Optimizing building form for energy performance based on hierarchical geometry relation

Automation in Construction 18 (2009) 825–833

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Automation in Construction j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a u t c o n

Optimizing building form for energy performance based on hierarchical geometry relation Yun Kyu Yi a,⁎, Ali M. Malkawi b a b

T.C. Chan center for Building Simulation and Energy Studies, University of Pennsylvania, 207 Meyerson Hall, 210 South 34th Street, Philadelphia, PA 19104-6311, USA School of Design, University of Pennsylvania, 207 Meyersonl Hall, 210 South 34th Street, Philadelphia, PA 19104-6311, USA

a r t i c l e

i n f o

Article history: Accepted 13 March 2009 Keywords: Optimization Form generation Hierarchy Genetic Algorithm (GA) Integration Performance

a b s t r a c t Most current research using optimization with building performance was restricted to simple geometry. It considered the building form as a box, polygonal shape, or simple curvature, restricting its applicability and integration with the design process. Generally, geometry variables including length, height, and depth usually control the objective values such as the area and volume of the building. Using these variables, the energy consumption data or simulation results per area or volume are compared to find the optimal form of the building. In addition, the algorithms used to predict performance in most of optimization studies are rather unsophisticated. There are technical constraints that are caused by specific problems that building simulation and optimization tools currently pose. For example, one major constraint can be lack of automated comparisons between different conditions and sharing geometry and boundaries with ease of operability. If the technical constraints can be overcome, building performance will much more easily be integrated into the design process. This paper introduces new method to control building forms by defining hierarchical relationship between geometry points to allow the user to explore the building geometry without being restricted to a box or simple form. It illustrates how the methodology allows the generation of optimized site-specific building form by integrating advanced simulation and optimization algorithm. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Attempts to find building form based on performance have been the subject of many publications. Most of these publications describe evaluations based on numerical optimization. Early work includes Radford and Gero's research [1] based on methods for multi-criteria optimization using Pareto optimization to find building form based on thermal load, daylighting, cost and utility. Petzold and Zum [2] focused on heat gain due to insulation through transparent and opaque partitions. Applying the criterion of minimum heat requirement, the optimum relation between the lengths of building walls and the optimum number of floors was determined. Several architectural research projects have been conducted using multiple optimization criteria [3–7]. Adamski and Marks [8] and Jedrzejuk and Marks [9] presented solutions for buildings of a given volume and octagonal plan. The decision variables were wall lengths, building height, wall angles, window size and thermal resistance of individual external

⁎ Corresponding author. Tel.: +1 215 746 0061; fax: +1 215 746 5599. E-mail addresses: [email protected] (Y.K. Yi), [email protected] (A.M. Malkawi). 0926-5805/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.autcon.2009.03.006

partitions. Adamski [10] formulated and solved a particular case of optimization for a building with vertical walls and a plan defined by two arbitrary curves, adapting the same method used by his previous research (1993). Additionally, researches [11–13] which proposed to optimize the volume of a building in arbitrary and polygonal plan have also been conducted. Other non-numerical techniques have also been used for optimization. Caldas and Norford [14] used Genetic Algorithms (GA) to control the DOE-2 [15] program to manipulate window size and placement as a means of minimizing a single objective function (energy consumption). Recently, GA control was used with a Computational Fluid Dynamics (CFD) program to present geometry evolution, which shows a possibility of using a morphological approach in optimization, allowing the user to experience the morphing of a design based on its performance, and continuing until the architect has the opportunity to visualize the evolution of the final set of design alternatives [16]. Finally, to enhance simulation with an evaluative component, several studies have taken advantage of knowledge-based systems that emerged out of the artificial intelligence field [17–23]. Most of the above-mentioned research using optimization was restricted to uncomplicated geometry. It considered the building form as a box, polygonal shape, or simple curvature, restricting its

