抄録
There are many optimization problems in which the objective function has local minima. If we apply gradient methods to such problems, we must repeat many calculations with different initial points. Furthermore, it is not guaranteed that the solution is a true global minimum, unless the initial points are numerous and widely scattered. Recently, genetic algorithm (GA) has been receiving strong interest as a tool for solving such problems. It is a population-and generation-based probabilistic search strategy. The global minimum can be found with higher probability by GA than by deterministic methods. However, it takes a long time for convergence. To overcome those difficulties, an effective method is developed by combining GA and the clustering technique. This method consists of the following procedures. (1) Perform GA up to an appropriate generation. There is no need for calculation until convergence is obtained. (2) Apply the clustering technique to the results of (1) and determine the cluster centroids. (3) Find the minima by certain gradient methods starting with the cluster centroids obtained in (2), and take the smallest result as the optimal one. Two sample problems are solved to demonstrate the applicability of the proposed method.
