector. Each measuring point corresponds to a subsurface on which the irradiation is supposed to be uniform. As
indicated in Fig. 1 the total irradiation is computed by multiplying
The set of inequality restrictions g j : Rn ! R; 8 j 2 f1; . . . ; mg
includes a special case of constraints due to the domain boundaries
~
~:~
~ 2 Rn . ~
~ the upper
L ~
xH
L; H
L is named the lower bound and H
bound of the domain.
In our case, the parameter space is defined by a geometrical
characterisation of the buildings and the measure to improve is the
received irradiation. For this, RADIANCE is used as a black-box (see
Fig. 2). The black-box response (irradiation as a function of building
form parameterisation) is found to be non-linear and noncontinuous. To address such problems, we need ‘‘fit for purpose’’
algorithms such as heuristics. A heuristic algorithm ignores if the
solution found can be proven to be correct, but generally provides a
good solution. Keeping in mind that with heuristics we can never
be certain of finding the global maximum within a reasonable time
frame, we have chosen to use evolutionary algorithms. More
Fig. 1. The irradiation calculation using Radiance.
Fig. 2. The optimisation algorithm applied to a black-box problem type.
8 j 2 f1; . . . ; mgg; M 6¼ ?
m2N
number of constraints
J.H. Kämpf, D. Robinson / Energy and Buildings 42 (2010) 807–814
809
Fig. 3. A RADIANCE generated image of the scene (left), a schematic view from top (right).
specifically, for our application, the hybrid CMA-ES (covariance
matrix adaptation evolution strategy) and HDE (hybrid differential
evolution) described in Kämpf and Robinson [2] is used with the
same parameters as those used in previous runs of the hybrid. That
is for a problem with n variables: for the CMA-ES a parent
population size m ¼ 2 þ b 1:5 log ðnÞ c , a children population size
l ¼ 4 þ b 3 log ðnÞ c , a mutation step size s ¼ 0:2 and for the HDE
the rand3 strategy ([16], pp. 48–49) with parent and children
population sizes NP ¼ 30, a differentiation constant F ¼ 0:3 and a
crossover probability Cr ¼ 0:1. The relative precision for the HDE
migration phase was chosen to be e2 ¼ 10% and the absolute
precisions were all set to zero.
Please note that the chosen indicator of performance (solar
irradiation) admittedly provides, for the present purpose of
demonstration of concept, only a partial basis for the minimisation
of urban energy consumption. In the future, we plan to adapt the
presented optimisation methodology for its use with an holistic
urban simulation tool [17].
2.3. Constraint handling
The hybrid CMA-ES and HDE of Kämpf and Robinson [2] is made
more realistic by adding constraint handling in each of the
hybridised methods. These constraints are written in the form:
g i ð~
xÞ 0; 8 i ¼ 1; . . . ; m
(2)
x are the n
where g i : Rn ! R is a function of the parameters, ~
parameters and m is the number of constraints.
For the CMA-ES, the method envisaged is to repeat the mutation
phase until a valid individual (satisfying the constraints) is found
but at maximum 10 times (in order to avoid an infinite loop). In the
evaluation phase, the remaining individuals not satisfying the
constraints are attributed a minimum fitness value (1). In the
selection phase, the usual comparison operator < is used to order
the population from the worst to the best, and an elitist selection is
made. When two individuals have the same fitness and are outside
of the constraints, we take into account total constraint domination for their ranking:
ð 8 i max ðg i ð~
x1 Þ; 0Þ max ðg i ð~
x2 Þ; 0ÞÞ ) ~
x1 ~
x2
(3)
The first operator < is the usual comparison operator between two
members of R. The second operator means that individual 1
dominates individual 2.
For the HDE, the minimum fitness value is similarly attributed
during the evaluation phase to individuals that do not satisfy the
constraints. Moreover, the same operator < as used for the CMAES is used in the selection phase; the comparison is applied
between the current and the trial individual. In case of fitness
equality and no constraint domination, the trial individual is
chosen to bring diversity to the population.
One of the advantages of this constraint handling method, is
that individuals not satisfying the constraints are not evaluated by
the objective function. Rather they are given a rank according to
the degree of violation of the constraints. They do however
participate in the recombination process, so bringing diversity to
the population and allowing the borders of the constrained
parameter space to be approached.
2.4. The first application: Manhattan style grid
In this application a hypothetical city comprised of cuboidal
shapes is created with the objective of maximising the annual
irradiation incident on all buildings. The initial configuration is
shown in Fig. 3. Each building may have its height varied so that
there are in total 25 parameters:
f~
x 2 R25 jxi 2 ½0; 123; i ¼ 1; . . . ; 25g
(4)
Those parameters are the number of floors (a maximum of 123) in
each building, zi 2 R; i ¼ 1; . . . ; 25. The parameters are rounded to
the nearest integer before the evaluation and the floors are
considered to be 3m high each. Simulating all possibilities would
require 12425 evaluations of the solar potential, which is not
feasible.