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for combining GA with agent-based points to manipulate the building form. GA is a stochastic global search method that mimics the metaphor of natural biological evolution. GA operates on a population of potential solutions applying the principle of survival of the fittest to produce better and better approximations to a solution [25]. At each generation, a new set of approximations is created by the process of selecting individuals (chromosomes) according to their level of fitness in the problem domain, and breeding them together using operators borrowed from natural genetics. This adapted GA process leads to the evolution of populations of individuals that are better suited to their environment than the individuals from which they were derived, just as in natural adaptation. The GA can be subdivided into three parts: population, evaluation, and reproduction. It begins with an initial population that may be a random combination of individuals. Next, it goes through a process in which each individual in the population group will be evaluated. The GA then assigns every individual a grade based on its characteristics (the function that gives these grades is called the fitness function). This fitness will be taken into account in order to decide some way of reproducing. Normally the better performing individual (with better fitness) will adapt to the new generation more than the other lower performing individuals. Part of the initial population gives place to the new population; this process is called “breeding” of the initial population. The cycle will run until some numbers of generations are completed or until some condition is satisfied (Fig. 1). To implement the GA as an optimizer for performance based formmaking, a geometrical representation that is suitable for this research must first be developed. The following section discusses this development.

Fig. 1. GA process.

applicability and integration with the design process. In addition, the algorithms used to predict performance in most of these studies were simplified. In cases when more advanced algorithms were used with optimization, these systems were not applied to form making [24]. This paper describes the development of a performance based form making optimization method. The following section describes the utilization of the method and its evaluation. 2. Optimization The Genetic Algorithm (GA) was selected as the technique for optimization. GA was investigated and the GA solution domain and the objective function for this research were developed. This section discusses the newly developed approach to control a building form by introducing agent-based points (nodes). It also presents the strategy

2.1. Agent-based representation of building form The ability to manipulate forms as objects with hierarchical relations is of great importance to developing a new representation that can be integrated with an optimization model. When introducing the deformed (3-dimension) shape to the optimum method the number of geometry variables increases, and it is difficult to relate geometry variables to optimization, which brings the issue of controlling the variables. To overcome the above challenge a new approach was developed. The new developed method introduces a point system that controls child points, Fig. 2. In this approach a point called an “agent” point controls the position of the child points; when an agent point moves from position a(x,y) to position b(x,y), that movement also changes the positions of its child points. This method allows

Fig. 2. Suggesting method for geometry optimization.

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Fig. 3. Creating a surface from points and manipulation of points by the agent point.

morphing the building form with few agent points rather than multiple individual points. The agent-base representation begins by defining hierarchical relations between points (nodes) that represent and can control the geometry. Three separate main points are necessary. These points are center point, agent point, and child point. A center point C(x,y,z) act as a pivot point of relations between agent and child points; it is used to fix the geometry from moving. An agent point A(x,y,z) is used to define the position of the child points, and child points P i(x,y,z) are the points that control a surface, which construct the building form. A child point P i(x,y,z) is represented in relation to the center point. The child point is located away from the center point with a variable displacement:

Pi ðx; y; zÞ = C ðx; y; zÞ + fPi ðx; y; zÞ − C ðx; y; zÞg

ð1Þ

where, Pi(x,y,z) child point i position C(x,y,z) child point position {Pi(x,y,z) − C(x,y,z)} displacement

from the center point to the agent point is tracked and applied to the child points (Fig. 3b). Each surface has its own agent point and for this research five agents are populated. Four agent points represent the four building facades, and one represents the roof surface. For ease of manipulation, this research assigned surface and agent points names according to their distance from the Cartesian coordinate axis origin point (0,0,0). If a surface is on the origin coordinate and aligned with the x-axis, it is called “Surface x_Low” and if a surface is aligned with the x-axis and is further from the origin coordinate compared to another surface that aligns with the same axis, this surface is named as “Surface x_high.” An agent point assigned to this surface will be named “a_X_high(x,y,z).” Thus, if a surface is aligned with the y-axis and far away from its origin coordinate, the surface is named as “Surface y_high.” The same rule applies to the rest of the surfaces (Fig. 4a). Interface points such as point P2 (Fig. 4b) are related to two surfaces. A point P2 is related with surface x-high and y-high, which means two agent points are related to point P2. Unlike P1, which is represented in Eq. (2), the point P2 has to respond to the two agent points (a_X_high and a_Y_high). This is represented as: P2 ðx; y; zÞ = C ðx; y; zÞ + fPi ðx; y; zÞ − C ðx; y; zÞg

ð3Þ

+ fa X highðx; y; zÞ − C ðx; y; zÞg

Initially, the agent point is located in the same position as the center point; if the agent point moves away from the center point the differences are monitored by the child point Pi(x,y,z):

