Evolutionary strategy for enhanced design of architecture, optimization

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The purpose of the present experiment consists in optimizing a building modifying its apertures (windows) and its geometry to reduce heating and air conditioning consumption. The optimization is performed using a Micro-Genetic Algorithm (Micro-GAs) programmed in C# embedded like a series of functions into GenerativeComponents (GC). EnergyPlus (E+) software is used to evaluate the HVAC consumption levels of the building. The aim of the optimization is to keep the temperature at 20ºC on the hottest and coldest day using the least possible energy (Jules). In conclusion, this article proposes a new technique based on parametric modelling, evaluation and evolutionary optimization to generate efficient buildings with HVAC consumptions.

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Introduction

Genetic Algorithms (GAs) were proposed and developed by John Holland in 1960s (Mitchell, 1996). A GAs is a programming technique which imitates the biological evolution as a strategy to resolve problems and/or search design that fits certain conditions. This paper explain in deep how can GAs can be applied to design optimized architecture. There are many books and literature about Genetic Algorithms and Evolutionary Computation. For further information please visit: [1 – 5].

Definition of the problem

Nowadays, one of the main problems in architecture is the HVAC consumption in the buildings. The problem to face up in this work consists in reducing the heating and air conditioning modifying the geometry and the windows’ positions and sizes. This problem is considered a multi-objective problem because both parameters are related and we cannot minimize one of it without increasing the other.

For example, if we have a big window, in summer the sun will heat all the pieces of furniture hence it will increase the temperature in the room and therefore, we will have to turn on the air conditioning to keep the room at 20ºC. The good news is that we can take advantage of the natural light for more time, and we can also refresh the house at night releasing the heat trapped on the walls by radiation during the day. In winter, the same window will capture the heat, but unfortunately all the heat will be lost very quickly because it will escape through the same window where it enters. Therefore, we will have to turn on the heating quickly and the worst is that all the heating produced will continue escaping trough the window increasing the heating consumptions.

If we reduce the window to the minimum possible size, what will happen during the summer is that we will not be able to release the heat trapped on the walls, so we will have to keep the air conditioning switched on for more time to cool the room and logically we will not be able to take advantage of natural light as much as when we have the big window. Besides, as we have a small window he will have to turn on the light earlier and since the artificial light heats, we will have to release this heating of the room too. In winter, the same small window will not heat the interior of the room and we will have to turn on the heating almost all the day and probably the night. In addition, we will have to turn on the light because the sunlight within the building will not be enough because winter is darker than summer.

To sum up, a large window performs well in summer and presents a very bad behaviour in winter. On the contrary, a small window will be a complete nuisance in summer, but it will have a better performance in winter. Therefore, the problem is not to enlarge or reduce the window to achieve a single parameter, but to find the optimum that balances both behaviours.

There is an extra help for this problem such as the possibility of modifying the geometry of the building which will allow us to search and explore creative solutions and to obtain better performances that will be out of reach if we only change the windows’ position and size.

This research pretends to be a seed in the contribution to the pursuit of sustainable development proposing an architectural design’s system to reduce the air conditioning and heating consumption by searching the best possible shape applying a Genetic Algorithm. The solution of the problem consists in answering the following question: Which is the best building’s geometry and windows’ configuration to keep the temperature at 20º during the hottest and coldest day of the year in order to consume less energy?.

Contributors and previous work

Many Scientists, engineers and architects have been working and experimenting with evolutionary techniques in the form finding of architecture. For further information please visit: [5 – 8]. Nevertheless This work is based on the paper “Architectural Constraints in a Generative Design System: Interpreting Energy Consumption Levels” by Luisa Caldas and Leslie Norford at the Seventh International IBSA conference in Rio de Janeiro, Brazil in 2001[9].

In that paper, the researchers encoded one of the buildings of the School of Architecture in Oporto-designed by Alvaro Siza- to apply a Genetic Algorithm to optimize daylight and energy consumed to heat and to cool the building. They used this building as test bed and its windows’ geometry as a framework to modify and explore different configurations during the iterations of the algorithm. To evaluate the HVAC consumptions they use DOE-2.1E which is a building simulation program and a Micro-Genetic Algorithm (Micro-GA), which is not described in depth.

