Effective hierarchical optimization using integration of solution spaces and its application to multiple Vehicle Routing Problem

Hierarchical optimization is an optimization method that is divided the problem into several levels of hierarchy. In hierarchical optimization, a complex problem is divided into simpler sub-problems, and each level is optimized independently. Several hierarchical optimization techniques have been proposed, including the hierarchical genetic algorithm (HGA). HGA is organized by multiple genetic algorithms, thereby the computational cost becomes huge depending on the problem. Moreover, the same solution space is searched many times at the upper level, and an unnecessary computational cost takes. In this paper, we propose a new effective searching technique using integration of solution space for hierarchical optimization. The proposed method is based on the Hierarchical multi-space competitive Distributed Genetic Algorithm (HmcDGA), which was proposed by the authors, and the duplicate solution space is integrated at the upper level. The probability of finding optimal solution is improved at lower level, because the population size becomes large by the integration of the solution space. We apply the improved HmcDGA to the multiple Vehicle Routing Problem (mVRP) and show the effectiveness of the proposed method.