A Generative Design System for Low-Energy Architecture Design ...

A Generative Design System for Low-Energy Architecture Design L.G.Caldas Departamento de Engenharia Civil e Arquitectura Room 3.46, Instituto Superior Técnico Av. Rovisco Pais, 1049-001 Lisboa, Portugal Ph: : + 351 218148346 Fax: + 351 218148344 E-mail: [email protected]

ABSTRACT: This paper presents a novel Generative Design System that applies goal-oriented techniques to help architects in the creation of low-energy architectural solutions. The system uses a Genetic Algorithm as a search engine, and the DOE2.1E building simulation software as the evaluation module. Three different applications are discussed. The first section researches the incorporation of architecture design intentions into the generative system, using a building by architect Alvaro Siza as an experimental platform. In the second part, the system capabilities are expanded to handle multicriteria problems, resorting to Pareto optimization concepts. Finally, the system is applied to three-dimensional shape generation, to investigate formal configurations with a high degree of adaptation to the exterior environment.

1 INTRODUCTION The field of Artificial Intelligence has provided designers from different areas with new possibilities that reach far beyond the mere use of computer simulations to assess design performance prior to actual construction. Goalbased design allows researchers and practitioners to invert the standard development direction of defining a solution, simulating its performance, and progressively refining it by means of sequential, parametric simulations. Using inverse-design methods, it is possible to establish performance goals, and apply search procedures to backtrack and determine which design features may lead to the closest achievement of the desired targets. Architecture and structural engineering have only recently started to embrace the advantages offered by diverse AI search methods, mostly reverting to the application of Genetic Algorithms and Simulated Annealing, which significantly improve on previously available techniques like linear and non-linear optimization, dynamic programming, and others. In the area of structural analysis, Shea (1997, 1998) applies Simulated Annealing [SA] to the optimization of geodesic-like domes. In this approach, the representation of structures is based on an analogy with a network, where design elements are joints and the relations between them represent the flow of forces through the structural members. Finite-element analysis is used to calculate the performance of the structure. Dome designs are based on triangles, which can be divided, joined, etc. Shea et al. (1997) first proposed a planar truss grammar, and only later Shea & Cagan (1997) developed a space truss grammar, which is used

to generate geodesic-like domes. The system applies shape-modifying rules in a dynamic, probabilistic way, and also size modification rules that alter, for example, the cross section of structural elements. Initial user specifications include number and location of supports, materials properties, and if symmetry is required or not. Constraints relate to structural stress, Euler buckling and geometric obstacles, among others. The objective functions that can used include efficiency [achieving minimum mass], economy [minimum number of distinct cross-sections and distinct lengths], utility [maximum enclosure space with minimum surface area], and even aesthetics [achieving a uniform metric or a golden ration metric]. The final objective function value is calculated as a weighted sum of the objective functions chosen, plus a weighted sum of constraints violation. The main flaw of this method is that it stills allows the generation of solutions that are not structurally viable. Monks et al. (1998) used a combination of SA and steepest descent to optimize the acoustical performance of architectural spaces such as auditoria, by setting acoustic performance targets and then backtracking from there. Variables used relate to physical characteristics of the space, like room geometry [tilt of reflectors and other surfaces], and materials properties. The objective function is a combination of six acoustical measures. Performance is calculated by a simulation software that uses an hybrid method of simulating early sound with beam tracing and late sound with a statistical approximation. The desired acoustic performance is set a priori, and the material and geometric parameters of the environment are determined by the optimization algorithm in order to approach that goal.

1

Within the area of low-energy architecture, work by others includes the GenOpt software for optimization purposes (Wetter 2000), which uses the Simplex method of Nelder and Mead with an extension by O'Neill. The main drawback of this search method is that it works well only in small problem sizes, up to about 10 variables. Radford used dynamic programming as early as 1978 to select window size and glazing materials to minimize energy consumption in a space, but the method was ineffective because the functions were non-separable. More recently, previous attempts to use DOE-2.1E to optimize design parameters of buildings include using regression analysis on data created by parametric DOE-2 runs (Sullivan et al. 1992). Simplified procedures like the LT method (Baker & Steemers 2000) use energy graphs to explore the impact of a few key building-design parameters but are unable to handle the level of detail and complexity enabled by the system presented in this paper. GAs have been used in building applications related to energy consumption mostly to optimize the sizing and control of HVAC systems (Huang et al. 1997, Wright 1996, Dickinson et al. 1995). 2 SYSTEM DESCRIPTION The Generative Design System presented [Plank] applies inverse-design methods to the search of lowenergy architectural solutions, by considering such key factors as the use of natural lighting, subsequent savings in artificial lighting, thermal behavior of the building, and its annual energy consumption. Development and testing of the system has been described elsewhere (Caldas & Norford 2000; Caldas & Rocha 2001). Plank couples a search procedure [Genetic Algorithm] with a building simulation software [DOE-2.1E], allowing hundreds of design alternatives to be evaluated, while requiring from the user only the effort of creating the initial DOE-2 input file. The evolution of design alternatives is guided by objective function values [in the simplest case, decreasing annual energy consumption]. Plank has both a method for creating new designs, a procedure to evaluate them, and a mechanism to evolve solutions towards improved performance. A GA was chosen as the search mechanism due to its flexibility regarding problem structure, and because it manipulates in parallel a population of solutions. This is particularly appropriate to architectural design, as the final output is not a single solution, but a number of highperformance alternatives that the architect can further develop by considering other criteria not included in the initial search process. A GA starts by generating a population of random solutions, evaluates their fitness [objective function], and subsequently applies the basic genetic operators of reproduction, crossover and mutation. This generates a new population with higher average fitness than the previous one, which will in turn be evaluated. The cycle is repeated for a user-defined number of generations. For more information on GAs, see Goldberg (1989). 2

DOE2-1E was chosen as the simulation engine because it provides a good compromise between accuracy of results and reasonable computational time, and because it incorporates both lighting and thermal analysis. Those aspects are interdependent when designing elements such as fenestrations, and a software that considers only one of them, even if in a more detailed way, would not be as useful a design tool as one that does a more holistic building analysis. In this study, even when annual energy consumption is used as the single objective function, that value incorporates both space conditioning and lighting energy. Better daylighting use is expressed as lower artificial lighting consumption. 3 EXPERIMENTS 3.1 Incorporating language constraints From the early stages of system development, it was clear that Plank would only be accepted by practitioners if it could handle the complexity of real-word applications, and if it could provide architects with the possibility of incorporating design intentions and architecture language into the system. The latter was a particularly sensitive point, and was the basis for the research described in this section. To investigate the integration of architectural design intentions into Plank, the first application area was the design of building facades. Studying an existing building was the approach chosen for these experiments. The School of Architecture at Oporto, designed by architect Álvaro Siza, was used as a test bed because the clear but complex composition rules used in the elevations provided an excellent framework to work upon. Due to the large dimension of the project, the study focused solely on one of the studio buildings, tower H [see figure 1].

