Research On Many-Objective Evolutionary Algorithm

Evolutionary algorithm is a heuristic method with group search strategy, and is ap-plied in science and industry successfully. In recent years, more and more researchers focused their attention on many-objective optimization problems, and more and more algorithms based on evolutionary algorithms have been proposed to solve those prob-lems. We have proposed two algorithms to deal with many objective problems with no constraints and with constraints respectively in this paper.1. Many-objective optimization problems have many objectives who may be con-flict with each other, so optimizing all objectives simultaneously faces many dif-ficulties, for example, we can’t compare solutions. We proposed a new many-objective evolutionary algorithm(MOEA) whose name is Pareto partial domi-nance on two selected objectives many-objective evolutionary algorithm (PPDSO-MOEA). In PPDSO-MOEA, we propose a method of choosing objectives, and only calculate the dominance relationship between solutions on the two selected objectives and then reflect this work on the choosing of parent population. The two objectives used in calculating dominance relationship between solutions are chosen through calculating the average objective distance to the best point Rpdnt and we select the two objectives with the biggest average distances. Rpoint stores the best value and is updated when new solutions come. We switch the two ob-jectives in every some evaluations to optimize all objectives and keep an archive population to store the Pareto optimal solutions. We verified its performance on DTLZ2and DTLZ4. MOEA/D, SPEA2+SDE, MyODEMR, PPD-MOEA, and an algorithm selecting objectives with random method are selected as rival algo-rithms. The experiment results show that our algorithm, PPDSO-MOEA, outper-forms other algorithms on many cases.2. Many problems in the real world have constraints but PPDSO-MOEA is devel-oped to solve the many-objective problems with no constraints. So, we improve the above algorithm to get a new algorithm, named PPDS02-MOEA, who is used to problems with constraints. There are many differences between those two algo-rithms. Here, we list the differences in PPDSO2-MOEA. PPDSO2-MOEA uses the greedy repair method to repair infeasible solutions. Solutions in the archive population are feasible solutions but may be not non-dominated solutions, be-cause the size of the archive population is equal to the size of the union popu-lation, and if there are no enough non-dominated solutions, then some feasible but non-dominated solutions will be chosen. The archive population of PPDSO-MOEA only keeps non-dominated solutions and its size is changing from time to time. When selecting individuals from the archive population as parent popula-tions, PPDSO2-MOEA needs to execute fast-nondominated-sort and calculate the crowding distance to choose solutions. Considering that if the chosen objectives are conflict with each other then the performance may can’t be improved, then we use once random method to choose objectives at the right time. The performance of PPDSO2-MOEA is verified on many0/1knapsack problems with knapsack numbe. Some state-of-the-art algorithms, PPD-MOEA, MOEA/D, UMOEA/D and the algorithm using random method to choose the objectives used in calcu-lating dominance relationship are used as rival algorithms. From the experiment results, we can see that our algorithm, PPDSO2-MOEA, outperforms all the other algorithms on most scenarios.