This work is based on a parametric model to constrain some relations of the building, to avoid failures in reports during the process of evaluation and to encode in a simple way the parameters of the building. A Micro-GA is used to search and optimize the geometry, although it presents some variations in comparison to the traditional way to build this algorithm. Other aspects to comment on are that the population is very small -5 individuals per generation- and not more than 15 generations are used to obtain the results. This work is programmed basically in C# in two different levels. The top level corresponds to GCScript, which is applied to control the geometry and manage the different classes to compose the GA and transactions files between GC <-> E+. And the bottom level, which is pure C# directly written in visual Studio 2008 and embedded into GC through a series of functions. The programming language C# is used to perform the hard tasks such as gaining speed during the process, developing the whole GA and carrying out all the transaction files between the programs. Finally, the evaluation of the building is performed by Energy Plus, which is the evolution of the software used by Caldas and Norford.

Method

This section consists of the explanation of how the whole process works, which is divided into the description of the parametric model into GC, the explanation of the thermal model into E+ and the description of the classes and how they are related to create the GA.

Parametric Model

The model is a perpendicular box to the north, composed by 6 flat surfaces and two windows. One of the windows faces east and the other west. The measures of the box are 12 meters in the X direction (east – west), 10 meters in the Y direction (north – south) and 4 meters high.

The first step of the construction consists in 4 parameters called coordXSrfWest, coordYSrfWest, coordXSrfEast and coordYSrfEast. These parameters are used to control the geometry of the box. The second step is to define 3 points. The first point lives in the center of the box (point01) and the others two are defined by the previous parameters and are named ptWest and ptEast. The Z coordinate of the three points is a fixed value that keeps the surfaces flat, otherwise E+ will not perform a correct analysis.

Two vectors (ByOriginDirectionPoint()), are defined from point01 to the points ptEast and ptWest. These vectors are used to host also two planes (ByDirectionAndDistanceFromOrigin()), one for the east side and the other for the west side. These planes host two coordinate systems (OnPlane()) at their bases and two polygons are created through a GCScript code . The windows are also generated by GCScript and their size depends on the flat surface dimensions (It cannot be bigger than the flat surface that contains it) and coordinate systems as origin. The rest four polygons are defined by the vertices of the original polygons.

Parametrizing a model needs a double effort, on one side you have to know exactly what you need to avoid extra steps in the generation and lose speed. On the other side, you must know which of these parameters constraints are and which of them are flexible. Once the model was parametrized it is tested under much iteration to observe the behaviour and detect possible bugs.


Figure 1 (The model with the geometric elements to build the shape.)


Figure 2 (Testing model after 200 iterations in which is possible to observe the different geometries that are able to support.)

Thermal Model

The thermal model corresponds to the other information that we need to describe the building. This data is necessary because it sets the physical characteristics such as where the building is located, the type of weather, which material the walls have, if the windows are double or simple and etc. This information and much more are defined in the E+ file.

The important part in this model is that the geometry (behavior) is defined and manipulated into GC and the physical characteristics (properties) are defined into E+. The correspondence between the two files must always be the same. For example, if in the IDF (EnergyPlus file) appears 6 flat surfaces the model must return always 6 flat surfaces.

The principal characteristics of the model into E+
Building location: Country terrain, Chicago IL.
Windows: Double Panel window with an interior camera of 3 mm.
Walls: Wood siding outside, fiberglass quilt in the middle, and plasterboard in the interior.
Roof: Roof deck outside, fiberglass quilt, in the middle and plasterboard in the interior.
The floor is defined by: Thickness(m): 0.10, Conductivity(W/m-K): 1.7296, Density(kg/m3): 2243.0, Thermal Absorptance: 0.9, Solar Absorptance: 0.65, Visible Absorptance: 0.65
The HVAC system used is a standard configuration: Heating Supply Air Temperature(C): 50, Cooling Supply Air Temperature(C): 13, Heating Supply Air Humidity Ratio(kg-H2O/kg-air): 0.015, Cooling Supply Air Humidity Ratio(kg-H2O/kg-air): 0.01
The output variables are defined into E+. In this case, the report corresponds to the consumption of heating and cooling during the hottest and coldest day of a year.

Classes

Two types of classes are written in C# in this research, one kind of classes is used for technical tasks, such as reading and writing files, calculating the distance between points and lines, exporting to excel, saving files, executing a program, sleeping the program and etc. The other type of classes performs the GA, in those we found the traditional genetic operators such as mutation, crossover, fitness function, selection and replace.

Technical Classes

The main technical classes into the GA are GCScriptFuncVerticesToIdf.cs, GCScriptFuncSleep.cs and GCScriptFuncReadSolution.cs. The class GCScriptFuncVerticesToIdf.cs transforms the polygons’ vertices in a list of strings, then extracts the information of the IDF file and replaces the old vertices for the new ones saving the file with the new data loaded. After this and through the class System.Diagnostic.Process, E+ is called to perform the thermal analysis with the new loaded geometry. This class is embedded into GC as a function called runSimulation().

