A Multi-Modal Multi-Objective Algorithm Based On Decomposition And Adaptive Search

Multi-objective optimization algorithms can obtain excellent solutions in the target space,but their convergence and diversity in the decision space cannot be guaranteed.With the increasingly complex application environment,the parameters of multi-objective optimization problems have practical constraints due to the practical significance of the problem,such as the length of time,how much cost,and whether the value is convenient.However,Multi-modal multiobjective optimization problems require obtaining the same solution in the target space but different solutions in the decision space.Designing algorithms to solve such problems can enable decision makers to choose more convenient and practical solutions based on actual constraints.Therefore,solving Multi-modal multi-objective optimization problems has extremely important significance.In the past decade or so,many scholars have proposed different Multi-modal multi-objective evolutionary algorithms and improvements.Among them,decomposition based Multi-modal multi-objective optimization algorithms have considerable potential,but the most advanced research on decomposition based Multi-modal multi-objective algorithms still has shortcomings.For example,the number of solutions in each subproblem of the MOEA/D-AD algorithm will gradually increase,and most of them are useless solutions.The MOEA/D-MM algorithm gives the number of solutions to the subproblem,but not every individual in each subproblem can achieve an ideal state.In addition,the metric they use is difficult to solve the problem of large search space because it cannot accurately reflect the convergence and diversity of the decision space when the population distribution is sparse.In response to the above shortcomings,we designed a decomposition based adaptive subpopulation Multi-modal multi-objective algorithm(MOEA/D-Adaptive Search,MOEA/D-AS).Firstly,the MOEA/D-AS algorithm solves the current decomposition based Multi-modal multi-objective optimization algorithm.The universality metric only considers the overall distribution of the population,without considering the local distribution of the subpopulations guided by each reference vector.To this end,we introduce a clearance distance metric that combines global and local information of the population,enabling a more scientific assessment of the state of each subpopulation.Secondly,based on the improved metric of clearing distance,an adaptive mechanism is designed to dynamically allocate resources and guide each subpopulation to search in the decision space.Currently,the subpopulations of decomposition based Multi-modal multi-objective optimization algorithms are difficult to effectively allocate search resources.As the target value and dimension of the problem increase,the search space exponentially increases,and the effectiveness of the algorithm is often poor.The adaptive mechanism can find a subpopulation that is currently likely to find a better solution based on the distribution state of the solution in the current subpopulation and the distribution state of the entire population,reallocating search resources,and improving the search ability of the algorithm.Finally,during the operation of the algorithm,the size of the subpopulation may be constantly changing.We have designed a matching subpopulation maintenance mechanism and a file mechanism to prevent the loss of excellent solutions,while maintaining the distribution of the population in the decision space.The maintenance process of subpopulations takes into account both the distribution and convergence of subpopulations.At the same time,the algorithm can control preferences through parameters,enabling the algorithm to select different preferences based on different needs of decision makers.We used the recognized CEC 2019 Multi-modal multi-objective optimization test set and the freely adjustable Multi-polygon test set to compare them with the other five algorithms in order to comprehensively test the performance of the algorithm.Through further analysis,we conclude that the MOEA/D-AS algorithm is suitable for solving problems with a large number of equivalent solutions,complex PS,large search space,multiple decision-making dimensions,large number of objectives,and large spacing between equivalent solutions.Compared to other algorithms,it performs very stable and is not susceptible to local optimal solutions.Through comparative analysis of ablation experiments,it is proved that the introduction of clearance distance greatly improves the convergence and diversity of the algorithm in the decision-making space.Finally,it is shown that compared to other comparative algorithms,MOEA/D-AS algorithm can more effectively solve Multi-modal multi-objective optimization problems,and it is still competitive compared to the most advanced Multi-modal multi-objective algorithm at present.