Convergence properties of E-optimality algorithms for Many objective Optimization Problems

In the paper, for many-objective optimization problems, the authors pointed 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 and propose a new evolutionary decision theory. The key contribution is the discovery of the new definition of optimality called E-optimality for MOP that is based on a new conception, so called E-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 for E-optimal solutions are proposed. Because the new relation <_E of E-dominance is not transitive, so a new way must be found for consideration of convergence properties of algorithms. A Boolean function better used as a select strategy is defined. The convergence theorems of the new evolutionary algorithms are proved. Some numerical experiments show that the new evolutionary decision theory is better than Pareto decision theory for many-objective function optimization problems.