1、554 2009 ASHRAEA simulation/optimization tool has been developed to design building shell that minimizes energy use costs associ-ated with heating and cooling systems. The tool couples an optimization algorithm to a building energy simulation engine to select optimal values of a comprehensive list o
2、f parameters associated with the envelope of residential buildings including the building shape. Three optimization methods are utilized including genetic algorithm (GA) approach, sequential search technique, and particle swarm technique. In this paper, the performance in terms of accuracy and effic
3、iency of the three optimization approaches was compared for various sets of building envelope parameters. For relatively large search spaces, it was found that the GA could identify the minimum cost point to with an accuracy of 0.4% using 60% of the simulations required by sequential search techniqu
4、e and only 40% of the simulations needed by the particle swarm optimization method.INTRODUCTIONIn order to reduce building energy consumption most effectively, heating and cooling loads due to the building enve-lope must be addressed early in the design process. Several design parameters can have an
5、 effect on these loads, including the shape of the building, wall and roof construction, founda-tion type, insulation levels, window type and area, thermal mass, and shading. All of these parameters interact and affect the energy performance of the building. Traditionally, this type of analysis has
6、been done with parametric runs using a building simulation engine such as DOE-2 (Winkelmann, 1993) or EnergyPlus (Crawley, 2000). However, varying one parameter while leaving others building envelope features constant can potentially miss important interactive effects, and full combinatory parametri
7、c studies are usually infeasible. A better solution is to couple an optimization algorithm to a simulation engine in order to find a minimum for a given cost function including life-cycle cost, annual operating costs, and annual energy use (Wright, 2002; Caldas and Norford, 2003; and Ouarghi and Kra
8、rti, 2006). The objective of this paper is to compare three different optimization techniques to assess their robustness and effi-ciency for application in building envelope optimization. Robustness is a measure of the algorithms ability to minimize the cost function, while efficiency is a measure o
9、f its speed which is defined in this study as the number of simulations required to reach the minimum cost level. The three methods investigated in this paper include the sequential search used in the Building Energy Optimization or BEopt tool (Andersen, et al. 2004), genetic algorithms or GAs (Gold
10、berg, 1989 and Haupt and Haupt, 2004), and particle swarm optimization or PSO (Wetter, 2006). Each of these methods does not require the calculation of differentials for the cost function, but instead uses discrete values of the cost function to determine the parameter values of the next iteration (
11、i.e. direct search).DESCRIPTION OF OPTIMIZATION APPROACHESOne approach to classify optimization techniques is by the nature of the problem search spacecontinuous or discrete. The character of the parameters affecting building envelope optimization lends itself to discrete optimization. A few paramet
12、ers, such as aspect ratio, orientation, and window area could be considered continuous, but almost all other parameters have a limited number of discrete options. For example, there are a finite number of available wall types for a realistic construction situation. It would be possible to opti-Compa
13、rative Analysis of Optimization Approaches to Design Building Envelope for Residential BuildingsDaniel Tuhus-Dubrow Moncef Krarti, PhD, PEAssociate Member ASHRAE Member ASHRAEDaniel Tuhus-Dubrow is a graduate student and Moncef Krarti is a professor and associate chair of the Civil, Environmental, a
14、nd Architec-tural Engineering Department at the University of Colorado, Boulder, CO.LO-09-052 2009, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2009, vol. 115, part 2. For personal use only. Additional reproductio
15、n, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission.ASHRAE Transactions 555mize on continuous R-value, but the chance that the optimum solution would correspond to an existing wall type is very small. The same is true of paramete
16、rs such as window type, foundation type, roof type, and shape. Continuous optimization methods include the Nelder-Mead simplex method, Hooke-Jeeves method, and various gradient-based approaches (Nash and Sofer, 1996). Because of the discrete nature of the envelope optimization problem, these continu
17、ous techniques were not investigated. Discrete optimization methods include global techniques such as genetic algorithms, simulated annealing, tabu search, and particle swarm, as well as direct search techniques such as the sequential search used in BEopt (NREL, 2007). For this study, genetic algori
