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Table 1 shows the definedvariables with their corresponding names.• Constraints: Building envelope-related variables are aimed at tak-ing advantage of energy efficient design. Based on China’s currentbuilding energy efficiency system [22,23], the constraints of vari-ables are summarized in Table 1.• Objective functions: Since the purpose of this study is to assistdesigners to achieve comfort-energy efficiency building design,both energy consumption and thermal comfort are selected as thetwo objective functions to be optimized using the optimizationmodel.The annual energy consumption of the building is calculatedby Energyplus. In this study the expected air conditioning systemload, maintaining the thermostat Setpoint between 18 ◦C and 26 ◦Cthroughout the year is used instead of annual energy consumption.The metric used to assess thermal comfort is the percentageof thermal comfort hours throughout the year, representing thenumber of hours at indoor temperature between 18 ◦C and 26 ◦Cpided by 8760 h.3.1.2. Optimization model frameworkIn this study, the genetic multi-objective optimization algorithmhas been used to select and optimize possible design based onthe prediction of energy consumption and indoor thermal com-fort performance, and obtaining the optimal solution. As a result,the designer needs to limit the range of input variables and thentake full advantage of the computer to comprehensively comparethe different solutions. The optimization framework of this studyis summarized in Fig. 2.First a model of the model building was created in Energyplusand validated using measured data. Using this model, a databaseof cases was created and used to train and validate the GA–BPnetwork. After training and validation, the GA–BP performed fastevaluations of the building performance, with a good accuracy andwithout simplifying the problem. Finally, NSGA-II was run by usingthe GA–BP to evaluate the potential solutions.3.2. GA–BP multi-objective predicting model3.2.1. Obtaining the samples for GA–BP prediction modelThe samples are chosen by following principles: enough sam-ples, accurate samples, representative samples, and uniformdistribution of samples. Therefore, the model building for this studyis typical three-storey residential buildings [24,25] in Chongqing,China. The floor height is 2.8 m; and the floor area of each house-hold is approximately 90 m2, which is the average household floorarea in Chongqing. Fig. 3 shows the plan view of the model building.A computer model of the house was developed in Energyplus.The energy consumption and indoor thermal comfort performancein Energyplus simulation was obtained when one of the 14 variables(building floor area, building story, orientation, shape coefficient,wall heat transfer coefficient, wall thermal inertia index, roof heattransfer coefficient, roof thermal inertia index, window heat trans-fer coefficient, area ratio of window to wall for east, west, south,north direction) changed inpidually. For example, when theremaining variables were unchanged, the results can be obtainedwhen the wall heat transfer coefficient changed from 0.8 W/(m2 K)to 2.0 W/(m2 K). As a result, the other data can be obtained when theother variables change inpidually. 100 sets of data as the trainingsamples and 44 sets of data were selected as the testing samples forthe GA–BP network according to the characteristic of BP network’sgeneralization capability, and also based on these simulation data.In order to improve the accuracy and convergence rate of theGA–BP network model, the training and testing samples’ data must be normalized. The normalization method is described in the fol-lowing equation. xi is samples’ input or output parameter value, ¯ xiis a real number between 0 and 1.¯ xi= xi− min(x)max(x) − min(x)i = 1, 2, . . ., m (1)3.2.2. Design of the BP neural networkHsu [26] found that a three-layer BP neural network can solverandom function’s fitting and approximation problem. As a result,a three-layer BP neural network is adopted in this paper.
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