Research On High-dimensional Multi-objective Evolutionary Algorithms Based On Decomposition

The optimization problem of high-dimensional multi-objective is closely related to our production,our life and our scientific research.Compared with the optimization problem of two or three objectives,the traditional multi-objective optimization algorithm performs poorly in high-dimensional problems due to the expansion of target space,the limitation of population size,the difficulty of evaluation of the individual,the reduction of convergence pressure and so on.It has become a hot topic for researchers in the field of evolutionary algorithms to find a new and effective high-dimensional multi-objective algorithm.Among the many methods,the multi-objective evolutionary algorithm based on decomposition has become one of the promising methods,because of its advantages of simple implementation,good convergence and uniform distribution of solution sets.However,in the face of high-dimensional multi-objective optimization problems,the traditional optimization algorithm based on decomposition will also face such difficulties as insufficient convergence pressure,difficulty in jumping out of the local optimal solution,and poor diversity of solution sets.In order to improve the performance of the algorithm and increase the pressure in population evolution,this paper focuses on the multi-objective optimization based on decomposition and makes the following work:(1)In order to better balance the convergence and diversity of the algorithm,we propose a new fitness function,which will give priority to the individuals with better convergence from the contemporary population and the descendant population,and then calculate their sparsity.At the same time,a multi-search strategy is proposed,which measures both the convergence degree and the sparsity degree of the solution,and selects the solution with the best of both as the new parent generation.Based on this method,we proposed a high-dimensional multi-objective optimization algorithm(MoOEA-FM)based on the new fitness function and multi-search strategy.At the same time,the effectiveness of the algorithm was verified by comparing with other four commonly used high-dimensional multi-objective algorithms through the numerical experiments on 45 test problems of CEC2018MaOP algorithm competition.(2)In order to better balance the global search and local search in the process of evolution,and increase the role of diversity in the population evolution,we are inspired by the single objective optimization algorithm based on barnacles and breeding,as the parent population,set up an adaptive parameter in the algorithm can dynamically in the process of changing the proportion of global search and local search.Calculated by the method based on classification of the father,on the other hand,the high density of population estimates and the diversity of the parent population,choose a number of individuals in a population from outside to join the current parent population,and based on the degrees of convergence of sorting,raised the pressure of the evolution of algorithm in high dimensional problem,at the same time improve the uniformity of the distribution of set.Based on this method,we proposed an adaptive multi-objective barnbarker algorithm(MOEA/D-BMO)based on decomposition,and carried out numerical experiments on two different test set functions.