A meta-optimization problem for global optimization and its solution by the Genetic Algorithm

This paper describes the application of the Genetic Algorithm for finding the best initial starting point in order to search the global solution by means of a local optimization algorithm. The optimization by means of currently used algorithms such gradient methods presents two phases of task. The first task is to select an optimization method that is suitable for application to the problem. The second is to choose the parameters initializing the selected algorithm, e.g., the initial starting points and/or parameters in termination rules, in order to obtain the best computational performance. Often the choice of these parameters can have impact on the computational results. The problem of optimizing the parameter of an optimization algorithm represents metalevel optimization. In this paper, the problems requiring the starting point which can lead a local optimization routine to the global optimum are considered as metalevel optimization problems, and the Genetic Algorithm as a metal-algorithm is applied to the meta-problems. The several experimental results indicate that the Genetic Algorithm has effectiveness as a metal-algorithm for global optimization. [In Japanese.]