The class GCScriptFuncSleep.cs sleeps the application for a couple of seconds meanwhile the analysis is performed and the new files are created.The class GCScriptFuncReadSolution.cs extracts the report analysis of the E+ and calculates the average of the consumptions, which is divided in three different values: the average heating consumption, the average cooling consumption and the average of the temperature in the building. Those values are returned into an array. This class is embedded into GC as a function called readDataSolution(). Its results are very important because these values are used as the fitness functions into the GA. The aim is to reduce these values as much as possible. Once the data is returned to GC another average is calculated to obtain a single value instead of the three original ones.

Genetic operator’s classes

Once the first series of classes is performed in order to create the first population, it is time to jump over the genetic operators. The first operator called in the code is CSChromosome.cs. This class takes the ptEast, ptWest, the two windows and its HVAC consumption (fitness) and decomposes the data in an array of 31 elements. At the end of the class the chromosome presents this structure as it is shown in Figure 4. The chromosome is saved in the population array and the fitness is printed in the console script. This class is embedded into GC as a function called genrChromosome().


Figure 3 (The chromosome is constituted by a list of doubles. From 0 to 14, the data on the list belongs to the east side and from the 15 to 29 to the west side. The last value (30) is the fitness which represents the HVAC consumption.)

After the population is created, the next operator that is applied is the CsnaturalSelection.cs. This operator is in charge of sorting the different chromosomes in the population from the best to the worst. Since we are working with very small population: Only 5 candidates per generation, the Roulette-wheel or other types of natural selection are not performed. What this class returns is the same population sorted from the “best” (the lowest HVAC consumption) to the “worst” solutions (the highest HVAC consumption). This class is embedded into GC as a function called pfrmElitism().

The next step produced into the GA is the crossover in which the best two solutions exchange part of their chromosome to constitute a new possible solution which inherits the properties of their parents. Since we are working with a small population this operator presents some differences in comparison with other traditional crossover systems. Several tests were made creating the crossover. For example, if we split the chromosome in two stripes and recombine them to produce two offsprings, this type operators will produce a rapidly convergence to a local minimum and stop the optimization at the second iteration. However, this kind of operator is very useful in other types of problems. Therefore, it is only necessary to create a new possible solution with the position of ptEast and ptWestpoints and the windows’ polygons which are related to the geometry that is generated randomly in order to avoid local minimum. Since we are working with only 5 generations it is necessary to explore all the possible solutions during this small period of time in which the GA runs.

At the end, the offspring is the coordinates of ptEastand ptWestpoints. This class is embedded into GC function under the name pfrmCrossOver(). The offspring and the best solution in the previous population are conserved for the next generation; nevertheless the offspring incorporates a very small mutation in its X and Y coordinates.

The class in charge of performing this mutation is CSMutation.cs. The mutation depends on a factor called MutationPercent and the best results in consumption set this value around 0.5. What it is done to perform the mutation is to calculate a random value between 0 and 1 (double r = Random.NextDouble()). Then, the MutationPercent is added and subtracted from the coordinate of a point to find a maximum and a minimum value:

double high = offspring [i] + percent, double low = offspring [i] – percent (1)


Figure 4 (Parent1 and Parent2 involved in the class crossover are split to create a new offspring. Random choices are made to define which types of offspring are returned. Windows data and HVAC consumption are discarded in this operator.)

After that, a simple equation is performed in order to save in the chromosome the new coordinates’ values:
offspringMutate[i] = low + r * (low – high) (2)

After the mutation is performed, the mutated offspring and the best solution are stored into the new population and 3 more possible candidates are generated randomly in order to complete the size of the population. The process is repeated N times or a stop condition can be defined by a consumption threshold.

Results

For this research, the GA system was tested 14 times with the same data environment and the same number of generations -5 in total-. Our results were that in 6 tries the GA optimized in all 5 generations, in other 6 the system was unable to optimize in one and finally in the other two, the algorithms were unable to optimize. The average consumption at the beginning of the generations in the 12 successful generations was: 1139.0286 w/h. The average consumption after the optimization was: 970.7155 w/h. The reduction represents the 17.21% less of consumption during the hottest and coldest day of a year. The best individual in all tests was: 840.4193.

Geometry

In relation to the geometry, the best results have some similarities. For example, the parameter coordXSrfEast was always around 10 in the best solutions, and the coordYSrfEast was always low, less than five. Something similar happened with the west side, coordXSrfWest was always within -5 and -12 and the coordYSrfWest was represented with low values between around 5 and -1, but only two times the values rose to 6 and 7.