Figure 1 – Southeast view of studio towers. Tower H is in the foreground

Tower H was chosen for this study for its rich spatial configurations and use of a variety of architectural light sources: fenestrations of different proportions and sizes facing distinct orientations [some including overhangs], zenithal light from roof monitors in the top floor, and a

loggia in the south façade [see figure 1]. From a computational perspective, tower H also presented some challenging features. The internal relations between the different spaces and their light sources give rise to a multiplicity of interactions that are hard to predict, and make the resort to computational analysis an interesting option. The fact that Tower H mainly houses studio teaching rooms also makes a strong case for the careful control of natural light in order to maintain adequate daylighting levels for drawing tasks while precluding direct sun over the drafting tables and excessive solar gains in the rooms. The objectives of these experiments were twofold: first, to study the incorporation of language constraints into the generative system, so that solutions generated are within certain design intentions; second, to examine the results generated by Plank from the perspective of the existing design by Siza, an architect well known for his control of light, and to analyze to what extent the inclusion of factors other than light [like the thermal performance of the building] could make solutions follow a different path. The generative system works on a complete threedimensional description of the building, including its geometry, orientation, spatial organization, construction materials, etc. In this study, building geometry, space layout and construction materials were left unchanged, and the algorithm’s search space related only to elevation design solutions. For the existing building layout, Plank generates a population of façade solutions that take into account the use of daylighting, artificial lighting, and energy used to condition the building. Although maximum use of natural lighting is a desirable goal, the control of heat gains and losses introduces a balance point to be achieved. It is this elusive balance point that the computer tries to locate. For each individual space in Tower H where daylighting is available, two lighting reference points were selected [typically the furthest points from the windows where a certain light level was to be achieved] and desired illuminances values were specified according to the type of occupation and tasks performed. Generally, 500 lux were used for studios and other working spaces and 150 lux for service areas. The artificial lighting system is supposed to be continuously dimmable [even though in Siza’s existing building such a system is not implemented], as this provides an efficient method to measure daylight use. The GS was run for two climates with distinct characteristics, to test its capability of adapting architectural solutions to different climatic requirements while subject to the same language constraints. Apart from Oporto’s mild climate, where the existing building is located, the other climate chosen was Chicago, USA, a climate dominated by extremely low winter temperatures.

To incorporate architectural design intentions into the GS, rules derived from Siza’s original design were used. Analysis of drawings and visits to the building allowed us to infer design rules that we consider to be applicable to the existing elevations. Those rules relate both to compositional axes of the facades and to general proportions of the openings. In tower H, different rules seem to apply to each elevation, while maintaining a strong coherence in the overall design of the building and in the relations with internal spaces [for example, long horizontal strip windows are always used in the studios]. This interpretation of existing design rules was followed by the determination of search areas for the generative mechanism, implemented as constraints to the algorithm. Those are bounded by maximum and minimum dimensions the openings can assume, and those limits were made sufficiently broad to allow for a significant search space that could promote the emergence of a rich variety of solutions. Other constraints implement the compositional axes determined during the analysis stage. In figure 3, the upper row represents the constraints applied. Compositional axes are shown in lighter lines. For each opening, the smaller area represents the lower bounds to the algorithm, and the larger area the upper bounds. For horizontal windows, the constraints are specified in a way that prevents the appearance of vertical openings. This set of constraints was proposed by us to control the generation of solutions within certain architectural intentions that we relate to Siza's design. Changing the constraints would allow for the exploration of many different design solutions, a path not pursued in this work. Once the constraints were graphically determined, they were used as inputs to the generative system. After the GS finished running, results from the search process could be inspected using an existing visualization program, to relate each design solution to a corresponding energy consumption profile. 3.1.2 RESULTS Results from the GS ranged from an almost exact coincidence with Siza’s solutions to some radical departures from the existing design. Figure 2 displays three-dimensional models of both Siza’s and the best solution found by the GS. Figure 3 shows the elevations of some representative GS solutions, including constraints used and the existing design.

3.1.1 ANALYSIS OF EXISTING BUILDING Figure 2 - 3D models of Siza’s and GS solutions. The images on the left show northeast views, with Siza’s on the left and GS on 3

the right. The images on the right show southwest views, with Siza’s on the right and GS on the left.

In the north façade, the large horizontal stripes generated by the algorithm very approximately resemble those created by Siza [except for the melodic variations in height in the original design], demonstrating that in Oporto’s mild climate the use of natural light in the studios clearly offsets heat losses through the large glazing areas, as Siza may have predicted. It can be observed in figure 3 that as the quality of solutions decreases [oporto_best, oporto_average, oporto_worst], north window sizes decrease too. Towards the west, the GS used small window sizes as Siza did, even further reducing them. This was due to the lower illuminance levels that the service areas [stairs and restrooms] require and to the reduced size of the spaces. As the openings get larger, the quality of solutions decreases. In the south orientation, the generative system solutions present more significant modifications in relation to the existent. In Siza’s design, the second and

third floors have south facing studios with long horizontal windows shaded by 2-meter deep overhangs. The algorithm solutions tend to suggest these overhangs may be too deep. When the overhang depth is kept as 2 meters [oporto_best], window sizes assume the largest dimensions allowed by the constraints. The deep overhangs block the admittance of daylight into the room, and to counteract that effect the GS increases the openings size. When overhang depth is a variable [oporto_shading], the algorithm reduces it to 0.5m, and also reduces window sizes to a dimension closer to that used by Siza. The shallower overhangs still manage to block direct sun and high solar gains, since in the hottest months the sun is high in the south quadrant and can be controlled with smaller overhangs. On cold winter months, when the sun is lower in the sky, useful solar gains are still admitted into the rooms, reducing the need for heating. It should be added that the oporto_shading solution has lower energy consumption than oporto_best. Figure 3 – Oporto solutions

In the 6th floor, the GS solution for the south-facing loggia must be analyzed in conjunction with the roof monitors. The 6th floor is basically occupied by a single space, lit from above by two roof monitors, from the south by a loggia window, and with blank walls in all other directions. The GS increases the south-facing loggia window to the maximum allowed by the constraints, and reduces the glazed area of the roof monitor that lights the space closer to the loggia (see figure 4). The roof monitor faces north and is a large source of heat losses in winter, particularly because warm air rises to the glazed areas. Increasing the south opening permits reducing the roof monitor without losing too much daylight in the studios. On the other hand, the second roof monitor assumes the largest dimensions possible in the GS solution [as in Siza’s design], since that area of the sixth floor has no other light source. This result suggests the tilt of the roof could be varied to allow for a larger roof monitor in that location, and is the basis for further experiments described later in this section.

Figure 4 – GS solution for the larger roof monitor, viewed from the outside [left]. Existing solution viewed from the inside [right].

