Research On Multisolution Evolutionary Algorithms For Multimodal And Multiobjective Problems

With the development requirements of industrialization and intelligence,multi-solution optimization problems appear in a large number of real-world applications,such as multisolution path planning,multi-objective portfolio optimization,and other engineering and scientific fields.These problems have many complex properties such as multivariates,multipeaks,multiconstraints,and multiobjectives,so the traditional optimization methods are no longer satisfied with the increasingly complex modern scientific and engineering optimization problems.Therefore,designing the efficient optimization methods for solving multisolution problems is an important issue.This thesis focuses on the research of multimodal optimization problems(MMOPs)and multiobjective optimization problems(MOPs).MMOPs require not only to locate the optimal solutions as more as possible,but also to refine the solution accuracy as high as possible;MOPs require obtaining the solutions on the Pareto front,and these solutions are as optimal as possible for multiple objectives of the problem.Therefore,MMOPs and MOPs require the algorithms not only to balance the ability of exploration and the exploitation of the population,but also require the algorithms to locate multiple optimal solutions simultaneously.Therefore,these problems can be collectively referred to as the multisolution problems.Currently,solving multisolution problems mainly relies on evolutionary algorithms,such as differential evolution(DE),genetic algorithm(GA),and particle swarm optimization(PSO).While these optimization algorithms have been widely used to solve a number of practical optimization probles,there are still some limitations and difficulities,which can be divided into the following three main points.(1)Since different evolutionary states requirethe corresponding parameters,a single parameter setting has an impact on the performance of the algorithm,such as the mutation factor F and crossover factor CR in DE.How to adjust parameters adaptively to different evolutionary states is a hot and difficult issue in current research.(2)The existing optimization algorithms,while achieving good results in most single-peak problems,tend to fall into local optima when dealing with multimodal and multi-objective problems.How to design an intelligent optimization algorithm that can avoid local optima and accelerate global convergence has been a challenging problem.(3)The problem of greedy selection in the evolutionary process results in unevenly distributed or poorly diversified solutions.It is also a challenging problem to design aevolutionary operator to obtain solutions with a uniform distribution and high quality.To better deal with the above problems,this thesis proposes some optimization algorithms for efficiently solving multimodal and multiobjective problems by analyzing the evoluationary states.The main contributions are as follows.(1)A novel differential evolution(DE)algorithm based on local binary pattern(LBP)is proposed in this thesis.The LBP makes use of the neighbors' information for extracting relevant pattern information,so as to identify the multiple regions of interests,which is similar to find multiple peaks in MMOP.It enables the LBP operator to form multiple niches,and further to locate multiple peak regions in MMOP.Moreover,based on the LBP niching information,we develop an adaptive parameter strategy(APS)to fully search the niching areas and maintain multiple peak regions.The APS adjusts the parameters of each individual based on its own LBP information,and guides the individual to the promising direction.(2)An adaptive guidance-based differential evolution(AGDE)with archive strategy is proposed in this thesis,including three novel components.Firstly,an adaptive mutation strategy(AMS)is introduced,which guides the current individual to move towards the peak that is closest to itself.Secondly,an iterative feedback archive(IFA)strategy is used to store the global optima of the population in iteration.Thirdly,a Gaussian disturbance-based elite learning(GDEL)strategy is performed on the archive to refine the accuracy of the solutions.(3)A multi-angle hierarchical differential evolution(Ma HDE)algorithm is proposed by considering the fitness quality and evolution stage.Firstly,a fitness hierarchical mutation(FHM)strategy is designed to divide the individuals into two levels(i.e.,low/high-level)Secondly,a directed global search(DGS)strategy is introduced for the low-level individuals in the late evolution stage,which provide these low-level individuals with the opportunity to re-search the global peaks.Thirdly,an elite local search(ELS)strategy is designed for the high-level individuals in the late evolution stage to refine their solution accuracy.(4)An outlier aware differential evolution(OADE)algorithm is proposed in this thesis,which includes three novel mechanisms.Firstly,a dimension-based and guidance-balanced mutation(DGM)strategy is proposed regarding to the dimension of the problem to generate more promising solutions.Secondly,an outlier-based selection(OBS)strategy is introduced based on both the fitness information and the distribution information of individuals,which increases the population diversity to help locate as many peaks as possible.Thirdly,a negative outlier-based re-initialization(NORI)strategy is proposed to help the early trapped negative outlier jump out of the local optima.(5)A hybrid selection-based genetic algorithm for MOPs is proposed,which is based on rank-based selection(S-Rank)and a random-based selection(S-Rand).S-Rank is a scheme that selects individuals based on its non-dominated ranks,if the individuals have the different non-dominated ranks,the individuals with lower(better)ranks will be selected for the next generation.On the contrary,we first select an objective randomly from all objectives,and then select the individual with the better fitness on this objective to enter the next generation.This is the S-Rand scheme that can increase the diversity of individuals(solutions)due to the random selection of objective.(6)Targed to better solve the portfolio optimization problem,a multi-population co-evolutionary particle swarm optimization(MPCo PSO)algorithm is proposed,which is based on multiple populations for multiple objectives(MPMO)technique.Firstly,a hybrid binary and real(HBR)encoding strategy is introduced to better represent the stock selection and the asset weight of the solutions in Mo CCPOP.Secondly,a return risk ratio heuristic(R3H)strategy based on the historical return and risk of each stock is proposed as a fast CC handing method to obtain feasible solutions.Thirdly,a new particle update method based on bi-directional local search(BLS)strategy is designed to increase the chance to improve the solution accuracy.Lastly,a hybrid elite competition(HEC)strategy is proposed to assist the archive update,which provides more promising solutions.To sum up,this thesis proposes a number of effective multisolution optimization algorithms for multimodal and multiobjective problems.The LBPADE,AGDE,Ma HDE,and OADE are proposed through in-depth exploration of evolution rules,which provide a good way to deal with multimodal optimization problems.For multiobjective problems between the objectives and the weight balance of the selection pressure problem,we adopt the multi-objective processing method based on multiple populations and based on the part of the ranking selection method to deal with them.Besides,these algorithms are tested on the portfolio optimization problem to provide the efficient reference to deal with multiobjective optimization problem.