To reduce the cost of the evaluation process to a reasonable
minimum, reflected radiation is ignored.
The constrained parameter space is defined by the total built
volume remaining within 10% of half of the maximum
(25 40 60 123 3=2 10% m3). The constraints expressed in
mathematical terms give:
vð~
xÞ vð~
xmax Þ 50% 110% 0
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
(5)
g 1 ð~
xÞ
xÞ þ vð~
xmax Þ 50% 90% 0;
vð~
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl
ffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
(6)
g 2 ð~
xÞ
where ~
xmax ¼ ð123; . . . ; 123Þ and vð~
xÞ is the volume corresponding
to parameters in ~
x. We thus have two linear constraints, giving a
range of possible volumes.
2.5. The second application: a photovoltaic extension of a Mansion
An extension of a Mansion was planned as part of an
architectural studio design project, with the idea of installing
photovoltaic (PV) panels on the newly created building surfaces. In
this the objective was to orient and tilt the roof surfaces so that
they would receive the maximum available irradiation throughout
J.H. Kämpf, D. Robinson / Energy and Buildings 42 (2010) 807–814
810
Fig. 4. A RADIANCE generated rendering of the scene (left), a schematic plan (right).
the year, with reflected radiation once again being neglected for
computation reasons. The scene is shown in Fig. 4, in which the
extension is decomposed into triangles on the schematic plan. Each
triangle vertex may take a height of between 3 and 6 m. In total
there are 31 parameters:
f~
x 2 R31 jxi 2 ½3; 6; i ¼ 1; . . . ; 31g
(7)
A key constraint is that the roof must maintain a convex shape, as
observed from above. In other words, the height of each internal
point must be greater than or equal to that of the external point(s)
to which it is connected. In total there are 32 constraints, which are
not detailed here in mathematical form.
2.6. The third application: 2D Fourier series
In this hypothetical application, the idea was to use a two
dimensional (2D) Fourier series to describe the geometry of a roof
as a continuous function with relatively few terms. Once again we
seek to maximise the utilisation of solar irradiation throughout a
year, this time on both the roof and the vertical facades. For this
application, the two-dimensional Fourier series expressed in terms
of sines and cosines with N and M impairs:
ððN1Þ=2Þ
ððM1Þ=2Þ
y
x
X
X
2pikL ððNÞ=N1Þ
þ2pilL ððMÞ=M1Þ
y
x
hðx; yÞ ¼
C kl e
k¼ððN1Þ=2Þl¼ððM1Þ=2Þ
¼
ððN1Þ=2Þ
X
ððM1Þ=2Þ
X
k¼ððN1Þ=2Þ
cos 2pk
(1) Akl ; Bkl 2 ½ 12 ; 12 but A00 2 ½0; 10
(2) Akl ; Bkl 2 ½1; 1 but A00 2 ½0; 10
(3) Akl ; Bkl 2 ½2; 2 but A00 2 ½0; 10
A minimum cut value was chosen in the height of the surface at
0 m, so that when the surface goes below the ground (placed at
0 m), it is not taken into account in the irradiation calculation.
Further constraints dictate that the volume under the surface must
remain within 10% of 80% of the maximum allowed volume which
is defined by a parallelepiped of 10 m by 20 m by 30 m (i.e.
10 mLx Ly ). In mathematical form these constraints are similar to
those of the first application (Eqs. (5) and (6)).
3. Results
Akl
l¼0
x
y
þ 2pl
þ Bkl
Lx ððNÞ=N 1Þ
Ly ððMÞ=M 1Þ
x
y
þ 2pl
;
sin 2pk
Lx ððNÞ=N 1Þ
Ly ððMÞ=M 1Þ
that Ak0 ¼ Ak0 . Likewise the coefficients Bkl for l ¼ 0 are
antisymmetric with k, i.e. Bk0 ¼ Bk0 . Therefore to describe a
surface that goes through N M points, we need N ðM 1Þ=2 þ
ðN 1Þ=2 þ 1 amplitudes for Akl and N ðM 1Þ=2 þ ðN 1Þ=2 for
Bkl ; which also gives N M amplitudes.
This observation allows us to use directly the amplitudes of the
sines and cosines as parameters in the optimisation process.1
For our numerical application, the domain boundaries were
chosen to be Lx ¼ 20 m, Ly ¼ 30 m and N ¼ M ¼ 5; giving 25
parameters. The amplitude A00 is the base amplitude, which is a
constant value throughout the domain. It was chosen to vary
between 0 and 10 m. The other amplitudes are limited between a
lower and an upper limit; in total three cases are tested:
3.1. The first application: Manhattan style grid
(8)
where h : R2 ! R gives the height as a function of the position (x; y)
in the plane, x 2 ½0; Lx; y 2 ½0; Ly, Lx and Ly delimit the domain of
interest in x and y, C kl 2 C are coefficients of elements in the Fourier
basis and Akl ; Bkl 2 R are the amplitudes of the sines and cosines.