The 4th and 5th floor south solutions must be analyzed together with east results, since in those floors the 4

studios share both south and east openings. The GS increases south-facing windows in relation to the existing design, and simultaneously reduces east-facing ones. East orientation is unfavorable due to high solar gains during the morning in summer months and reduced daylighting levels during the afternoon for most of the year. South-facing openings perform better both in terms of natural light admission and control of heat gains. When the algorithm has the possibility of trading between the two options, it consistently favors south. Figure 3 shows that as the size of east facing windows increase, the quality of solutions decreases. However, when the algorithm was allowed to place overhangs in the east façade too [oporto_shading], it significantly increased window sizes in the second floor, while placing quite deep overhangs to shade the low morning sun. It should be noted that the studio in the second floor has only east-facing windows. For the studios on the 4th and 5th floors, which have both eastand south-facing windows, the GS kept east openings small [although slightly larger than in the unshaded case] with shallow overhangs, and again privileged southfacing openings. Table 1 shows annual energy consumption levels for the several solutions represented in figure 3. For Oporto’s climate, the worst solution found by the GS has about 26% higher energy consumption than the best solution with shading as a variable. Siza’s design consumes about 10% more energy than the best GS solution with shading added. Finally, Figure 5 shows results broken down by energy end-use: lighting, space heat, space cooling, ventilation fans and others (pumps, etc.). Solution oporto_best_shading oporto_best oporto_average oporto_existent oporto_worst

MWh 87.58 89.99 96.22 96.45 110.55

Table 1 – Annual energy consumption for Oporto solutions

MWh

To further analyze daylight patterns in the space, a lighting simulation program that combines radiosity with ray-tracing was used to visualize both the existing and GS solutions at some representatives days of the year [solstices and equinoxes]. The room simulated was the 4th floor studio, a space where the GS could trade off between south and eastfacing windows, to try to understand the mechanisms behind the final choice. Figure 6 shows the renderings for the summer solstice at 9am, 10am, noon and 3pm. The GS solution shown is the best solution without using shading as a variable. From the figure it can be seen that, during the summer, the large unshaded east-facing windows in the existing solution allow direct sun penetration in most of the room during the morning. In the GS solution, although both windows are still unshaded, the southfacing one allows significantly less direct sun into the room, and the east-facing window is used only to light the back of the room. In the afternoon, the existing solution becomes quite dark, while the GS solution presents higher and more evenly distributed light levels.

Figure 6 – Comparison of existing and GS solutions [summer solstice, 9am, 10am, noon and 3pm]

120

100

80

60

40

Others

20

Vent fans Space cool Space heat Lights

0 oporto_best_shading

oporto_best

oporto_average

oporto_existent

oporto_worst

Figure 5 – Energy consumption levels for Oporto solutions

3.1.3 LIGHTING SIMULATIONS

To further investigate daylight patterns during the afternoon, illuminance contours in lux were produced (figure 7). In Siza’s solution, daylighting levels never achieve the specified setpoint of 500 lux. In the furthest corner from the windows, light levels are only around 200 lux. The same location, in the GS solution, has a daylight illuminance level about 4 times higher. In general, the GS solution achieves quite high luminance levels throughout the space. Close to the south-facing windows, illuminance levels may even be too high, but this could be solved by placing a shallow overhang over the south window, as the GS did when it was allowed to use shading devices as variables. 5

Chicago’s cold climate. This façade-level solution may allow for an extrapolation in terms of spatial organization, suggesting that north-facing studios should be avoided in this type of climate. It is also interesting to observe that, for the north orientation, the best solution for Chicago is very similar to the worst solution for Oporto (fig. 4).

Figure 7 – Lighting levels contours for existent [left] and GS [right] solutions. Scale goes from 0 to 2500 lux.

3.1.4 SHAPE MANIPULATION A first attempt to introduce shape manipulation into the generative system is described in this section. The GS was allowed to vary the roof tilt of Tower H, and thus control the size of the rooftop monitors. This experiment was a consequence of the results previously described, which suggested that the GS would tend to change the size of the roof monitors if allowed to do so by the roof configurations. To simplify the experiments, it was assumed that the roof monitors would always cover the entire width of the building, as in Siza’s original design. The height would be determined by the tilt of the corresponding roof, as the glazed opening would have the same height as the wall. The roof tilt was allowed to vary between 10º and 45º. The northernmost rooftop had to be at least 2 meters set back from the north façade so that it could not be read as part of the elevation. Figure 8 represents some solutions extracted from those generated by the GS. The best solution is in the middle of the top row.

Figure 8 – Roof tilt solutions generated by the GA.

3.1.5 CHICAGO EXPERIMENTS The extremely cold Chicago climate originated some interesting departures in relation to Oporto solutions (fig. 9). For north-facing studios, the windows were reduced to the minimum dimensions allowed by the constraints, due to high heat losses through the glazing and to the absence of solar gains that would be beneficial in 6

Figure 9 – Chicago results

Towards the south, unshaded windows were made quite large, since they couple daylight admission with useful solar gains. However, shaded windows were reduced to minimum dimensions, as both natural light and solar gains are blocked, and heat losses prevail. When overhang depth was used as a variable, the algorithm reduced it to the minimum allowed and simultaneously increased window sizes [result not shown in the image]. It can be concluded that south shading may be undesirable in this climate. Towards the east, rooms that have only eastfacing windows received average-sized openings [1st and 2nd floors], a compromise between such positive factors as daylight admission and morning solar gains, and such negative factors as high heat losses through the glazing. For studios with both east- and south-facing windows, east openings were made quite small because once again south was preferred. West fenestration received minimum dimensions. 3.2 Applications to multicriteria problems This section presents an extension of Plank to handle multiple objective functions. Most decisions in architecture design are made considering different criteria. More often than not, those criteria are in conflict with each other. Architects are trained to consider many simultaneous factors in decision-making, but when quantitative aspects are at stake, computer approaches that help providing relevant information can prove to be particularly useful tools. The most common multicriteria optimization methods are plain aggregating approaches, combining by means of weighting factors the several criteria under assessment, to provide a single figure of merit that aims at completely characterizing the quality of a solution. The main flaw with this approach is that the final result is heavily dependent on the weights attributed to each factor, and provides little insight into performance according to each of the objectives. Pareto optimization is based on the work of Italian economist Vilfredo Pareto (1848-1923). It rejects the search for single, optimal solutions, and avoids artificial aggregations using weighting factors. Instead, Pareto

optimization supplies decision-makers with information on the best trade-offs achievable for a specific problem formulation and constraints. This information is presented under the form of Pareto fronts. The decisionmaker will then chose where in the front will the final solution be located, that is, what compromises will be made in the design. This is a particularly suitable approach to handle multicriteria problems in architecture, since there is usually no single solution that performs best in terms of all the criteria, meaning there is no ‘optimal’ solution. Optimal performance according to one objective often implies unacceptably low performance in one or more of the other objective dimensions, creating the need for a compromise to be reached. In any case, there are solutions that represent better trade-offs than others. For example, if cost of a solution is being considered against performance, the Pareto front will provide information on the best possible performance for a given cost. However, for a higher cost, a better performance may be achieved. On the other hand, it may be possible to find a more economical solution, but performance will most likely degrade. What is undesirable, in any situation, is that for the same cost one may chose a worse solution, and the determination of Pareto fronts can be instrumental in avoiding this situation. 3.2.1 PARETO GENETIC ALGORITHMS Pareto optimality makes use of the concept of dominated and non-dominated solutions. To explain the idea of a dominated solution, x dominates y if x is better than y for at least one objective function, and at least as good on all the others (Tamaki 1996). A solution is Pareto optimal if it is not dominated by any other solution. In graphical terms, this concept can be observed in figure 10, for a maximization problem with two objective functions. In figure 10, A is clearly a better solution than C, but between A and B it is not possible to immediately say which one is a better solution. A performs better than B in terms of the x axis, but the opposite is true for the y axis. A Pareto search will exclude all points of type C (dominated ones), and find only points of the type of A and B, which will form what is known as a Pareto front. To decide for one of the points in the front, the designer will later have to exert judgment and preference. In Pareto optimization, no preference information is included in the search, contrarily to plain aggregating approaches, where complete preference information is given. y 5 4

B = (2,4)

