Energy and Buildings

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1 Energy and Buildings 42 (2010) Contents lists available at ScienceDirect Energy and Buildings journal homepage: 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 ARTICLE INFO ABSTRACT Article history: Received 30 October 2008 Received in revised form 24 November 2009 Accepted 26 November 2009 Keywords: Optimisation Building geometry Geometrical parametrisation Evolutionary algorithm Hybrid CMA-ES/HDE 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. 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.: ; fax: address: jerome.kaempf@epfl.ch (J.H. Kämpf). results. We conclude by discussing the relative effectiveness of this new approach as well as possibilities for increasing the scope of its application 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 m 2 sr 1 ), 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 /$ see front matter ß 2009 Elsevier B.V. All rights reserved. doi: /j.enbuild

2 808 J.H. Kämpf, D. Robinson / Energy and Buildings 42 (2010) 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 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 m 2 sr 1 ). 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 point irradiation (in Wh/m 2 ) by the corresponding sub-surface area (in m 2 ) 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 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). sup f f ð~xþj~x 2 M R n g (1) with: n 2 N dimension of the problem f : M! R objective function M ¼f~x 2 R n jg j ð~xþ0 feasible region 8 j 2f1;...; mgg; M 6¼? m 2 N number of constraints The set of inequality restrictions g j : R n! R; 8 j 2f1;...; mg includes a special case of constraints due to the domain boundaries ~ L ~x H ~ : ~ L; H ~ 2 R n. ~ L is named the lower bound and H ~ the upper 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.

3 J.H. Kämpf, D. Robinson / Energy and Buildings 42 (2010) 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 þb1:5 log ðnþc, a children population size l ¼ 4 þb3 log ðnþc, a mutation step size s ¼ 0:2 and for the HDE the rand3 strategy ([16], pp ) 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 e 2 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] 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) where g i : R n! R is a function of the parameters, ~x are the n 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~x 1 Þ; 0Þ max ðg i ð~x 2 Þ; 0ÞÞ )~x 1 ~x 2 (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 CMA- ES 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 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 R 25 jx i 2½0; 123Š; i ¼ 1;...; 25g (4) Those parameters are the number of floors (a maximum of 123) in each building, z i 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 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 ( =2 10% m 3 ). The constraints expressed in mathematical terms give: vð~xþ vð~x max Þ50% 110% 0 (5) fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} g 1 ð~xþ vð~xþþvð~x max Þ50% 90% 0; (6) fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} g 2 ð~xþ where ~x max ¼ð123;...; 123Þ and vð~xþ is the volume corresponding to parameters in ~x. We thus have two linear constraints, giving a range of possible volumes 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

4 810 J.H. Kämpf, D. Robinson / Energy and Buildings 42 (2010) 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 R 31 jx i 2½3; 6Š; 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 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: hðx; yþ ¼ ¼ ððn 1Þ=2Þ X ððm 1Þ=2Þ X k¼ð ðn 1Þ=2Þl¼ ððm 1Þ=2Þ ððn 1Þ=2Þ X k¼ ððn 1Þ=2Þ ððm 1Þ=2Þ X l¼0 A kl C kl e 2pik x LxððNÞ=N 1Þ þ2pil y LyððMÞ=M 1Þ x cos 2pk L x ððnþ=n 1Þ þ 2pl y þ B L y ððmþ=m 1Þ kl x sin 2pk L x ððnþ=n 1Þ þ 2pl y ; (8) L y ððmþ=m 1Þ where h : R 2! R gives the height as a function of the position (x; y) in the plane, x 2½0; LxŠ; y 2½0; LyŠ, L x and L y delimit the domain of interest in x and y, C kl 2 C are coefficients of elements in the Fourier basis and A kl ; B kl 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 L x ððnþ=n 1Þ and T y ¼ L y 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 2½0; LxŠ and y 2½0; LyŠ. 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 A kl for l ¼ 0 are symmetric with k,so that A k0 ¼ A k0. Likewise the coefficients B kl for l ¼ 0 are antisymmetric with k, i.e. B k0 ¼ B k0. 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 A kl and N ðm 1Þ=2 þðn 1Þ=2 for B kl ; 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 L x ¼ 20 m, L y ¼ 30 m and N ¼ M ¼ 5; giving 25 parameters. The amplitude A 00 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: (1) A kl ; B kl 2½ 1 2 ; 1 2 Š but A 00 2½0; 10Š (2) A kl ; B kl 2½ 1; 1Š but A 00 2½0; 10Š (3) A kl ; B kl 2½ 2; 2Š but A 00 2½0; 10Š 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 ml x L y ). In mathematical form these constraints are similar to those of the first application (Eqs. (5) and (6)). 3. Results 3.1. The first application: Manhattan style grid 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.

