遺伝的アルゴリズムを用いた最適制御問題の数値解法

抄録

Direct methods utilizing nonlinear programming such as SQP (Sequential Quadratic Programming) are frequently used as a numerical method for optimal control problems. Although they have advantages in terms of the computational robustness and the usefulness for practical problems, it is usually difficult to select appropriate initial solutions. Therefore, GA (Genetic Algorithm) has become popular as a global search method without particular attention in selecting initial solutions. Since original GA solves the unconstrained optimization problem, the penalty function approach is utilized to handle the constraints. However, the estimation of the appropriate penalty parameter is so difficult that good convergence property is seldom obtained. Therefore, this paper proposes a new selection method, which introduces the multiple criteria, i.e., the distance of the genes, the performance index, and the penalty function. Through the application to the simple test problem and to the ascent trajectory optimization problem of a space plane, it is demonstrated that the proposed method can simultaneously and effectively achieve the global search of the performance index as well as the feasibility search, and it can provide an excellent initial guess for the direct method using nonlinear programming.