Figure 5 (The figure shows the 12 successful tests where the optimization was performed. It shows the initial and final consumptions.)

Discussion

The results show that the system performed in most cases very good results decreasing the consumptions of HVAC levels around 17%. Before the GA performed, the coordXSrfEast parameters were higher than ten in all the cases and the coordXSrfWest parameters were low. This means that a big space will logically need more consumption to keep the temperature at 20ºC than a small one. For the coordYSrfEast and coordYSrfWest parameters, the values are in general high, which means in geometry that the two surfaces facing east and south receive the sun directly in the morning and in the afternoon. This type of geometry will increase the cooling consumption in the hottest day, and if the windows are big the consumption will be a complete disaster for the coldest day too.

The best solutions in general have low values in the coordYSrfEast and coordYSrfWest coordinates which means that the shape is folded to reduce the area exposed to the east and west. The Y values control the orientation of the building determining how much of the area is exposed to the sun. These small values indicate that the east and the west surfaces are facing south direction. For the coordXSrfEast, the values are around 10 and for the coordXSrfWest are around -6 and only in one of test -12. The X values basically determine the size of the building such as the length of the building that pulls in both surfaces’ directions to face east and west. A big value to the east and small value to the west mean a large building. These parameters affect directly the total volume of the building and as a consequence it influences the performance of the HVAC consumption.


Figure 6(Perspectives of the 12 tests where the optimization was successfully performed.)

Since this experiment was focused on the manipulation of the geometry, the windows were always left at random sizes and positions. However, it is possible to observe some similarities among the windows in the different tests. For example, in all the cases the GA preferred small windows located near the edges of the surfaces instead of a center big window as the architects prefer. Another special feature was the disposition of the windows. The east windows were always disposed on the right side of the surface and in the west it occurred exactly the same. Nevertheless, if we look at the building from the east to the west directions, the building has the east windows on the right side and the west windows on the left side in the best test. The GA in almost all the cases proposed for the east side bigger windows than for the west side. Besides, the east windows in almost all the cases are vertical meanwhile the west are horizontal. The GA disposed 10 times the west window near the roof and proposed high and horizontal windows, but the east windows were left more freely generating windows near the floor and in only 4 cases near the roof. When this type of windows’ configuration occurs the GA reduces the consumption by decreasing the total volume of the building.

The GA in all the cases tried to reduce the total volume of the building and fold their geometry facing the east and west surfaces to the south (10 times) or to the north (twice). It never faced the east or west surfaces directly. The GA tried to capture more energy from the east than from the west proposing bigger windows for the east side 9 times. In general, the system left the east side with big windows at medium height and the west side with small horizontal windows near the roof.

Conclusion

The GA was able to generate out of 14 tests 12 possible solutions with low energy consumption levels. This makes the building more sustainable which is an issue that concerns the architectural discipline. Small consumption are reflected in the budget of the building monthly, which is related to the cost that is, another issue that concerns the architectural discipline.

The minimum size of the windows was not constrained. In some cases, the GA proposed the geometry of the windows with minimum sizes, which can represent an uncomfortable spatial relationship between the interior and the exterior of the building. Therefore, this issue should be revised in the next works.This simple thermal analysis takes a typical laptop about 3.7 seconds to perform. This analysis generates all the documentation necessary to read the solutions and gives the geometry the situation of the HVAC consumption. This time consumption is ideal and a normal GA with a population of 30 individuals and 300 iterations will be the best idea too in contrast to the system proposed in this paper. Nevertheless, the focus of this research points to big scaled projects, where the analysis may take more than1 hour. For example, 5 individuals per 5 generations are at least 25 hours of computing costs. This is the main reason to propose this GA. The system in this stage is still under development, and some features must be checked. For example, when a new population is replaced, goods reports recommend the use of individuals with good fitness that were saved in previous generations instead of generating new ones completely randomly (Zitzler, Kalyanmoy, Thiele and Coello, 2001). In previous stages of development, different genetic operators were tested (mutation, crossover and natural selection) without good results. One of the main problems with small populations is to fall in minimum locals. In other words, the high power of inheritance in a complete crossover (windows and parameters) stops the optimization in the second or third generation falling directly in minimum locals.

For further  information, please visit A.I. IN DESIGN section.

References

Mitchell, M., 1996, An Introduction to Genetic Algorithms, Cambridge, Massachusetts,
Zitzler, E., Kalyanmoy, D., Thiele, L. and Coello Coello, C.A. 2001, Evolutionary Multi-Criterion Optimization, Springer-Verlag, Zurich,.
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