A Regularity Model-Based Multi-Objective Estimation Of Distribution Algorithm And Its Application

Many optimization problems,in scientific research and engineering areas,belong to multi-objective optimization problems.Multi-objective problems are not different with single objective problems,the optimal solutions of multi-objective problem is a set of solutions.As multi-objective evolutionary algorithms themselves are based on the population and the solutions from them are non-dominated solutions set,they are becoming the most effective approach to solve multi-objective problems.In recent decades,multi-objective evolutionary algorithms became hot spots and achieved many good results in multi-objective area.Traditional multi-objective evolutionary algorithms(MOEAs) were guided to generate new individual solutions by crossover and mutation operator,the better solutions were preserved by certain selection operator.In this way,the individual solutions from population approximate the Pareto set quickly.However,the offspring generation strategy by crossover and mutation operator bring out another problem,that the crossover and mutation operator loss its original meaning and also reduce the performance of the algorithms when the algorithm is close to convergence.Not same as MOEAs,estimation of distribution algorithms(EDAs) don't use crossover or mutation.Instead,they explicitly extract globally statistical information from the selected solutions and build a probability distribution model of promising solutions,based on extracted information.New solutions are sampled from the model thus built.EDAs were first used in single objective optimization.In 2004,since Thierens and his colleage first introduce EDAs to the field of multi-objective optimization,many domestic and foreign scholars began to study Multi-Objective Estimation of Distribution Algorithm.It has been observed that under mild smoothness conditions,the Pareto set(in the decision space) of continuous MOP is a piecewise continuous(m-1)-dimension manifold,where m is the number of objectives,but many researchers do not take the regularity into consideration.In 2007,Qingfu Zhang etc.have developed a regularity model-based multi-objective estimation of distribution (RM-MEDA).RM-MEDA captures and utilizes the regularity of the Pareto set in the decision space.Systematic experiments have show that,overall RM-MEDA outperforms GDE2, PCX-NSGA-â…¡and MIDEA,on a set of test instances with variable linkages.However,RM-MEDA has its drawbacks and shortcomings.The first problem of RM-MEDA is that when the new solutions can far away from the Pareto set,and distribution of the population have no obvious regularity,particularly in early stage of algorithm,the model be built is not capable of guiding the search to destination direction.The scond,a randomly method to generate initial population in RM-MEDA is not able to make the initial population scatter evenly in the feasible solutions space.This paper takes the advantage from RM-MEDA and traditional MOEAs,overcome the shortcomings from them.Based on the study and analysis of A Regularity Model-Based Multi-Objective Estimation of Distribution Algorithm(RM-MEDA),and propose an improved regularity model-based multi-objective estimation of distribution algorithm(IRM-MEDA), including IORM-MEDA and IURM-MEDA.The IRM-MEDA had some features.1) generate initial population with experiment design,including orthogonal design and uniform design,so that the individuals make a more representative distribution of the feasible solutions.2) introduce a new convergence criterion to determine when the genetics-based method,i.e.crossover, mutation and when the EDA-based method should be used to generate offspring.3) combine genetics-based and model-based offspring generation instead of only model-based method in RM-MEDA.The experiment result on a number of test problems proved that in most case both IORM-MEDA and IURM-MEDA are able to find much better convergence near the the true Pareto-optimal solutions and better spread of solutions than RM-MEDA.Satellite constellation design aims at exploying satellite resource as little as possible,and achieving system performance as high as possible by setting reasonable orbit parameter. Constellation design of regional coverage often involves sevral feature points and performance metric,so it can be attributed to a typical multi-objective optimization problem.This paper introduces a LEO regional constellation instance,and optimizes it by the algorithms:RM-MEDA, IORM-MEDA,IURM-MEDA.The experiment result Show that improved RM-MEDA, including IORM-MEDA and IURM-MEDA,are better than RM-MEDA.It can provide a useful reference for decision maker.In order to set different parameters and show experiments result for RM-MEDA,this paper design an experiment platform.