A Study On New Many-objective Optimization Dominance

The evolutionary multi-objective optimization algorithm has been widely used in solving multi-objective optimization problems. The existing multi-objective optimization algorithms can effectively solve the multi-objective optimization problems which have 2-3 objectives. However,when the number of objectives in optimization problems is more than 3 which is called many-objective optimization problem, the Pareto dominance based multi-objective optimization algorithms are faced with many problems. It is necessary to propose a new dominance in the many-objective optimization algorithms.Based on the ideas of linear weighted aggregation-based methods and dominance-based methods which are the two mainly framework to compare the multi-objective solution, this paper proposes a new dominance called LWM-dominance (Linear Weighted Minimal/Maximal dominance), which is proposed to relieve the rapid growth of non-dominated solution in the many-objective optimization problems. It has been theoretically proved that LWM non-dominated solution is a subset of Pareto non-dominated solution set,and the important corner solution is reserved. We also proved that the convex combination of LWM non-dominated solutions is not a LWM non-dominated solution, whch indicates the distribution of LWM non-dominated solution in the objective space.Then by substituting for the Pareto dominance used in NSGA-? algorithm, a many-objective optimization algorithm based on the LWM dominance is established to verify the corollaries of LWM dominance. Firstly, we study on the stochastic solution space to analyzing the range of objective number which LWM dominance can handle. Then, we experiment on 7 many-objective optimization problems to compare the number of non-dominated solutions in the population during the evolutionary process. The experimental results show that the LWM dominance increases the selection pressure of non-dominated in population than Pareto dominance. The LWM dominance relation also can be used to reduce the Pareto non-dominated solutions producted by the evolutionary multi-objective optimization algorithm. By analyzing the experimental results of the reduction on 14 multi-objective optimization benchmarks' Pareto non-dominated solutions, the suitable type of optimization problems is identified.