Research On Evolutionary Multi-objective Optimization Algorithm And Its Application

Multi-objective optimization problem(MOP)is a special optimization problem that is commonly encountered in engineering practice and scientific research.Different from single-objective optimization,which contains only one objective to be optimized,MOP contains several objectives that need to be optimized simultaneously and the objectives are often contradictive.As an intelligent optimization algorithm,evolutionary algorithm(EA)has shown its advantages over traditional optimization methods in solving some complex problems.Since the optimal solution for a MOP is a set,this makes EA very suited for solving MOP.Evolutionary multi-objective optimization algorithm(EMOA)has been the most effective method for MOP so far.Despite the significant progress of evolutionary multi-objective optimization algorithm(EMOA),some key topics remains to be studied.First,the problem of tackling the constraints for constrained multi-objective optimization.Existing constraint-handling techniques may fail to make the balance between optimality and feasibility and most techniques rely on some hyper-parameter,this has limited their range of application,reduced their accuracy and increased their difficulty of usage.Second,the problem of controlling the parameters of EMOA.The performance and robustness of EMOA often rely on the settings of its hyper-parameters,this is another critical issue faced by EMOA.The study of adaptive parameter control mechanisms is of great value to improve the adaptability and robustness of EMOA.Finally,engineering applications of EMOA.How to design more efficient algorithms and give full play to EA's ability according to the nature of a specific engineering problem is another important problem faced by MOEA to extend its application.Aiming at the above problems,this thesis focuses on the study of constraint handling techniques and adaptive parameter control mechanisms in multi-objective optimization.Also,multi-objective optimization is used to solve an engineering problem,system reliability optimization.The main contributions of this thesis are as follows:(1)A basic framework for EMOA and three main components of this framework are achieved through the study on two classical EMOAs.The framework consists of three main components,which includes fitness evaluation,the sorting and selection operation,configuration of the evolutionary operators to generate new solutions.Fitness evaluation presents a quantitative measure for the comparison of solutions.Sorting and selection operation give the specific strategy for the selection of solutions.Configuration of the evolutionary operators to generate new solutions makes the evolutionary algorithm sample new points in the search space without a break.With the guidance of this framework,insights of constrained multi-objective optimization problem and the parameter control techniques used in EA are achieved.(2)c MOEA/H is proposed for constrained multi-objective optimization problem(c MOP).The difficulty of c MOP lies in that the optimizer should not only optimize several objectives,but also take the feasibility of the solutions into consideration.Thus,a balance between optimality and feasibility could be achieved.A new sorting method,which is called constrained non-dominated sorting(CNS),is proposed in the framework of hybrid evolutionary multi-objective optimization to evaluate the quality of the solutions.This method achieves the balance between optimality and optimality.Besides,a dynamic resource allocation mechanism is introduced into the framework to fully explore the sparse regions in the objective space.Experimental results indicate that the proposed mechanisms are effective.(3)A distance dependent parameter control algorithm,MOEA/D-DPA,is proposed to control the parameters of EMOA.Multi-objective evolutionary algorithm based on decomposition(MOEA/D)successfully combines traditional mathematical programming method with EA.It decomposes an original MOP into a series of sub-problems and solves them simultaneously in a single run.Each sub-problem is solved by utilizing the information provided by its neighborhood sub-problems.Based on the MOEA/D framework,a distance dependent parameter control mechanism is proposed in MOEA/D-DPA,which utilizes similarity of the solutions to control the parameters of differential evolutionary operator(scaling parameter F and crossover rate CR).During the process of optimization,F and CR are determined according to the distance between the DE parents.Besides,the distance between the DE parents is also controlled to balance exploitation and exploration.Experimental results indicate that MOEA/D-DPA is effective,especially on the WFG test suite.(4)A reinforcement learning aided parameter control algorithm called RL-MOEA/D is proposed.Some traditional parameter control mechanisms are only suited for the adaption of some specific parameters.These mechanisms are usually not applicable when much more parameters need to be controlled.Reinforcement learning provides a generic way of controlling the parameters and it has been preliminarily applied in controlling the parameters of EA.How to design more efficient and reasonable reinforcement learning algorithm according to the nature of multi-objective optimization determines if reinforcement learning could successfully tackle the parameter control problem.Thus,in RL-MOEA/D,reinforcement learning is introduced into multi-objective evolutionary algorithm based on decomposition(MOEA/D)and the immediate reward and observables of the environment are redefined according to the nature of multi-objective optimization.The defined observables are used to describe the state of the solutions in the objective and variable space during the process of evolution.Based on these definitions,the joint adaption of T and DE variants in MOEA/D is achieved.Experimental results on ten test instances indicate that reinforcement learning has a great potential to control the parameters of EMOA.(5)c MOHGA-TM is proposed for multi-level system reliability optimization.In the field of power,aeronautics and astronautics,system failure would result in enormous losses.The improvement of system reliability by means of redundancy is of great value.This thesis focuses on the multi-level redundancy allocation optimization problem(MRAOP).Two difficulties of this problem are: First,optimization of system reliability under some cost constraints makes this problem a constrained optimization problem.Second,the problem is a discrete optimization problem.Compared with continuous optimization problems,the optimization of the tree structure of a system a harder.In c MOHGA-TM,MRAOP is formulated as a constrained multi-objective optimization problem.This on one hand increases population diversity.On the other hand,the search regions are more focused as a consequence of the constraints introduced,thus results in a higher search accuracy.Besides,a targeted mutation mechanism is proposed according to the characteristic of a multi-level system.Pareto sorting is implemented among the redundant units in the middle levels of the system and the dominated substructures are reconstructed.This improves population diversity and maintains a moderate selection pressure.Experimental results indicate that the constraints introduced could focus the search thus improve the quality of the solutions.The targeted mutation mechanism is also proved effective through the experiment.