5 J.H. Kämpf, D. Robinson / Energy and Buildings 42 (2010) 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.

6 812 J.H. Kämpf, D. Robinson / Energy and Buildings 42 (2010) Table 1 Irradiance values comparison for the optimised case and the corona case. Parameters Irradiation (GWh) Volume (10 7 m 3 ) Stairs shape (floors are multiple of 22, see Fig. 7(b)) (82%) Corona shape (border buildings with 105 floors, internal ones with 1 floor) (93%) Optimal values after 12,000 evaluations (100%) 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 h i ¼ 3m;i ¼ 1;...; (91%) Maximum values h i ¼ 6m;i ¼ 1;...; (92%) Optimal values after 12,000 evaluations (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 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 m 2 for facades and 1000 kwh m 2 for roofs) is exceeded, as a basis of determining the viability of solar energy (e.g. PV) conversion systems The third case: 2D Fourier series The results, also after 12,000 evaluations, are shown in Figs We observe that the volumes for the optimal cases are close to the maximum allowed value of 5280 m 3 (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 L x ¼ 20 m L y 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).

7 J.H. Kämpf, D. Robinson / Energy and Buildings 42 (2010) 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 (m 3 ) Flat roof (A kl ; B kl ¼ 0 except A 00 ¼ 8:8) (68%) 5280 Small amplitudes (A kl ; B kl 2½ 1 2 ; 1 2 Š except A 00 2½0; 10Š), Fig (76%) 5234 Medium amplitudes (A kl ; B kl 2½ 1; 1Š except A 00 2½0; 10Š), Fig (84%) 5222 Large amplitudes (A kl ; B kl 2½ 2; 2Š except A 00 2½0; 10Š), Fig (100%) 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 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),

8 814 J.H. Kämpf, D. Robinson / Energy and Buildings 42 (2010) 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, CO 2 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. References [1] United Nations, World Urbanization Prospects: The 2003 Revision, [2] J.H. Kämpf, D. Robinson, A hybrid CMA-ES and HDE optimisation algorithm with application to solar energy potential, Applied Soft Computing 9 (2009) [3] G. Ward Larson, R. Shakespeare, Rendering with Radiance: The Art and Science of Lighting Visualization, Morgan-Kaufmann, San Francisco, [4] J. Mardaljevic, M. Rylatt, An image-based analysis of solar radiation for urban settings, in: PLEA 2000, Cambridge, UK, (2000), pp [5] J. Mardaljevic, M. Rylatt, Irradiation mapping of complex urban environments: an image-based approach, Energy and Buildings 35 (2003) [6] R. Compagnon, D. Raydan, Irradiance and illuminance distributions in urban areas, in: Proceedings of PLEA 2000, Cambridge UK, (July 2000), pp [7] R. Compagnon, Solar and daylight availability in the urban fabric, Energy and Buildings 36 (2004) [8] D. Robinson, A. Stone, Irradiation modelling made simple: the cumulative sky approach and its applications, in: Plea2004, Eindhoven, The Netherlands, [9] M. Montavon, J.-L. Scartezzini, R. Compagnon, Solar energy utilisation potential of three different Swiss urban sites, in: Energie und Umweltforschung im Bauwesen, Zurich, [10] D. Robinson, J. Scartezzini, M. Montavon, R. Compagnon, Solurban: Solar Utilisation Potential of Urban Sites, Tech. Rep., Swiss Federal Office of Energy, June [11] V. Cheng, K. Steemers, M. Montavon, R. Compagnon, Urban form, density and solar potential, in: PLEA, Geneva, Switzerland, [12] L.G. Caldas, L.K. Norford, A design optimization tool based on a genetic algorithm, Automation in Construction 11 (2) (2002) [13] M. Wetter, J. Wright, A comparison of deterministic and probabilistic optimization algorithms for nonsmooth simulation-based optimization, Building and Environment 39 (8 SPEC. ISS.) (2004) [14] J.H. Kämpf, M. Montavon, J. Bunyesc, R. Bolliger, D. Robinson, Optimisation of buildings daylight availability, in: CISBAT, Lausanne, Switzerland, (2007), pp [15] J.H. Kämpf, M. Montavon, J. Bunyesc, R. Bolliger, D. Robinson, Optimisation of buildings solar irradiation availability. Solar Energy, in press, /j.solener [16] V. Feoktistov, Differential Evolution: In Search of Solutions, Springer, [17]D.Robinson,F.Haldi,J.H.Kämpf, P. Leroux, D. Perez, A. Rasheed, U. Wilke, CitySim: comprehensive micro-simulation of resource flows for sustainable urban planning, in: Proceedings of the 11th International Building Performance Simulation Association Conference, Glasgow, Scotland, (July 2009), pp [18] P.J. Littlefair, M. Santamouris, S. Alvarez, A. Dupagne, D. Hall, J. Teller, J.F. Coronel, N. Papanikolaou, Environmental Site Layout Planning: Solar Access, Microclimate and Passive Cooling in Urban Areas, Construction Research Communications Ltd., 2000.