3 2

A = (4,2) C = (3,1)

1

1

2

3

4

5

x

Figure 10. Dominated and non-dominated [Pareto] solutions. C is dominated by A. Both A and B are Pareto solutions

Although GAs are most commonly used in singlecriterion problems, their implicit parallelism makes them particularly suitable for multicriteria problems, since a GA searches a population of solutions in parallel. As Pareto fronts are populations of optimal solutions, GAs prove to be adequate procedures to locate them. There are several implementations of Pareto GAs described in the literature. The one used in these experiments is a Nondominated Sorting Genetic Algorithm [NSGA] (Srinivas 1995), and includes, apart from the most common features, sophisticated ranking and niche induction techniques that ensure the whole front of Pareto solutions for a given problem formulation to be sampled, providing the user with a high degree of confidence that the best trade-offs are being located and presented. For more detailed information on these methods, see Goldberg (1987) and Srinivas (1995). 3.2.2 EXPERIMENTS WITH NSGA This section presents the use of a NSGA with Plank to help selecting construction materials for external walls, and for fenestration sizing in a building. It assumes the external finishes have been chosen, and only the materials constituting the interior of the wall are under study. The criteria considered are: initial construction cost, the building’s annual energy consumption, and environmental impact of the materials applied. The building used for the experiments was a simplified model which can be seen in figure 11. It has four similar rooms, facing the four cardinal directions. There is only one window per room, on the longest wall. Window dimensions are variables to the program. External wall materials are similar for the entire building. In the first set of experiments, two criteria were used: cost of construction materials, both for walls and windows, and annual energy consumption.

Figure 11. Schematic building layout for Pareto experiments

The list of construction materials for the GS to choose from is presented in table 2. Those materials were selected from the materials library of DOE2.1E, which contains an extensive pre-defined list, and allows the user to add ones. Sixteen materials were selected, eight with insulating characteristics (polystyrene, polyurethane and air layers with varying thickness), and eight masonry types (concrete blocks with different densities, thickness, and some perlite-filled). Many other 7

materials could be included, the choice belonging to the architect. Even though the glazing type could be variable too, it was kept constant to simplify result interpretation. The double-glazing unit used had two layers of 6mm clear glass, with a 6mm air layer. The U-value was 3.16 W/m2·k, the shading coefficient was 0.81, and the visual transmittance 0.78. Costs for the different materials were obtained by telephoning several retailers in the US, and averaging the different prices obtained. Those values are not to be considered particularly accurate ones, but they give a relative measure of the comparative costs of the different materials. In a real-world application, care should be taken in obtaining accurate values. If quantity discounts exist, they can be handled using simple if-then rules, of the form ‘if material x area is greater than y, then cost of material x equals z, else if … ‘. In general, costs per unit area of insulation materials were lower than those for concrete block. Expanded polyurethane was more expensive than expanded polystyrene. Air layer costs were set to zero. Window costs were significantly higher per unit area than any other materials. #

DOE2

Material

Thickness

1

AL11

Air layer

≤ 1.9

2

AL21

Air layer

1.9 to 10.2

3

AL31

Air layer

≥ 10.2

4

IN33

Expanded polystyrene

2.54

5

IN35

Expanded polystyrene

5.08

6

IN36

Expanded polystyrene

7.62

7

IN43

Expanded polyurethane

2.54

code

8

8

IN45

Expanded polyurethane

5.08

9

CB21

CMU, medium weight, hollow

10.2

10

CB23

CMU, medium weight, perlite filled

10.2

11

CB26

CMU, medium weight, hollow

15.2

12

CB28

CMU, medium weight, perlite filled

15.2

13

CB41

CMU, lightweight, hollow

10.2

14

CB43

CMU, lightweight, perlite filled

10.2

15

CB46

CMU, lightweight, hollow

15.2

16

CB48

CMU, lightweight, perlite filled

15.2

Table 2 - Library of DOE2 materials

Figure 12 illustrates the layout for exterior wall construction. The interior finish was gypsum board, and the exterior had 2.5 cm of mortar. Materials for the three internal layers were chosen by the GS. Material 1 represents the layer closest to the exterior. Material 2 the intermediate layer, and Material 3 the innermost one. Because some of the material options are air layers, constraints prevented materials 1 and 3 to be air layers, due to buildability issues. Figure 12 Wall construction scheme

3.2.3 RESULTS

[cm]

Figure 13 shows the search progression of the Pareto front for the Phoenix climate [Arizona, USA], from the initial population [gen 1] with points randomly scattered around the graph, to generation 100, where the Pareto front is already clearly visible. Running another 100 generations [gen 200] made only some minor improvements in the front.

cost ($)

1 4 0 0 0

1 2 0 0 0

1 0 0 0 0

8 0 0 0

6 0 0 0

4 0 0 0

2 0 0 0

gen 1 g e n 1 0 0 g e n 2 0 0

0 21

2 2

2 3

24

2 5

2 6

27

2 8 M W h

Figure 13. Pareto front results for Phoenix climate

The following step was to analyze which design configurations led to the appearance of this frontier of best trade-offs. Table 3 shows the solutions belonging to the Pareto front. The area of each window is indicated in square meters. Materials are represented using DOE2 codes from table 1. Results are displayed in ascending order according to energy consumption [KWh], with lowest energy levels first. Note that solution 2 is not Pareto optimal. # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Window areas Materias Obj. functions South East North West Total Mat 1 Mat 2 Mat 3 KWh Cost [$] 8 5 7 3 23 IN45 IN36 IN36 21682 7276 13 5 5 3 26 IN45 IN36 IN36 21787 7917 12 5 8 3 27 IN45 AL31 IN36 21793 7286 8 3 7 3 22 IN45 IN33 IN36 21824 6653 11 3 5 2 21 IN33 IN36 IN36 21986 6331 11 4 3 3 21 IN35 IN35 IN36 22051 6294 12 3 4 2 21 IN33 IN35 IN36 22158 6127 8 3 3 3 17 IN45 IN36 IN36 22175 6093 8 5 3 3 20 IN33 IN36 IN36 22215 6019 12 3 4 2 21 IN33 IN35 IN36 22241 5971 11 3 3 2 19 IN33 IN35 IN36 22278 5736 11 3 1 3 18 IN33 IN36 IN36 22426 5619 8 3 1 3 14 IN36 IN36 IN36 22464 5507 8 4 1 3 16 IN36 IN35 IN43 22499 5388 8 4 1 3 16 IN36 IN43 IN43 22550 5318 11 2 3 1 17 IN33 IN35 IN36 22607 5256 8 3 1 3 16 IN33 IN35 IN36 22623 4962 8 3 1 2 14 IN33 IN36 IN36 22647 4834 8 3 3 3 16 IN33 IN35 IN33 22791 4606 8 2 1 2 14 IN33 IN43 IN36 22819 4527 8 2 1 1 12 IN33 IN35 IN36 22915 4284 8 3 1 2 14 IN33 AL31 IN36 22983 4038 6 1 0 1 9 IN33 IN43 IN36 23698 3509 4 3 1 1 10 IN45 AL31 IN33 23879 3315 4 1 0 1 7 IN36 IN35 IN33 24026 3248 6 1 0 1 8 IN33 IN43 IN33 24269 2829 1 3 1 1 6 IN36 AL11 IN33 25430 2517 1 1 1 1 4 IN45 AL31 IN36 25438 2752 1 1 1 1 4 IN33 AL31 IN36 25622 2461 1 1 2 1 5 IN33 AL31 IN43 25857 2278

