Research On MOEA In Searching Robust Optimal Solutions

Multi-Objective Evolutionary Algorithms (MOEAs) are widely applied in a scientific research and engineering practice, the characteristic of MOEAs is that the objective weights are unnecessary, and a solution set can be obtained after a run, the decision-makers can choose one solution or more in the solution set according to their preference. As the depth study in MOEAs, the performance of MOEAs is improved. However, the researches most emphasize the convergence and diversity of the algorithms, but give less attention to the robustness of algorithms. While in the engineering practice, the environment usually has some uncertainty, the robustness of the algorithms are very significant in practice.The paper aims at doing some works on robustness , the main jobs includes:Firstly, In optimization studies including multi-objective evolutionary algorithms, the main focus is placed on finding the global optimum or global Pareto-optimal solutions. However, in practice,the environment is not static,we need to find robust solutions. Due to environmental uncertainly and the lack of suitable test function, multi-objective robust optimization problem is very little research. In this paper, we have tested the performance of the algorithm in the presence of the noise through experiments. Experimental results show that the original test function is no longer applicable, we need construct robust test function.Secondly, Robust optimal solution is of great significance in engineering application. It is one of the most important and difficult topics in evolutionary computation. Monte Carlo Integral (MCI) is generally used to approximate effective objective function (EOF) in searching robust optimal solution with multi-objective evolutionary algorithm (MOEA). However, due to the low degree of accuracy in existing MCI method, the performance of searching robust optimal solution with MOEA is unsatisfactory. Therefore, we proposed to use Quasi-Monte Carlo (Q-MC) method to estimate EOF. Through lots of numerical experimentations, the results demonstrate that the proposed Q-MC methods—Korobov Lattice can approximate EOF more precisely when compared with the existing crude Monte Carlo (C-MC) method, and consequently the efficiency of searching robust optimal solution with MOEA has been improved at a substantial level.