A New Evolutionary Decision Theory for Many-Objective Optimization Problems

In this paper the authors point out that the Pareto Optimality is unfair, unreasonable and imperfect for Many-objective Optimization Problems (MOPs) underlying the hypothesis that all objectives have equal importance. The key contribution of this paper is the discovery of the new definition of optimality called ε-optimality for MOP that is based on a new conception, so called ε-dominance, which not only considers the difference of the number of superior and inferior objectives between two feasible solutions, but also considers the values of improved objective functions underlying the hypothesis that all objectives in the problem have equal importance. Two new evolutionary algorithms are given, where εdominance is used as a selection strategy with the winning score as an elite strategy for search -optimal solutions. Two benchmark problems are designed for testing the new concepts of many-objective optimization problems. Numerical experiments show that the new definition of optimality is more perfect than that of the Pareto Optimality which is widely used in the evolutionary computation community for solving many-objective optimization problems.