Table 3. Pareto front results for Phoenix climate

One significant point to analyze is that window costs dominate the overall cost. Thus, a main strategy of the GA to reduce costs is to decrease window size, as illustrated in figure 14, where it is apparent that the more expensive solutions have larger window areas, mainly towards the south. However, those solutions are also the ones with better energy performance. There is a strong relation between reducing fenestration size and a decrease in the building’s performance. West seems to be an exception, since even in the best solutions window sizes are small. Figure 14. Pareto front for Phoenix. Solution 1 is in the top row

In terms of wall materials, even though in the first random solutions many instances of heavyweight, masonry elements appear, in the final Pareto solutions only lightweight, insulation materials are used (in the wall sections in figure 14, the lighter hatch represents polystyrene, the darker hatch is polyurethane, and white represents an air layer). One determining factor is probably that the cost per unit area of insulation materials is lower. However, it might be expected that in a hot climate like Phoenix some thermal mass would be applied in the walls, leading to the choice of masonry materials. Instead, the GS may be using the thermal mass from the concrete floors and roofs as heat storage to dampen peak loads, allowing the walls to become lightweight, ni sulating elements. Finally, it is possible to see that the lowest energy solutions use better insulation materials, like #6 and #8. To reduce construction costs, the GS progressively starts using large air layers and lower quality insulation materials, combining that with a reduction in window sizes. It is worth noting that one of the individuals the initial random generation [gen1] already performed almost as well as the best Pareto solution in terms of energy, but its construction costs were about 33% higher. Using the Pareto front search, it was possible to achieve a similar performance while saving about 1/3 in costs. In terms of the average performance of the populations, the energy reduction from gen1 to gen100 was only 6% [from about 24.7 MWh to 23 MWh], but cost reduction was about 41% [from $8,434 to $4,965], suggesting that Pareto searches may be an effective measure for achieving similar performance levels at lower costs. Finally, there is a 19% difference between the best and worst solutions in terms of energy consumption, and a 69% difference between the highest and lowest cost, suggesting that there is a large margin for decisionmaking within the Pareto results. 3.2.4 INCLUDING MATERIALS EMISSIONS This section expands the work on Pareto fronts to include the Global Warming Potential [GWP] of materials used. Two objective functions are considered: annual energy spent for space conditioning [MWh], and Greenhouse Gas Emissions [GGE, measured in kg CO2 eq.] related to the use of a material. GGE emissions can also serve as an indicator of the embodied energy of the material. Materials used are mostly the same as in the previous experiments. The main difference is that material #4 was replaced from 2.54cm of expanded polystyrene to 8.9cm of cellulose fill, as this is considered to be an environmental-friendly insulation material, and including it in this experiment could possibly yield interesting results. The data used for GGE emissions [table 4] were appropriate for Switzerland, but it was considered acceptable to apply it in the context of this study. Once again, emissions data are not intended to be highly accurate, but to provide an approximate measure of the environmental impact of each material. 9

Materi

Air

Cellulos

Expanded

Expanded

al

layer

e fill

polystyren polyurethan

GGE

0

0.113

e

e

2.31

13.75

Cement Perlite

0.0737

0.67

Table 4. GGE emissions [kg CO2 eq./ kg of building material], Switzerland data

Figure 15 presents the results obtained for the Oporto climate, and displays very low GGE levels associated with materials used in the Pareto-front solutions. This happens because the GS uses mainly cellulose insulation for the external walls, due to its reduced GGE rate. The two solutions in the graph with the lowest energy levels use other insulation materials, like lightweight concrete blocks and expanded polystyrene, but the corresponding decrease in energy use is negligible, while the increase in GGE is significant. An additional consideration is that most wall configurations proposed by the GS have buildability and structural problems, as they are not self-supporting. Although the cellulose insulation walls could be built in a composite panel configuration, with exterior rigid panes and interior insulation, they would require an internal frame, whose cost and GGE emissions should be included in the analysis for a more correct comparison with the masonry walls. Figure 15.

Pareto front for Oporto climate, relating energy consumption with materials GGE emissions

Kg CO2 eq

In terms of window areas, and because glass has a high GGE level, the GS privileges south windows to 7000 6000 5000 4000

targets. Methodological questions are first presented, concerning the encoding of initial layouts and the emergence of new design features. Results from experiments are then presented, using Energy Use Intensity as the objective function, and also considering the use of penalty functions. To use this method, the architect defines the search space or universe of possible solutions through the use of a set of formal symbolic rules, constraints, relations, etc. Then, the GS manipulates the three dimensional geometry of the building, its space layout and window positioning and size, to approach the desired targets. 3.3.1 Parametric shape manipulation Finding simplified initial layouts that could allow for the emergence of a rich variety of formal solutions when manipulated by the GS was one of our first research questions. Determining adjacencies was perceived as a major problem, so a simple experimental layout was chosen where all spatial adjacencies were predetermined. The basic layout from where the new solutions could emerge was simply, in plan, a square divided in four similar squares [see figure 16]. In the 1st floor, this corresponded to four rooms [R1, R2, R3 and R4], which could vary in their length and width, but were constrained to have the same height. In the 2nd floor, there were four other rooms [R5, R6, R7, and R8] that could vary in height too. The tilt of the roof could vary from a flat roof to a maximum of 45º, and the roof azimuth could also vary from 0º to 90º, as shown by the arrows in figure 16. Whenever there is a tilted roof, a roof monitor with length equal to the corresponding wall is also generated. Figure 16. Basic layout for 1st and 2nd floor. Arrows show the possible directions for each roof tilt.

3000 2000 1000

gen 1 gen 200

0 22

24

26

28

30 MWh

achieve low energy consumption in the building, and progressively reduces fenestration areas in all the other facades. Only when minimum areas are reached towards the other directions does the GS make a reduction in the south openings. This strategy is repeated until minimum areas are reached in all orientations simultaneously. 3.3 3D SHAPE GENERATION EXPERIMENTS This section presents the application of Plank to the manipulation of three-dimensional architectural shape, guided by goals of daylighting use and energy conservation. Departing from an initial schematic design and a set of rules and constraints that encode the architect’s intentions, the system searches the solution space for design configurations that respond to the initial 10

This apparently simple problem has nevertheless 44 independent variables and generates about 350 dependent variables, which must all be correctly coded for the program to run without mistakes. By looking at the specificities of passing geometrical information into a heat transfer simulation program, it will be possible to understand this large number of dependent variables. The Building Description Language [BDL] used by DOE2 has three coordinate systems, namely the building, room and wall systems. To locate a new space in the overall building layout, it is necessary to correctly determine its coordinates in the building coordinate system. The building coordinate system origin (0,0,0) was fixed as the intersection point of the two axes defining the four rooms. From that reference point, it is possible to correctly locate each of the spaces, even though their dimensions are variables generated by the genetic algorithm. Using the insertion point of each room as its lower left corner, and considering the room’s azimuth [North = 0, East = 90, South = 180, West =

