Effective hierarchical optimization by a hierarchical multi-space competitive genetic algorithm for the flexible job-shop scheduling problem

We propose an effective hierarchical optimize method HmcDGA.The HmcDGA not only optimizes individuals, but it also optimizes solution space.The HmcDGA can find an optimal solution at low computational cost.The HmcDGA does not require special operations for specific problems.We apply the proposed HmcDGA to the FJSP, and evaluate its effectiveness. In this paper, we propose a new optimization technique, the hierarchical multi-space competitive distributed genetic algorithm (HmcDGA), which is effective for the hierarchical optimization problem. It is an extension of the multi-space competitive distributed genetic algorithm (mcDGA), which was proposed by the authors. The mcDGA efficiently finds an optimal solution with a low computational cost by increasing the number of individuals in a solution space in which it is likely to exist. An optimization method that is divided into several levels of hierarchy is called a hierarchical optimization. Several hierarchical optimization techniques have been proposed, including the hierarchical genetic algorithm (HGA). In hierarchical optimization, a complex problem is divided into a hierarchical collection of simpler problems, and each level is optimized independently. In this way, complex problems can be solved without the need to develop problem-specific operators. However, in the conventional HGA, this results in a high computational cost because the genetic algorithm (GA) is repeated many times at upper and lower level. The HmcDGA is a hybrid of the mcDGA and HGA, and it has some of the advantages of each one; for example, the HmcDGA can find an optimal solution at low computational cost and without requiring special operations. This allows it to be applied to a wide variety of optimization problems. Therefore, the HmcDGA may become the powerful optimization algorithm that can solve various problems. In this paper, we apply the proposed HmcDGA to the flexible job-shop scheduling problem (FJSP) which is one of the complex combinational optimization problem and confirm its effectiveness. Simulation results show that the HmcDGA can find solutions that are comparable to those found by using GAs developed specifically for the FJSP, the HmcDGA is not required a lot of computational costs comparing to the HGA.