18、thms were compared to the sequential search, and the particle swarm method was used to validate results. Sequential SearchThe sequential search technique used in BEopt is a direct search method that identifies the building option that will best decrease the cost function after each successive iterat
19、ion (Christensen et al., 2005). It begins by simulating a user-defined reference building. It then runs a simulation for each potential option one at a time. The most cost-effective option is chosen and used in the building description for the next point along the path. There are a number of discret
20、e options in differ-ent categories such as azimuth, aspect ratio, wall type, and ceiling insulation. The most cost-effective option is defined as the one that gives the largest reduction in annual costs for the smallest reduction in source energy use. Annual costs are a combination of mortgage costs
21、 (which increase as more expensive energy-efficient options are included) and utility costs. The process is repeated, ultimately defining a path from the reference building to the minimum cost point, and then to a zero net energy building. Without modifications, this simple algorithm would not relia
22、bly find the correct least-cost path, due to the problem of interactive effects between different options. Three special cases have been identifiedinvest/divest, large steps, and positive interactions (Andersen et al., 2006). The invest/divest case is a result of negative interactive effects. In thi
23、s case, BEopt removes options which may result in a more cost-opti-mal point. For example, a highly efficient HVAC system may have been selected as the most cost-effective option at an early point in the process. Later in the search process, however, the improvement of the building envelope may caus
24、e the efficient HVAC option to not be cost-optimal, so it is removed from the building design. The large steps case is another example of negative interaction among options. There may be a large energy-saving option that is available at a current point, but is less cost-effective than another option
25、 that does not save as much energy. The latter option is chosen, and then the most cost-effective option is again chosen at that second point, which results in a third point. However, it is possible that the original large energy-saving option available at the first point is more cost-optimal than t
26、he third point. In order to solve this problem, BEopt keeps track of points from previous iterations and compares them to the current point. If a previous point is more cost-optimal, it replaces the current point. A positive interaction occurs if two options are more cost-effective when present toge
27、ther than they would be if considered separately. An example could be the presence of both large south-facing windows and thermal mass for passive solar heating. BEopt will only find these positive interactions if one of the options is first selected individually. This inability to always identify s
28、ynergistic options is a potential deficiency with the sequential search method. Genetic AlgorithmsGenetic algorithms (GAs) use the evolutionary concept of natural selection to converge on an optimal solution over many generations GAs (Goldberg, 1989 and Haupt and Haupt, 2004). They differ from tradi
29、tional optimization methods in a number of areas. First, rather than working with one potential solution at a time, the technique works with a set of solutions called a population. This ensures a global approach to the opti-mization and helps the GA avoid getting stuck in local minima, which can be
30、a problem with other methods. Second, the GA works with encodings of the parameters, not the parameters themselves. Parameters are traditionally encoded as binary strings, although other encoding options can be used. Finally, GAs use probabilistic methods for determining the parameter values in each
31、 successive iteration, rather than deterministic rules. This means that each time a GA is run, the path toward convergence is different, and the end result may be different as well.Each individual in the population represents a different solution to the problem. Every option for each parameter has a
32、 corresponding binary representation, and the parameters are concatenated to form the complete binary string. A new gener-ation is formed at the end of each iteration, consisting of a new population, and this process is repeated until satisfactory convergence criteria are reached, or the maximum num
33、ber of generations is reached. The algorithm uses only three opera-tors to produce a new population for the next generation - selection, crossover, and mutation. There are a number of different ways to handle selection. One method is to rank the population in ascending order by fitness value (after