270], the insertion point of each space is calculated. A similar procedure was used to locate the 2nd floor spaces, with the difference that the Z coordinate was equal to the height of the 1st floor [2.8 m]. Since the height of 2nd floor rooms was allowed to vary, the Z coordinate for the roofs was variable too. Because roof azimuths were not fixed either, roof insertion point coordinates would be different if the azimuth was set to 0º or 90º. This method for handling a variable building geometry represents one of the simplest parts of the problem. When building geometry is fed into a program like DOE2, that calculates heat transfer across surfaces, other layers of information [e.g. spatial adjacencies and other topological characteristics] become crucial. In the example used, the problem was simplified by choosing a layout where space adjacencies are fixed. However, adjacencies to the external environment are not entirely described once the spaces start to be dynamically parameterized by the GA. Figure 17 illustrates the simplest example of altering just one room dimension. While in the first case there is only an internal wall between R1 and R2, in the second case a previously nonexistent exterior wall has appeared in R1. In the third case, a new exterior wall also appears, but now belonging to R2. Within BDL, the interior wall must be declared for both R1 and R2, but the new exterior wall should only be declared for the room it belongs to.

exterior walls is that they may have windows, which are determinant factors in the performance of the building. In the 2nd floor, the generation of new external walls becomes more complex, since the rooms are also allowed to vary in height. For each possible adjacency situation, four different possibilities have to be predicted, which are depicted in figure 18. In the first case, no new external wall is created for R1. In the second case, a vertical external wall appears [E1]. In the third case, a horizontal one appears [E2]. In the forth case, an L shaped external wall appears, which has to be decomposed in two pieces [E1 and E2], as shown in the figure, due to BDL format specificities. These four possibilities, that in geometric terms are quite simple, pose nevertheless a data representation problem for the generative system. Because the GS does not have a CAD interface, from which it could read information on building geometry and generate the respective BDL file, the system needs to work with a fixed-format BDL file. This file must ni clude from the beginning all the possible geometric occurrences within the problem setup.

Figure 17. Example of external walls appearing due to parametric variation of room dimensions

While in geometrical terms the interior and exterior walls may be the same vertical planes, in construction

Figure 18 – New walls in R1, according to R2 dimensions

terms those entities are usually built with different materials, and that is coded into DOE2. In terms of heat transfer they are even further different. An interior wall is just a boundary between two interior environments that are usually not very different, and thus heat transfer across the wall is small. In contrast, an exterior wall is a boundary between indoor and outdoor environments that can be very different, and thus the wall would have significant heat transfer across it. Furthermore, for the exterior wall the azimuth it faces is important, due to its relation to sun position. Another characteristic of

In this example, the most complex case would be the L shaped wall, with occurrence of both E1 and E2 components. Given this, all rooms must predict the possible existence of E1 and E2 entities. If a given entity does not occur when the genetic algorithm generates a new individual, that entity parameters and coordinates must be driven to 0. If that entity exists in the current geometric formulation, its parameter values [like width, height, and other possible information about construction materials, wall solar absorptivity, internal light reflection, etc.] must be calculated from the independent variable values, and its insertion point coordinates determined for correct positioning in relation to the space, now using the room coordinate system. For simplicity, the code prevents the appearance of windows in these external walls, whose existence is uncertain, as this would add 11

another layer of complexity to the problem. However, in a more complex problem formulation it would also be possible to predict the appearance of new openings in the newly generated facades. A similar procedure to that used for 2nd floor external walls was applied to 1st floor roofs, and exterior floors slabs of 2nd floor rooms. In all of them, the most complex case is the existence of an L shaped element, and thus all rooms must incorporate the possibility of the occurrence of this case. If any elements do not exist in a given solution, the program must drive their values to 0. Forgetting to include any of these surfaces can introduce significant errors into the search procedure, as they represent important heat transfer areas. Finally, interior walls between adjacent spaces must also be calculated. As for window size and positioning, a number of issues emerge when dealing with variable building shapes. When the building shape is fixed, it is possible to easily determine the upper bounds for window size, as those are limited by the dimensions of the exterior wall. However, if the wall size is not known in advance, it is not possible to determine that upper bound. This represents a major drawback in terms of the standard genetic algorithm functioning. In common GA implementations, the constraints for each variable are determined prior to running the program. To overcome the fact that constraint bounds are not known in advance, the constraints would have to change dynamically during the course of the program. Since this dynamic constraints GA has not yet been implemented, it was necessary to find a simplified solution to realize the experiments. This solution was to make the window width equal to wall width minus external walls thickness, thus becoming a dependent variable. In terms of height, 1st floor windows posed no problems, as wall height was fixed and constraints could be determined in advance. For the 2nd floor, the maximum window height was set equal to the minimum wall height, to ensure windows would always fit ni to the respective wall, no matter what their height might be. These simplified rules have the drawback of allowing little variation in façade design. Windows always stretch from wall to wall, and can only vary in height. This led to a certain standardization of generated window solutions, which is nevertheless counteracted by the great variety of shapes that are generated by the GS. To introduce more diversity into the experiments, and also as an useful environmental analysis strategy, window height can be driven to 0, meaning that if the GS finds that excluding a window introduces benefits in terms of overall building performance, it is allowed to do so. The location of daylighting reference points has to be calculated by the program for each generated space geometry. The rule for placing the sensors were: one sensor in the center of the space, and the other 2 meters away from the innermost walls, that is, the walls that have no windows. This tries to ensure that natural light is used throughout the space, and that it penetrates into the deeper areas of the rooms. The Z coordinate of the sensors is 0.75m, approximately desktop height. 12

Other parameters, like room area and volume, have to be calculated after the independent variable values are generated. In calculating the volume, it must not be forgotten that when a tilted roof exists, the corresponding volume under it must be added to the basic parallelepiped volume. Air volume can significantly influence the energy consumption of HVAC systems. A remark should be added about self-shading calculations. DOE2 will not calculate building selfshading unless appropriate surfaces are explicitly declared as shading surfaces. Since from the outset it is unknown what surfaces will be shading others, all exterior planes [wall, exterior floors, roofs] should be declared as shading surfaces so that they are considered as such. This can be particularly important in cases where a 2nd floor space projects over a 1st floor one, and acts as an overhang for it, influencing both solar gain and daylighting levels, or for rooms with different heights, tilted roofs, and recessed external walls in relation to adjacent ones. 3.3.2 Experiments Some initial random configurations generated by the GS using the previously described layout are shown in figure 19.

Figure 19 - Some initial random configurations.