By definition, the function hðx; yÞ is periodic in x and y. The
period is T x ¼ Lx ððNÞ=N 1Þ and T y ¼ Ly ððMÞ=M 1Þ respectively
for x and y. The multiplication by the factors ððNÞ=N 1Þ and
ððMÞ=M 1Þ is introduced in order to avoid repetition in the
domain of interest x 2 ½0; Lx and y 2 ½0; Ly.
By considering the Fourier series in (8) as a backward discrete
Fourier transform we have a continuous function that can pass
through a grid of N M regularly spaced points in the domain of
interest. Such points are shown in Fig. 5, with the corresponding
backward Fourier transform superimposed (for N ¼ M ¼ 5). It can
be shown that the coefficients Akl for l ¼ 0 are symmetric with k, so
A candidate solution, presented in Fig. 6, was found after some
12,000 evaluations. Buildings at the northern edge of this grid are
all at maximum height, whereas buildings at the east and
particularly south and west edges are irregular, with some at or
approaching the maximum height and some considerably lower.
This arrangement provides solar access for the lower interior
buildings and (more particularly) for the southern facades of the
building at the northern edge.
Fig. 7(a) shows the evolution of the fitness (annual solar
irradiation) of the candidates along with the evaluations made in
the evolutionary algorithm. The CMA-ES part of the algorithm
provides a steep rise in fitness at the beginning of the simulation,
whilst the HDE part goes deeper in fine-tuning the solution.
In Table 1, we can see that the improvement gained with our
optimisation algorithm relative to two subjectively chosen
1
Note that an alternative could have been to work with the N M grid-point
heights, and to smoothen the roof with a backward Fourier transform in order to
produce a continuous and differentiable function.
J.H. Kämpf, D. Robinson / Energy and Buildings 42 (2010) 807–814
811
Fig. 5. A roof represented by a 2D Fourier series (left), a contour plot representing the height (right). All units are in meters.
Fig. 6. Optimal case for the city shape after 12,000 evaluations, on the left the model with an irradiance map in Wh, on the right a two-dimensional representation with the
number of floors of each building.
variants – the corona and stair shaped layouts shown in Fig. 7(b);
both of which satisfy the constraints mentioned earlier. Relative to
the corona shape the optimised shape (which would not necessarily
be arrived at by intuition) yields an 8% improvement for a similar
built volume; whereas relative to the star layout the improvement is
22%. This is interesting because conventional site planning guidance
suggest that buildings should be progressively stepped-up towards
the north of a site, to maximise solar access [18].
Fig. 7. The results and comparison for the small city center. (a) The fitness (solar energy potential) evolution within the evolutionary algorithm for the small city shape and (b)
corona and stairs shapes.
J.H. Kämpf, D. Robinson / Energy and Buildings 42 (2010) 807–814
812
Table 1
Irradiance values comparison for the optimised case and the corona case.
Parameters
Irradiation (GWh)
Volume (107 m3)
Stairs shape (floors are multiple of 22, see Fig. 7(b))
Corona shape (border buildings with 105 floors, internal ones with 1 floor)
Optimal values after 12,000 evaluations
282.2 (82%)
319.5 (93%)
344.9 (100%)
1.188
1.216
1.217
Fig. 8. Optimal case for the photovoltaic extension after 12,000 evaluations.
Table 2
Irradiance values comparison for the optimised case and flat roofs at minimum and
maximum allowed values (second case).
Parameters
Irradiation (GWh)
Minimum values hi ¼ 3 m;i ¼ 1; . . . ; 31
Maximum values hi ¼ 6 m;i ¼ 1; . . . ; 31
Optimal values after 12,000 evaluations
1.118 (91%)
1.131 (92%)
1.234 (100%)
3.2. The second case: a photovoltaic extension of a Mansion
For this case a candidate solution, shown in Fig. 8, was once
again found after 12,000 evaluations. Compared to flat roofs at
heights of 3 m and 6 m, the improvement is about 10% in annual
irradiation (see Table 2). With an annual irradiation of 1.234 GWh
and an average photovoltaic efficiency of 10%, the gain is
equivalent to 11.6 MWh electrical energy which is non-negligible.
Roof-integrated PV would appear to be viable in this case.
An interesting alternative to the above fitness function might
be based on the proportion of the total envelope for which
an irradiation threshold (e.g. 800 kWh m2 for facades and
1000 kWh m2 for roofs) is exceeded, as a basis of determining the
viability of solar energy (e.g. PV) conversion systems.
