Research On Multi-Objective Evolutionary Algorithm Based On Determinantal Point Processes

Multi-objective Optimization Problems(MOPs)refer to optimization problems which use a set of decision variables to control several objective functions simultane-ously.MOPs balance the relationship between the objective functions by adjusting the values of the decision variables,and MOPs expect that all objective function values can reach relatively optimal.At the same time,Evolutionary Algorithm,as a kind of bionic algorithm that simulates the biological evolution process in nature,thas the characteris-tics of self-adaptive,unsupervised,and self-organizing.At present,researchers usually solve Multi-objective Optimization Problems based on Evolutionary Algorithms,and a series of algorithms proposed are collectively referred to as Multi-objective Evolution-ary Algorithms(MOEA).At present,researchers are expanding the application scope of MOPs to optimize application scenarios of more than 10 objectives simultaneously.However,the current Multi-objective Evolutionary Algorithms have problems such as the decrease of population selection pressure after the algorithms evolve for certain generations,and the decrease of algorithms'performance when solving optimization problems of more than 10 objectives.At the same time,because the determinantal point process is an algorithm framework that can design offspring sampling methods according to different user requirements,it is more compatible with Multi-objective Optimization Problems.Therefore,we plan to propose a Multi-objective Evolution-ary Algorithm based on population evaluation by improving the determinantal point process,and then propose a distance calculation formula that can calculate the differ-ence between different objectives within an individual-Multi-Dimensional Difference Distance(MDDD),and based on MDDD proposes a Multi-Objective Evolutionary Al-gorithm based on hierarchical population evaluation.Specifically,the main work done in this paper is as follows:(1)Aiming at the problem that the population selection pressure decreases after the algorithm evolves for a certain number of generations,this paper proposes a Multi-objective Evolutionary Algorithm based on Population Evaluation.First,based on the kernel matrix,this paper proposes a population information model that can quantita-tively evaluate the relationship between different individuals in the population.The similarity relationship and convergence relationship between any two individuals in the population of this model are represented by a certain element in the kernel matrix.The kernel matrix composed of all elements reflects the distribution and convergence of the population in the objective space.The population information model provides a data basis for selecting offspring.Secondly,in order to increase the selection pressure of the population after certain generations,this paper improves the traditional determinan-tal point process and proposes a population subset extraction method.The improved method uses the grid sampling method to dynamically select the reference vectors so that the reference vectors are more evenly distributed in the objective space,and the reference vectors are more objective for the evaluation of the individuals.Finally,this paper applies the population subset extraction method to the population information model,and proposes a Multi-objective Evolutionary Algorithm that can alleviate the decline in population selection pressure.(2)Aiming at the phenomenon that most of the current multi-objective evolution-ary algorithms have poor results when solving problems with more than 10 objectives,this paper proposes a Multi-objective Evolutionary Algorithm based on Hierarchical Population Evaluation.Specifically,this paper proposes a distance calculation for-mula that can calculate the difference between individuals on different objectives-Multi-Dimensional Difference Distance,and divides the parent population into two levels based on MDDD.Individuals in the first-level parent population have greater differ-ences in different objectives and better diversity,so they have a higher chance of gen-erate offspring.The Multi-Objective Evolutionary Algorithm proposed based on the above method can alleviate the problem of algorithm performance degradation caused by the increase of optimization objectives.Compared with five representative algorithms,the two algorithms we proposed have achieved better results on DTLZ,WFG,and MaF datasets with different objectives.Experiments prove that the two algorithms we proposed are effective on different types of datasets.