A major concern in these experiments was that the main strategy the GS would use to reduce building energy consumption would be reducing building area. No matter how efficient and adapted to the outdoor environment a large building is, it will always use more energy than a very small building. So, the predicted outcome from experiments using energy consumption as the objective function would be a population of minimum possible dimensions buildings, with some variation in façade design. It was thus evident from the outset that building area would have to be included in the fitness function. This was implemented in two different ways. One implied the use of penalty functions related to area requirements violations, and the other used Energy Use Intensity [EUI] as the objective function, which translates energy use per unit area. 3.3.3 Penalty functions The use of penalty functions was first experimented. The strategy used was that each of the building floors should have a certain area, related to functional and programmatic requirements. The GS could assign different areas to each of the four spaces in that floor, in

the best way it found in terms of environmental performance, but the total area of the floor would have to equal a given number of square meters. The penalties were then calculated according to the amount by which that area requirement had been violated by a solution. Penalties were equally applied both for too small and too large spaces. These penalties would then be added to the original fitness value of the solution [annual energy consumption], and would degrade that fitness according to the extent the area violation. This method intended to ensure that if the GS tried to reduce floor area to a minimum so that the energy consumption would be low, a high penalty function would significantly degrade that solution’s performance and make the GS move away from it. The penalty values could vary by a large extent, since they are based on floor area calculations, and floor area is allow to vary significantly in this problem set. Each room dimension can vary between 3 m and 15 m, so room area can range from 9m2 to 225 m2. This represents already a large variation, but if those areas are aggregated into the total area for each floor, combining the four rooms, each floor plan can range from 36 m2 to 900 m2, a very significant variation. For this reason, the penalty values for solutions that seriously violated the area requirements could be quite high. The penalties were based on a required area for each floor of approximately 470 m2, which is about half of the allowed range. Following this method, the penalty for each floor area was: penalty= (abs (470-floorarea) / 470) * 70 The factor of 70 was adopted after parametric experiments, as it was found that too small penalty factors would still make area reduction the best strategy for energy savings. The penalty function method was developed because there is no formal way in genetic algorithms to constraint the outcome from a combination of variables. For example, it is possible to place upper and lower bounds in a room’s length and width, but not in a room’s area, since it is the result of a multiplication of two independent variables. Figures 20 and 21 show results for experiments using penalty functions, for Oporto’s climate. A population size of 30 individuals was used, from which only 9 are represented. The GS was run for 200 generations. Figure 20 shows six good results, and figure 21 shows three poor-performance ones. From figure 20 and table 5, some conclusions can be drawn. The values in the table show that the best solutions use different strategies to achieve low fitness values. While some stay closer to the required areas, increasing energy consumption but decreasing penalty values [#1, for example], others prefer to reduce their energy consumption levels by cutting on floor area, while still achieving a good final fitness value [#2]. Solution #

1 2 3

Fitness with no penalty [MWh]

Penalty

96 82 98

1 26 11

4 5 6

92 105 85

19 9 30

111 114 115

Table 5 - Initial fitness values in MWh [solution numbers correspond to those in figure 20], penalty for area constraints violation, and final fitness values

Solution 1 is the best. Even though it complies with area requirements, it manages to do it without greatly increasing energy consumption values, what reveals a good degree of adaptiveness to the environment. It creates elongated spaces facing south, with generous openings to this orientation, but reduced ones towards west. In general, east/west facades are smaller that south/north ones. Towards the northern side on the building, it avoids the northeast orientation, which is always unfavorable due to reduced lighting levels for most of the day, placing very small spaces in that corner. Towards northwest, it used larger volumes [even if smaller than those towards the south], and used the 2nd floor volume to shade the 1st floor west-facing opening, to control solar gains, as it did with the southwest room. In the overall, this seems a balanced and reasonable solution, and demonstrates the GS is able to create appropriate geometries for a given problem. Figure 20. Best solutions for Oporto using penalty functions. 1 is the best solution. For each building there is a SW [45º] and a NE view [225º]. Drawings not to scale.

Final fitness value

97 108 109

Solution 2 is not very dissimilar to 1 towards the south side, but towards northwest it substantially 13

reduced room areas. This generated an energy reduction, but also a quite large area penalty, which lead to a solution over 10% worse than 1. Solution 3 is not too dissimilar to 1, but has higher energy consumption even though its area has been reduced [as shown by the penalty function value], probably because of the exposed south-facing 1st floor roofs, since the 2nd floor is recessed into a terrace configuration. It also has quite larger west-facing openings. Solution 4 is interesting in that it plays with the tilts of the roofs to generate south and north lighting sources, privileges south-facing spaces, and uses projected volumes to shade 1st floor west facing windows. However, it reduces too much the north side volumes, and is penalized in terms of areas. Solutions 5 and 6 start to be more hybrid. 5 stays close to the area requirements, but has high energy consumption levels, probably due to the large glazing areas towards east and west, namely due to steep roof tilts facing those orientations. Solution 6 has a very high area penalty, and probably too big east-facing windows. Raising the issue of the interactivity between the architect’s intentions and the GS, after being presented with these initial solutions, the architect can decide what paths of exploration he is willing to pursue to achieve solutions closer to his intentions. He can decide to change some constraints, run a MicroGA to explore the neighborhood of good solutions like 1, or manually perform same changes and simply do a DOE2 simulation of the modified design to assess the impact of those changes. Looking at poor performance solutions is also an useful exercise, to assess which design feature have a negative impact on a solutions performance. In figure 21 and table 6, the worst solutions in the final population are presented. In general, these solutions not only have large penalty values for area violations, but they also show high energy consumption levels. This is mainly due to large west and east facing glazing areas from roof monitors generated by the steep roofs, and deep overhangs shading south and north openings, thus blocking daylight and useful solar gains. It should be added that the external floors were modeled with no insulation [they are just concrete slabs with an interior finish] so in general the appearance of large projected volumes is not encouraged.

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Figure 21Worst solutions in the last generation, using penalty functions. W1 is the worst solution. For each building there is a SW [45º] and a NE view [225º]. Solution #

Fitness with no penalty [MWh]

W1 W2 W3

109 113 119

Penalty for area violation

44 29 22

Final fitness value

153 142 141

Table 6 - Initial fitness values in MWh of the worst solutions [numbers correspond to those in image 21], penalties for areas violation, and final fitness values

The use of penalty functions introduced another level of complexity into the interpretation of results. The two factors [energy use and floor area violation] become difficult to isolate for result analysis. For this reason, another set of experiments was done using a different objective function: Energy Use Intensity [EUI], which expresses energy consumption per unit floor area. This way it was easier to evaluate the relative environmental performance of different solutions, independently of the overall floor area. 3.3.4 ENERGY USE INTENSITY [EUI] FOR OPORTO EXPERIMENTS Figure 22 shows results for Oporto climate using EUI as the final objective function. The best individual is solution 1, which is somehow different from the one found using penalty functions. Since in this case the GS is not asked to assign a given total area to the building, it sizes and distributes spaces in a different way. Slim, shallow, allglazed elements are used towards the south, in a configuration that resembles a sunspace. Larger spaces, of more bulky proportions, are used towards the north of the building. Those spaces have lower surface to volume ratio, and thus have less heat transfer surfaces to lose energy from. However, these deep spaces become more difficult to bring daylight into. For that reason, the GS generates quite large openings, mainly north-facing ones, [including roof monitors], but also towards east and west. In general, the proportions of the building tend to orientate the widest facades towards south and north, and the shorter ones to east and west. The best performing shapes are quite compact, with reduced exposed roof areas in the 1st floor, and few overhangs or projecting elements.

Knowing that these configurations lead to lower performance can either make the designer move away from them, or if the type of architectural language the architect is looking for somehow matches these configurations, they should be counteracted by properly insulated external surfaces, more sophisticated glazing systems, and appropriate use of shading. These solutions will usually imply higher construction costs, so if lowcost construction is an issue, the architect may try to infer from the GS results the type of shapes that lead to better performance by adaptation to the environment.

Figure 22. Best solutions for Oporto using EUI. #1 is the best solution. For each building there is a SW and a NE view.

