Capability of Global Search and Improvement in Modal Trimming Method for Global Optimization

Abstract

A global optimization approach named "Modal Trimming Method" has been proposed to derive suboptimal solutions for equality constrained nonlinear programming problems. To obtain a tentative suboptimal solution, a local optimal one is searched by a conventional gradient method. To improve the tentative suboptimal solution, a feasible one is searched by an extended Newton-Raphson method. In this paper, it is shown that the capability of global search for feasible solutions is obtained by the behavior of solutions with the chaos, and the mechanism for its occurrence is clarified. The method is revised to prevent the trap into local optimal solutions because of the behavior of solutions with the cyclic vibration. The method is also extended to consider inequality constraints including upper and lower limits for variables as well as discontinuous feasible regions. The method is applied to various test problems, and it turns out that the method has a high possibility of deriving the global optimal solutions as the suboptimal ones for a wide range of problems.