Thinking and methodology of multi-objective optimization

Multi-objective optimization is one of the most important aspects of operational research, and has been applied widely. Most of the existing research works on multi-objective optimization focused on the concrete solutions to detailed optimization problem in reality, lacking of the deep investigation on the fundamental thinking and methodology of the multi-objective optimization problem. To fill this gap, this paper studies the multi-objective optimization problem from a Chinese traditional philosophic angle. Based on the theories and ideology of I Ching, we investigate the basic thinking and methodology of multi-objective optimization, and summarize three methodological patterns for modeling and solving the problems, which are local optimization for global moderation, divide and conquer after comprehensive consideration, and combination of division and integration. Basic ideas, approaches and examples for such three patterns are introduced, and the relationships among the three patterns are discussed from both philosophic and mathematical aspects. Furthermore, for the computational solutions of multi-objective optimization problems, we summarize four thinking patterns based on traditional Chinese philosophy, which are changing thinking, fuzzy thinking, uncertainty thinking, and imaginable thinking. Algorithms that are inspired by the four thinking patterns are presented. This work seeks to study the fundamental thinking and methodology of multi-objective optimization problem from a combination angle of science and philosophy, which is expected to inspire new ideas and methods for solving the problem.