3.3. The third case: 2D Fourier series
The results, also after 12,000 evaluations, are shown in
Figs. 9–11. We observe that the volumes for the optimal cases
are close to the maximum allowed value of 5280 m3 (see Table
3), suggesting that the volume that intercepts rays should be as
large as possible. It is also noteworthy that in each case
depressions are created in the volume about its center and a
tendency to maximise the peaks to the north end of the building.
There seems to be an attempt, with this continuous trigonometric function, to emulate the staggered arrangement of
example 1 which maximises solar access to south facing
collecting surfaces. Note that, as with example 1, incident
irradiation on facades is also taken into account.
The dimensions Lx ¼ 20 m Ly ¼ 30 m are arbitrary and the
calculation in RADIANCE is scale free; so that the resultant forms
are equally applicable to proportionally smaller or bigger
buildings.
Fig. 9. Result for small amplitudes after 12,000 evaluations: 3D view (on the left) and contour plot (on the right).
J.H. Kämpf, D. Robinson / Energy and Buildings 42 (2010) 807–814
813
Fig. 10. Result for medium amplitudes after 12,000 evaluations: 3D view (one the left) and contour plot (on the right).
Fig. 11. Result for large amplitudes after 12,000 evaluations: 3D view (one the left) and contour plot (on the right).
Table 3
Optimal irradiation after 12,000 evaluations for roof forms defined by a Fourier series compared that of a flat roof enclosing a similar volume.
Parameters
Irradiation (GWh)
Volume (m3)
Flat roof (Akl ; Bkl ¼ 0 except A00 ¼ 8:8)
Small amplitudes (Akl ; Bkl 2 ½ 12 ; 12 except A00 2 ½0; 10), Fig. 9
Medium amplitudes (Akl ; Bkl 2 ½1; 1 except A00 2 ½0; 10), Fig. 10
Large amplitudes (Akl ; Bkl 2 ½2; 2 except A00 2 ½0; 10), Fig. 11
1.1292
1.2728
1.4075
1.6685
5280
5234
5222
5131
This methodology is equally applicable when expressing the
constraints not only in terms of volume, but also in terms of
habitable floor area. Indeed, given typical floor to ceiling height
(e.g. 3 m) we can sub-divide a volume into individual storeys,
perhaps also excluding parts of these storeys, such as at roof level
for which the floor to ceiling height is below some minimum
threshold (e.g. 1.5 m). This way of expressing our constraints may
be closer to what practitioners require.
4. Conclusion
In recent years there has been considerable interest in studying
urban forms which maximise the utilisation of solar energy within
the urban context, whether by passive or active means. The
methodologies employed thus far have been based on evaluating a
small sample of subjectively chosen configurations from within
(68%)
(76%)
(84%)
(100%)
the essentially infinite number of theoretically possible combinations. The probability of identifying an urban form which optimises
solar radiation utilisation is therefore somewhat small. To resolve
this we have used a hybrid evolutionary algorithm that was refined
in order to handle constraints. By way of example three different
problems have been investigated: a group of cuboid shaped
buildings within an urban grid; a small group of geometrically
more complex buildings adjacent to a large existing building; a
building of rectangular plan whose volume has been parameterised as a Fourier series.
From this, we have found that:
the new algorithm consistently converged to a good solution
whilst taking constraints into account,
the solar energy available for utilisation may be increased by up
to 20% (with respect to an initial subjectively chosen form),
814
J.H. Kämpf, D. Robinson / Energy and Buildings 42 (2010) 807–814
the forms of these solutions tend to be highly non-intuitive (and
correspondingly unlikely to be arrived at by subjective selection).
Concerning the latter point, it is hoped that computational tools
of this nature might provide a useful source of inspiration to
architects, from which to derive an architectural solution to a given
design problem. An alternative study that could be carried out in
the future with a similar methodology would involve solar
irradiation ‘‘minimisation’’ for hot (arid and humid) climates, in
which self shading building configurations would be profitable.
In the meantime, the algorithm described in this paper will be
integrated with a new simulation program for simulating the energy
performance (i.e. demand and supply) of urban masterplanning
proposals [17]. Optima to urban design problems may then be found
in response not only to a richer set of variables but also to more
comprehensive indicators of performance (fitness functions) such as
life cycle (embodied and operational) energy, CO2 and cost.
Acknowledgements
The financial support received for this work from the Swiss
National Science Foundation, under the auspices of National
Research Programme 54 ‘‘Sustainable Development of the Built
Environment’’ is gratefully acknowledged. Many thanks to Dr
Julien Nembrini from Media & Design Lab (EPFL) for providing the
second application presented in this paper.
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