## 1 Introduction  
In various environmental problems, global warming is a serious problem all over the world. It is considered that an increase of greenhouse gas causes global warming. Hence, many countries have conducted smart city demonstration projects for reduction of total consumption energies and CO\({}_{2}\) emission [1; 2]. Smart city is an eco-city which can realize low carbon emission and energy consumption by Internet of Things (IoT), renewable energies, storage batteries, and so on. For example, in Japan, after the Great East Japan Earthquake, introduction of the smart city was investigated, especially in Tohoku area [3]. Basically, it is difficult to evaluate the actual CO\({}_{2}\) emission reduction in the actual smart city. Therefore, a smart city model including various sector models should be utilized for the evaluation. Static models which can treat various energy balances and dynamic models which can treat dynamic behaviors have been developed separately in each sector [4; 5; 6; 7]. However, a smart city model, which can calculate various environmental and energy loads among all sectors considering environmental and energy flow among various sectors, had not been developed. Considering these backgrounds, a smart city model was developed in order to evaluate energy costs and CO\({}_{2}\) emission of the whole smart city considering environmental and energy flow among various sectors in Japan [8; 9; 10]. Using the smart city model, the authors have proposed total optimization of energy network in a whole smart city for minimization of energy costs, electric power loads at peak load hours, and CO\({}_{2}\) emission by Particle Swarm Optimization (PSO) [11], Differential Evolution (DE) [12], Differential Evolutionary PSO (DEEPSO) [13], BSO [14], MBSO [15], GBSO [16], and GMBSO [17]. In addition, considering energy facility characteristics, energy load characteristics, cost characteristics, and continuity of weekday operation of various energy facilities, the authors have proposed reduction methods of search space in order to solve the problem effectively [11; 12]. Therefore, GMBSO considering the reduction of search space can obtain the highest quality solution so far [17]. However, there is still room for improvement of quality of solution. Multi-population based evolutionary computation methods have been verified to improve quality of solution [18; 19; 20; 21; 22; 23; 24; 25; 26]. Using the methods, one population with numbers of individuals is divided into several sub-populations with small numbers of individuals. Individuals at each sub-population perform solution search separately. Interaction models of multi-population can be divided into three groups: the migration model [18; 19; 21; 23; 24; 25], the abest model [20; 22], in which abest is the best searching point so far among all of sub-populations, and a model using both migration and abest. To the best of the authors' knowledge, since a model using both migration and abest has not been proposed, the authors propose the model [26]. However, the most suitable model has to be investigated for each evolutionary computation method. Considering these backgrounds, this paper proposes total optimization of energy networks in a smart city by MP-GMBSO with only migration. MP-GMBSO with migration is newly proposed in order to realize improvement of quality of solution. The proposed MP-GMBSO with migration-based method is applied to a model of mid-sized city such as Toyama city. The results of the proposed method are compared with those of the GMBSO based method with a single population, and the MP-GMBSO based methods with only abest, and with both migration and abest model.