2レベル最適化問題に対する能動学習統合型最適化手法

抄録

This paper presents an approximate method to solve a bi-level optimization problem which is composed of an upper and a lower level. The upper level determines the optimal value of an unknown parameter in the lower level, in consideration of the lower level optimal solution depending on the parameter, based on the upper objective and constraint functions, while the lower level optimal solution is determined under the parameter assigned by the upper level, based on the lower objective and constraint functions. When the upper level can obtain only response data of the lower level optimal solution corresponding to the parameter assigned by the upper level, upper level performs optimization by composing an approximate model of the optimal response mapping of the lower level successively. The process is an integrated procedure by alternating optimization by meta-heuristics and active learning in which effective parameter data are generated for searching the upper level optimal solution successively. Results of computer simulation for simple problems are shown to confirm effectiveness of the presented integrated optimization method for bi-level optimization problems.