Clustering-based Multi-objective Evolutionary Algorithm And Its Application

There are many multi-objective optimization problems(MOPs)with multiple variables and constraints in the real world,which are of great difficulties to obtain satisfactory results by traditional optimization method.One can get only one solution by transforming the MOP into a single objective optimization problem.Multi-objective evolutionary algorithms(MOEAs)have advantages on solving MOPs through population evolution and parallel search.However,many existing MOEAs often prefer to use feasible solutions when solving constrained MOPs,which usually lead to falling into local optima,the poor convergence and diversity.Therefore,the aim of this paper is to improve the MOEAs for constrained MOPs using unfeasible solutions.The main contributions of this paper are as follows:The difficulties of multi-objective optimization problem are analyzed.By analyzing we know MOEAs are suitble for solving the MOPs,so the existing MOEAs is classified and summarized.The principles of multi-objective particle swarm optimization algorithm and clustering-based multi-objective evolutionary algorithm are introduced,and their merits and demerits are analyzed.The existing constraint handling techniques are summarized which are used in the MOEAs.A multi-objective particle swarm optimization(CSMPSO)algorithm is proposed,in which two global optimal solutions are used to guide the flight of particles.An external archive containing unfeasible solutions is introduced in the algorithm,in which unfeasible solutions can be used to help jump out of local search.The diversity of population is improved.An improved shrinkage factor is used to limit the velocity of the particles.The comparison experiments show that the CSMPSO algorithm has good ability of solving problems,and the performance of the CSMPSO algorithm has been improved obviously for CTP series constraint problems with complex PF.The ED-MOEA algorithm is analyzed and improved.The effectiveness of the hybrid crossover operator is verified by experiments.The random strategy is used in ED-MOEA for selecting cluster in crossover operation,which make the stability of the algorithm poor.Therefore,a new method of selecting cluster by selecting the fixed number of cluster with crowding distance is used in this paper,which can improve the stability of the algorithm.The advantages and disadvantages of three kinds of uniform design methods in ED-MOEA are analyzed.To make full use of the unfeasible solutions,a new method of selecting the next population is used,with which a certain proportion of unfeasible solutions are selected to guide the evolution of next population.The comparison experiments on the widely used benchmarks are conducted to test the performance of the improved ED-MOEA,the results indicate that the improved algorithm has good performance in convergence,uniformity,diversity and stability.The influences of the parameters in the algorithm are also analyzed.The ability of solving practical problems of the algorithms is verified by solving several engineering design problems and a multiobjective optimization problem for the reliable data storage in clouds.Analysis of performance of the algorithms are conducted,and the results indicate that the CSMPSO algorithm has good ability of solving all the problems,the improved ED-MOEA algorithm has a good result for the problems with continuous variables,but the problem with discrete variables cannot be solved well.In summary,the two algorithms can provide effective solutions for the practical problems.