## 6 Simulations  
### Simulation Conditions  
The proposed MP-GMBSO with migration is applied to a typical mid-sized city model referring to data of Toyama city in Japan. The numbers of models in each sector in the model are shown below. They are determined so that sector load ratios of the model are approximately the same as the sector load ratios of Toyama city [32]:  
Industry model: 15, Building model: 50, Residential model: 45,000, Railroad: 1, Drinking water treatment plant: 1, Wastewater treatment plant: 1.  
Usually, each smart city has each goal. Therefore, this paper considers the following three cases in order to consider different goals of smart cities:  
* a goal of a general smart city considering all three terms of the objective function equally, \(w_{1}:0.333,\ w_{2}:0.333,\ w_{3}:0.333\)
* a goal of an industrial park which usually concentrates only minimization of total energy cost \(w_{1}:1,\ w_{2}:0,\ w_{3}:0\)
* a goal of local government of a city which usually concentrates only minimization of CO\({}_{2}\) emission. \(w_{1}:0,\ w_{2}:0,\ w_{3}:1\)  
The results of GMBSO based method are compared with those by the conventional DEEPSO, BSO, MBSO, and GBSO based methods. In addition, the results of the MP-GMBSO based method are compared with those by the originally proposed GMBSO based method with a single population, the MP-GMBSO based methods with only migration (the proposed method), with only abest, and with both migration and abest.  
The following parameters are utilized for conventional DEEPSO:  
* 0.2, \(\tau^{\prime}\): 0.006, \(p\): 0.75, the initial weight coefficients (A, B, and C): 0.5, the number of clones: 1.
* The following parameters are utilized for conventional BSO, MBSO, GBSO, and GMBSO:  
* 0.5, \(p_{generation}:0.5,p_{OnCCluster}:0.2,p_{TwoCluster}:0.2,pr:0.2\) (for MBSO, GMBSO), \(c_{max}:0.7\), \(c_{min}:0.2\) (for GBSO and GMBSO).  
The following parameters are utilized for the conventional and the proposed MP-GMBSO based method.  
* The initial weight coefficients of each term (D) is set to 0.5,
* The number of sub-populations (NumSubPop): 2, 4, 8, and 16,
* The total number of individuals (NumInd): 1280 (640 individuals/sub-population for 2 sub-populations, 320 individuals/sub-population for 4 sub-populations, 160 individuals/sub-population for 8 sub-populations, and 80 individuals/sub-population for 16 sub-populations), 640 (320 individuals/sub-population for 2 sub-populations, 160 individuals/sub-population for 4 sub-populations, 80 individuals/sub-population for 8 sub-populations, and 40 individuals/sub-population for 16 sub-populations), 320 (160 individuals/sub-population for 2 sub-populations,  
20 individuals/sub-population for 8 sub-populations, and 10 individuals/sub-population for 16 sub-populations), and 80 (40 individuals/sub-population for 2 sub-populations, 20 individuals/sub-population for 4 sub-populations, 10 individuals/sub-population for 8 sub-populations).
* Migration topology: Ring with various numbers of sub-populations (see Figure 7a-d), trigonal pyramid (\(MT_{T}\)), cube (\(MT_{C}\)), and hyper-cube (\(MT_{H}\)) (see Figure 8a-c),
* Migration interval: 10 to 100 in 10 increments,
* Migration policy: _W-B_, _R-B_, _B-B_, _W-R_, _R-R_, _B-R_, _W-W_, _R-W_, _B-W_.  
The following parameters are utilized for all methods.  
* The number of trials: 50
* The maximum iteration number for BSO, GBSO, MBSO, and GMBSO based methods: 2000
* The maximum iteration number for DEEPSO based method is set to 1000  
The conventional DEEPSO based method evaluates the objective function twice at each iteration for both new and clone individuals. Therefore, the maximum iteration number for DEEPSO is set to be half in order to keep the same number of objective function evaluation among all methods. Initial searching points are randomly generated for all methods. The simulation software has been developed using C language (gcc version 4.4.7) on a PC (Intel Xeon E5-2660 (2.20 GHz)).