+ fa Y highðx; y; zÞ − C ðx; y; zÞg where,

Pi ðx; y; zÞ = C ðx; y; zÞ + fPi ðx; y; zÞ − C ðx; y; zÞg + fAðx; y; zÞ − C ðx; y; zÞg ð2Þ

{a_X_high(x,y,z) − C(x,y,z)} degree of movement (agent a_X_high) {a_Y_high(x,y,z) − C(x,y,z)} degree of movement (agent a_Y_high)

where, A(x,y,z) agent point position {A(x,y,z) − C(x,y,z)} degree of movement Once the relations between the points are established, child points are used to create a surface. At least three or four child points have to be determined to construct a surface (triangular or rectangular). Five additional child points are introduced to represent a surface and to allow more control (Fig. 3a). Each of the 9 points is independent of each other, but they change their positions according to the movement of one agent point. This means that as an agent point moves from its initial position, where initially the center point is also located, the degree of movement

The movement of a point P2 in response to the two agent points and to its degree of change is larger than point P1, which only responds to one agent point. To spread or equalize the degree of changes among the points, the point P2 has to reduce the degree of changes (Fig. 5). For example, when a point is related with “n” number of agent points, then the degree of change is divided by “n”, so that point P2 is represented as: P2 ðx; y; zÞ = C ðx; y; zÞ + fP2 ðx; y; zÞ − C ðx; y; zÞg + ½fa X highðx; y; zÞ − C ðx; y; zÞg + fa Y highðx; y; zÞ − C ðx; y; zÞg = 2

ð4Þ

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Fig. 4. Agent points and surfaces (left, a). Relation of child points and surfaces (right, b).

The ratio factor is added to distinguish the degrees of change in the same surface. Even if the points are in the same surface, one point can change its degree more than others when it is necessary: ð5Þ

Pi ðx; y; zÞ = C ðx; y; zÞ + fPi ðx; y; zÞ − C ðx; y; zÞg + ½fA1 ðx; y; zÞ − C ðx; y; zÞg

+ fA2 ðx; y; zÞ − C ðx; y; zÞg + : : : + fAn − 1 ðx; y; zÞ − C ðx; y; zÞg + fAn ðx; y; zÞ − C ðx; y; zÞg = n × w

2.2. GA solution domain and object function The individual (chromosome) is the element that constructs the solution domain (genetic structure). One possible representation, which we used in this research, is a matrix format. The matrix has a size of N_ind × L_ind, where, N_ind is the number of the individuals in the domain and L_ind is the length of the genotype (g) representation of those individuals. Each row corresponds to the length of the individual's genotypes (g), which are typically binary values:

where, w

ratio factor

This representation of geometry is used to develop the GA for optimizing performance based form-making, which requires that two main elements be defined: 1) A genetic representation of the solution domain 2) An objection function to evaluate the solution domain the following section describes the definition and development of those two elements specific to this research.

(6) Representing individuals (chromosomes) in the matrix format allows ease of manipulation. This means individuals can multiply (be sorted) when they are in evaluation and reproduction stages.

Fig. 5. Points degree of movement with related agent points.

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In this research, each agent point (a) that is describe in the previous section is represented as an individual (chromosome) in the solution domain. Each agent point's position values in the Cartesian coordinate system (X,Y,Z) is the genotype: 6 6 a1;x 6 6 a2;x 6 Domain = 6 6 a3;x 4 v an;x

a1;y a2;y a3;y v an;y

7 a1;z 7 7 a2;z 7 7 a3;z 7 7 v 5 an;z

6 3 6 a1;x f1 6 6 f2 7 6 a2;x 6 7 6 6 f 7 = 6 a3;x 6 37 6 4 v 5 4 v an;x fn

a1;y a2;y a3;y v an;y

7 a1;z 7 7 2 3 a2;z 7 px 7 4 5 a3;z 7 7 × py v 5 pz an;z

of “n” number of walls (i.e. The building has “n” number of agent points), total heat flow at generation “g” is the sum of each agent point's simulation result (heat flow) value.