This overall layout is kept in solutions 2 and 3, with some minor variations, but starts to suffer more significant changes as the fitness of the solutions decreases, with results becoming more difficult to interpret those intermediate solutions. Table 7 shows the fitness function values for each of the solutions shown in figure 22, in terms of EUI [kWh per square foot]. Among the six best solutions, the variation in EUI values is over 10%. Solution #

1 2 3 4 5 6

Final fitness value [EUI]

9.02 9.57 9.69 9.79 9.88 10.04

Table 7. Fitness values in EUI of best solutions [solution numbers correspond to figure 22]. EUI is in kWh/sq. ft

Worst-performing solutions help finding patterns of elements leading to poor behavior. Fig. 23 shows three poor-performance individuals, with the worst one on the left [#1]. The main characteristics of these solutions are: high surface-to-volume ratios, caused by slim, elongated shapes; exposed external surfaces, like external walls, 1st floor roofs, and floors from projected 2nd floor elements; large glazing areas facing unfavorable orientations like east and west.

Figure 23. Worst solutions for Oporto, using EUI. W1 is the worst solution.

Solution # W1 W2

W3

Fitness value [EUI] 13.18 11.85 11.79

Table 8 . Worst solutions for Oporto using Energy Use Intensity [numbers correspond to those in figure 23].

4 CONCLUSIONS This paper presents an overview of several applications of a new Generative Design System that aims at operating in early conceptual phases of the design process, to help architects in developing architecture designs that are less energy-intensive and more adapted to the exterior environment. Solutions generated by this GS must not be interpreted as definite or optimal answers, but as suggestions for further architectural explorations, building thus an innovative and promising interaction between architecture and computation. The experiments using an existing building by Architect Álvaro Siza proved the Generative System to be flexible enough to incorporate constraints that allow the architect to manipulate certain architectural design intentions, while reducing the energy consumption levels of the final solution. The close coincidence between GS and Siza’s solutions in some situations was of particular interest in showing that a close control of architectural language is possible within the GS. On the other hand, the departures from the existing design proposed by the algorithm suggest that this generative system may be a 15

useful tool in exploring multiple paths during the design process to achieve lower energy designs. Another interesting dimension of the GS is its capability to account for interactions between different elements of the building, and to make the design for each specific element dependent on its integrated role in the architectural whole. The system also proved to be able to provide alternative solutions adapted to different climatic conditions, within similar architectural language constraints. Results from the Pareto-based studies proved in general to valuable in understanding how the trade-offs between conflicting objectives influence design solutions located by the Generative System. The final algorithm implementation did successfully locate spread-out, welldefined Pareto fronts, what provided enough confidence on the results obtained. The Pareto front was usually quickly found by the GS [a similar behavior to that documented in the literature about NSGAs], and most of the computational effort was spent in small refinements of the front. This suggests computational time could be reduced if the algorithm was run for less generations, without significant loss in the quality of solutions. The materials studies were valuable in suggesting that using highly insulated walls and leaving thermal mass for floors and roofs slabs may be a cost-effective and energy-efficient means of construction. The experiments using GGE as the objective function proved cellulose insulation to be an excellent alternative to conventional insulation, both in terms of environmental impact and to achieve good thermal resistance levels. Wall thickness tends to become much higher when cellulose fill is used, but that can be turned to architectural benefit too, for example by having recessed windows in deeper facades, which would provide some free shading, and give the architect the opportunity of plastically exploiting these type of solutions. The expansion of the Pareto search method to include more than two objective functions could lead to other interesting results, and remains as future work to be developed. Finally, the shape generation experiments showed how, departing from identical initial schematic layouts, the Generative System was able to create a variety of architectural shapes that respond to the climate where they were located, both in terms of daylighting use and control of heat losses and solar gains. The use of penalty functions for area requirement violations proved to be a somewhat unstable method, as the solutions generated adopted different strategies to achieve low annual energy consumption levels. Despite the high penalty factors used, some solutions still used reduced areas to maintain small fitness function values. Energy Intensity Use provides a more reliable measure to assess the effectiveness of different building configurations, combined with specific façade solutions. Future work will also address the issue of incorporating dynamic constraints into the system, so that an extra

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degree of flexibility is added to design elements like windows, roof monitors and other light sources. This GS is not to be regarded as an optimization tool, but instead as a generative mechanism whose goals are not only to reduce energy consumption in buildings, but also to suggest alternative building configurations and work as an augmented design aid. The particular shapes generated in these experiments are a result of the initial layout, rules and constraints applied. Different initial conditions would lead to the emergence of other design solutions, suggesting this Generative System can be a powerful tool for architects to quickly study alternative low-energy designs and understand which architectural features are more decisive towards achieving desired performance targets.

REFERENCES Baker, N. & Steemers, K. 2000. Energy and Environment in Architecture: A Technical Design Guide, E & FN Spon, London Caldas, L. & Norford, L., 2000, Energy Design Optimization Using a Genetic Algorithm, Automation in Construction, Special Issue 2000, Elsevier Caldas, L. & Rocha, J., 2001, A Generative Design System Applied to Siza’s School of Architecture at Oporto, Proceedings of CAADRIA’01, Sydney, April 19-21, pp. 253264 Deb, K. & Goldberg D., 1989, An Investigation of Niche and Species Formation in Genetic Function Optimization. ICGA Dickinson, S. & Bradshaw, A. 1995. Genetic Algorithm Optimization and Scheduling for Building Heating Systems, In Genetic Algorithms in Engineering Systems: Innovations and Applications, 12-14 September 1995, pp. 106-111, University of Sheffield: Conference Publication No. 414, Institution of Electrical Engineers Goldberg, D. & Richardson, J., 1987, "Genetic Algorithms with Sharing for Multimodal Function Optimization." Goldberg, D. 1989. Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Publishing Company Huang, W. & Lam, H. 1997. Using genetic algorithms to optimize controller parameters for HVAC systems, Energy and Buildings, 26, 277-282 Monks, M., Oh, B. & Dorsey, J., 1998, Audioptimization: Goal based acoustic design, MIT Technical Report MIT-LCSTM-588 Radford, A., 1978, Some Room / Environment Optimization Models Using Dynamic Programming, Computer Report CR30, Department of Architectural Science, University of Sydney Shea, K., Cagan, J. & Fenves, S., 1997, A shape annealing approach to optimal truss design with dynamic grouping of members, ASME Journal of Mechanical Design, V.199, N.3, pp.338-394 Shea, K. & Cagan J., 1998, Generating Structural Essays from Languages of Discrete Structures. In Artificial Intelligence in Design ’98, Gero, J. S. and Sudweeks, F. (Eds). Kluwer Academic Publishers. London, pp. 365-404

Srinivas, N. & Kalyanmoy D., 1995, Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms, Evolutionary Computation 2(3):221-248. MIT Press Sullivan, R., Lee, E. & Selkowitz, S, 1992. A Method for Optimizing Solar Control and Daylighting Performance in Commercial Office Buildings, ASHRAE/DOE/BTECC Conference on the Thermal Performance of the Exterior Envelopes of Buildings V, Dec 7-10, Clearwater Beach, FL Tamaki, H., Kita, H. & Kobayashi, S., 1996, Multi-Objective Optimization by Genetic Algorithms: A Review, IEEE Wetter, M., 2000, Design Optimization with GenOpt, Building Energy Simulation User News, Vol. 21, September/October 2000 Wright, J., 1996, HVAC optimization studies: Sizing by genetic algorithm, Building Services Engineering Research and Technology, Vol.17, No.1, pp.7-14

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