Designing Elementary School Districts Using a Genetic Algorithm: Case Study of Suita City, Osaka Prefecture, Japan

The purpose of this paper is to present an optimization model for designing elementary school districts using a genetic algorithm (GA) and to examine its effectiveness when compared with existing zone design methods.<br> The objective function of this model is to minimize the total distance to school. It sets the following four constraint conditions: the appropriate number of students, the maximum distance to school, retaining the continuity of each school district, and retaining the correspondence between community centers and schools.<br> There are a number of ways of solving such a (school) zone design problem: integer programming, the automated zoning procedure (AZP), the point approach GA of Bacão and Painho (PAGA), etc. The integer programming method can obtain an explicit solution but it takes a long operation time to solve a large-scale problem. The method presented in this paper is one that adapts a basic GA to the zone designing problem. Here, this method is called the Emphasizing Continuity GA (ECGA).<br> GA is inherently an algorithm that simulates the process of biological evolution. ECGA is characterized as a GA adopting the mutation based on a topologic relation between areal units. This mutation occurs near the boundary of the district.<br> I applied the model to the case of Suita city, Osaka Prefecture. The time period of the study considers school zoning issues from 2004 to 2010. The basic spatial units are cho-cho-moku (town block) divided along railways, principal roads, or existing school districts. The distance to school is measured by the road distance from centroids of basic spatial units to each school.<br> First, the performances of AZP, PAGA, and ECGA for the school zone designing problem are compared. According to the results of this experiment, only AZP and ECGA gave solutions that satisfy the constraints. AZP does not take a long time to compute, but in terms of the total distance to school, the evaluated value of ECGA is better than the result of AZP. Second, using ECGA, the model is applied to all school districts in Suita city and only to areas related to the appropriate school size project by Suita city. The solution method using these models is the ECGA. In the first case, the optimized plan decreased the average distance to school and retained the appropriate school size. In the latter case, the model was applied to four schools involved in the project. Then, it was determined whether the four schools could retain the appropriate school size, and whether some of the four should be closed, in analyzing which plan gives the best objective value. In this result, it would be difficult for the four schools to retain the appropriate school size because the distance to school substantially increased. The plan to close a school in the project showed the best objective value, and approximately matched the project plan. Thus the plan of the project is approximately equal to the optimal plan.<br> This research clarified that the ECGA is a more effective method than the existing methods for the zone designing problem. This model will prevent generating outliers in school districts. In addition, it is possible to compare the current school districts with this model because it uses the basic spatial unit based on the cho-cho-moku boundary. The result of applying this model to the school districts in Suita city is better than the current school districts. The plan of the appropriate school size project by Suita city is approximately equal to the optimal plan.