Rg =

n         X rg = rg + rg + : : : + rg n

j=1

1

2

ð8Þ

g generation (iteration) simulation result number of walls (agent points) g generation (iteration) each walls simulation result

Rg n rg

For “n” number of agent points and “g” generations with performance result value for an agent point (rg), the object function (F(x)) is represented as:

F ðxÞ =

      n   X rg rg rg rg = + +: : : + ir ir ir ir n n 1 2 j=1

when minF ðxÞ

The result is the object function value (f(n)) of the agent points. These values are passed to the fitness function, which ranks or scales the object function values and generates the fitness values for the selection. Changing the position of the agent points will transform the building form, allowing designers to determine the performance of the different forms by simulation. Once the solution domain is decided, the object function of the GA optimization must be determined. The object function's goal for this research is to minimize the energy consumption of the building in the context of the conditions of its physical surroundings. The goal is to minimize the heat flow between indoors and outdoors. The form of the outer building skin is the main element that is responsible for heat flow in a building. The objective F(x) is to minimize simulation results (heat flow) in comparison to the initial building form. If the “g” generation (iteration) of building form's simulation results (heat flow) are lower than the initial building simulation result then the “g” generation achieves the goal of the object function. For this research, at each generation's (iteration's) simulation, the result (heat flow) value is divided by initial building's simulation result (heat flow). This means generation (iteration) at “g” building simulation result (heat flow, Rg) is divided by the initial building simulation result (heat flow, iR). By doing this, each generation's simulation result (heat flow) value becomes a relative value in relation to the initial simulation result (heat flow). This makes the object value easier to compare between the generations. ð9Þ

where, F(x) Rg iR

ð10Þ

where,

F ðxÞ b tF ðxÞ

Rg F ð xÞ = iR

n

ð7Þ

where the rows of the matrix are the agents and the columns are the position values for the x, y, and z axes. Once the agent points (individuals) are populated in the matrix format, each agent point was used in the evaluation (f(n)) by multiplying performance value (p(i)) with each agent point (individual a(n,i)): 2

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objective function value g generation (iteration) simulation result initial simulation result

To calculate the result (heat flow) (R), each wall's simulation result (heat flow) value (r) must be added. Here, the solution domain, based on agent points, is introduced to the object function: the performance values associated with their correspondent walls in the geometry which is controlled by the agent points. So, if the building is composed

ð11Þ

when maxF ðxÞ F ðxÞN tF ðxÞ where, tF(x)

target objective result value

In order for the object function to perform properly in the domain, or search space, the constraints of the problem have to be defined. The constraints for the problem were represented as form and performance constraints. In the building form constraint, the volume has upper and lower bounds. In addition, the agent position (that controls the geometry) has upper and lower bounds. The performance constraints are associated with radiation, conduction, and convection. These elements are constrained by the wall heat flow, heat loss and heat gain; these have upper and lower bounds too. Using the same method applied above, penalties are developed by dividing “g” generation (iteration) values with the initial values (Eq. (12)).

p=

pg ip

ð12Þ

where, p pg ip

penalties g generation initial penalty values

To increase the effectiveness of the objective function, weighting factors (a, b) are applied to Eq. (11). By adding the penalties and weighting factors to the objective function, Eq. (11) is represented as:

F ð xÞ = a

n   X rg × ðp × bÞ ir n j=1

where, a, b

weighting factors

ð13Þ

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Fig. 6. Process of integrating agent base geometry modeling and GA.

Fig. 7. Different heat flow between different building forms.

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3. Integration of GA with agent-based form-making Based on the mathematical relation between agent points' positions and child points, boundaries for the model are defined. From the

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defined model information, two agent points are populated: first generation (iteration) agent points and initial (baseline) agent points. The first generation (iteration) agent points are randomly populated from the range of agent point positions. This range has upper and

Fig. 8. Energy simulation input values.

Fig. 9. Selected generation of form changes (Latitude = 42′N, a: Heat gain and loss (W/m3), b: Heat exchange (W/m2)).

