Research On Indicator And Boundary Selection Of Many-objective Optimization Algorithm

After decades of development, the multi-objective evolutionary optimization algorithm has achieved many relatively mature research results. However, with the requirement of actual industry and the development of research, more and more scholars have turned their attention to the many-objective optimization. In the many optimization problems, there exist some problems such as Pareto dominant relationship failure, interaction of convergence and diversity, and visualization. With the dimension increases, the performance of the algorithm is also increased. And it is a serious challenge to the algorithm designer.Kata Praditwong et al. proposed the Two_Arch algorithm which was the first algorithm proposed with two archives focusing on convergence and diversity in2006.Convergence archive aims to enhance the convergence of the algorithm,diversity archive aims to enhance the diversity of the algorithm. However, this algorithm is a Pareto-based algorithm, which is not ideal when dealing with high dimensional problems. Another drawback is focused on the convergence archive without maintenance mechanism of distribution that will lead to the stagnation of the algorithm in some cases.In order to solve these problems, this paper proposes a HB_Two_Arch algorithm based on the HD indicator and boundary elimination selection. This algorithm has been improved as follows: Firstly, convergence archive aims to guide the population to the true PF. Diversity archive aims to add more diversity to the population in a high-dimensional objective space and the sizes of the convergence archive and diversity archive are fixed. Secondly, the individual removal operation will be carried out by HD indicator when convergence archive overflows. Calculate the fitness value of each individual in CA, delete the individual with the smallest fitness value, and then update the fitness value of the remaining individuals in CA.The individual removal operation will be carried out by boundary elimination selection when diversity archive overflows. The sequence of the coordinate axes is disturbed by random, the selected coordinate axes are selected as the standard axes, and the individuals who select the minimum value of the current function as the excellent individuals enter the next generation DA. At the same time according to the selected excellent individual to set the penalty area, the individual in the penalty area will not be selected in the subsequent selection.Thirdly, this algorithm makes crossover between convergence archive and diversity archive but mutation on convergence archive only during the process of reproduction.Lastly, DA is the final output population.In order to evaluate the performance of HB_Two_Arch on ManyOPs, we have compared it with MOEA/D?IBEA?NSGA-??AGE-II and Two_Arch on WFG and DTLZ with different numbers of objectives. The experimental results show that HB-Archive algorithm can cope with ManyOPs(up to 20 objectives) with satisfactory convergence, diversity, and complexity.At the end of this paper, the work of this paper is highly summarized, and the possible direction of improvement is put forward.