34、the cost function is evaluated for each indi-vidual), and assign probabilities for selection based on each individuals rank. This is called rank weighting. A virtual roulette wheel is spun (by generating a random number between 0 and 1) to determine the members in the new popu-lation selected for re
35、production. Once the population for reproduction is selected, the indi-viduals are paired off and “mated” using the crossover process. A crosspoint is selected at random for each pairing, and two new individuals are created by joining the first part of the first string with the second part of the se
36、cond string, and vice versa. Mutation is the last step in the formation of the population for the next generation, and involves flipping a bit 556 ASHRAE Transactionsat random in the population from a 0 to a 1 or vice versa muta-tion is intended to prevent the GA from converging prema-turely and hel
37、ps to maintain a global search. The mutation rate is set at the beginning of the algorithm. Finally, this mutated population becomes the population of the next generation, and the process is repeated until convergence is reached. Particle Swarm OptimizationParticle swarm optimization (PSO) was chose
38、n as the third optimization method because it is the simplest technique to implement that can deal with discrete options. PSO shares many similarities with genetic algorithms (Kennedy and Eber-hart, 1995). Like GAs, the technique works with a set of solu-tions called a population. Each potential sol
39、ution is called a particle. Instead of using evolutionary methods, however, the PSO is based on the social behavior of bird flocks or fish schools. Each particle is characterized by a velocity with which it explores the cost function. The velocity and position of each particle are updated after each
40、 successive iteration of the algorithm. The particle velocity and position are governed by equations (1) and (2):(1)(2)where:v = particle velocityp = particle position r1,r2= independent uniform random numbers between 0 and 1c1= cognitive acceleration constantc2= social acceleration constantplocalbe
41、st= best local solution (best particle in current population)pglobalbest = best global solution (best particle so far in all generations) The two acceleration constants are usually numbers between 0 and 4. The particle swarm optimization has become popular for the same reasons as the GA, in that it
42、is easy to implement with relatively few parameters to adjust. EVALUATION METHODOLOGYIn order to test the different optimization techniques, and validate them against each other, three test cases were carried out these consisted of “small”, “medium”, and “large” opti-mizations, described in more det
43、ails later on in the following section. The accuracy and the efficiency of genetic algorithms are compare to the sequential search and the particle swarm method.The sequential search technique was tested using BEopt, a software tool available from the National Renewable Energy Laboratory (NREL, 2007
44、). The particle swarm method was implemented using GenOpt (Wetter, 2006). GenOpt is a generic optimization program that can be used to minimize an objective function evaluated by an external simulation program. The genetic algorithm was programmed in MATLAB. Building FeaturesThe basic features of th
45、e residential building used throughout the comparative analysis are shown in Table 1. It consists of a typical detached single-family home commonly used in the Building America Program (Hendron, 2004 and 2006). The economic parameters used in the comparative analysis are shown in Table 2. All the pa
46、rameters that are not optimized had the fixed values shown in Table 3. The lifetime for all options was set to 20 years.DISCUSSION OF RESULTSThe optimization results for the small and large test cases are described in details below for the sequential search, genetic algorithm, and particle swarm opt
47、imization methods. The results for the medium test case are summarized at the end of this section (refer to Figure 4). The cost function that is minimized is the annual cost of the mortgage plus utilities for the building. The annual mortgage cost consists of the addi-tional cost of building compone
48、nts relative to the reference building, divided by the mortgage period. The costs of build-vnewvoldc1r1plocalbestpold()c2r2pglobalbestpold()+=pnewpoldvnew+=Table 1. Building CharacteristicsParameter ValueLocation Boulder, COFloor area 1800 ft2Number of floors 2Number of bedrooms 3Number of bathrooms
49、 2Wall height 8 ftGarage NoneRoof FlatTable 2. Economic ParametersParameter ValueElectric rate: Marginal 0.08 / kWhElectric rate: Fixed $8 / monthNatural gas rate: Marginal $0.80 / thermNatural gas rate: Fixed $8 / monthProject analysis period 20 yearsElec. Source/Site ratio 3.0Gas Source/Site ratio 1.0ASHRAE Transactions 557ings components such as wall insulation and window glazing are obtained from RS Means (2007).Small OptimizationThe small optimization test case investigated four param-eters, each with four discrete options. The four parameters and associated options are liste