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lower boundaries for generating agent points. In addition, initial (baseline) model agent points are also populated based on the information the user provides. These two agent point values are passed to a CAD model to create the two geometries for first generation and baseline building. Once the CAD model is created, information such as each child point's position values and surface area are passed to a geometry database. The values from the geometry database are used to build two geometries for Energy Simulation (ES), and used for the simulation. Next, the results of the ES simulation are used to calculate simulation-based performance values, and these values are saved in a performance value database. Both first generation (iteration) and initial (baseline) agent points position values, and their simulation performance values are passed to the evaluation processes, where the objective function calculates the first generation (iteration)'s performance by dividing it from the initial (baseline) geometry performance value. Once the object function values for each agent point are found, these values are passed to a fitness test to find the best rankings among agent points. If object function value is not satisfied, the agents' position values are passed to a reproduction (breeding process). The reproduced offspring, which the new population of agents' position values are passed to a CAD model and simulation program to generate next generation (iteration) simulation performance values. These values are then used with initial (baseline) performance values in the next iteration evaluation process. Once the iteration has reached its maximum number of generations, or the target of the object function value is achieved, the process stops and the outcome is generated (Fig. 6). 4. Evaluation of agent-based form-making with GA To evaluate the method developed, a test was conducted for a specific location with a site size of 21 × 21 m, and an initial building size of 15 × 15 m with the height of 10 m. To understand how the optimal form might change according to the local climate conditions, the evaluation was completed without consideration of the site

Fig. 11. Total energy consumption (Unit: Wh/m2).

surroundings. The result from this study was then compared to the initial building form. The objective function for the evaluation includes targets surface heat flow, heat gain, heat loss, and volume. Different forms of the outer-skin (envelope) have different total amounts of heat flow in the course of the year (Fig. 7). Using GA will generate agent position values of x, y, and z coordinates, which change the child points of each agent, and ultimately will change the form of the building. As the form of the building changes, the total amount of the heat flow will change from one iteration to another and GA will try to find the best agent positions that minimize energy flow. The simulation engine utilized was EnergyPlus. The inputs for the EnergyPlus include high level parameters (Fig. 8). The remaining detail is generated from defaults, building energy standards, and computer routines that automatically generate a complete input description (Fig. 8). Matlab was used to implement the representation developed for the GA optimization. The objective function discussed in the previous section was programmed using m-file. For manipulating geometry, this research utilized the parametric digital design system

Fig. 10. Comparison of the initial and optimized building form without surrounding (Philadelphia, PA, USA).

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called Generative Components (GC) developed by Bentley Systems [26]. Fig. 9 shows the selected form changes by the generation. In early generation stages, the degree of form change is significant as number of generations increase the degree of the form change is insignificant. Figure shows that the heat gain and loss per volume and the surface heat flow per surface area are reduced compared to the initial building form. The results demonstrate that during the summer, the optimized form has more shaded surface areas, because its south, east and west surfaces are concave. These concave surfaces are not deep enough, however, to generate shade in the winter period (Fig. 10). This optimized building showed approximately a 12% reduction of heat load per total volume compared to the initial building and 6% reduction of heat flow per total surface area. A comparison between the initial and the GA results for total annual energy consumption is shown in Fig. 11. The figures show that the energy consumption of the optimized building forms is 8.42% less overall than that of the initial building. 5. Discussion and conclusion The research explored GA as the optimization algorithm for performance-based form-making. The research developed a new representation for building geometry, controlled by introducing hierarchical relationships between points (nodes). This was used as a base to integrate modeling software with GA. The research explored GA as the optimization algorithm for performance-based form-making. The system developed was tested and the results were discussed. The developed method of representing geometry by implementing agent points (nodes) showed a novel solution for form-making. Grammar-based geometric representation allowed the generation and control of complex forms and patterns from a simple specification. The result shows that adapted GA's evolution algorithm enabled the morphing of one initial building form to new building forms better suited to their environments. The further study and fine tuning are needed to improve the developed method. The test of the representation of geometry by agent points (nodes), undertaken with simple geometry, suggested the need for a future test utilizing more complex geometries. For GA to perform better optimizations, different types of GA operators (reproduction methods, object functions, etc.) are needed to perform future tests, and to find better solutions. The possibility of the developed method can be extended. The objective of optimization tested in this research was based on energyperformance, but also building performance related to other domains such as wind speed, acoustic, incident solar radiation, etc. can be applied to the developed method. References [1] Antony D. Radford, John S. Gero, Design by Optimization in Architecture & Construction, Van Nostrand Reinhold Company, New York, 1988.

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