A Knee-Point-based Evolutionary Algorithm Using Weighted Subpopulation For Many-objective Optimization

Among many-objective optimization problems(MaOPs),the proportion of nondominated solutions is too large to distinguish among different solutions,which is a great obstacle in the process of solving MaOPs.Thus,this paper proposes an algorithm which uses a weighted subpopulation knee point.The weight is used to divide the whole population into a number of subpopulations,and the knee point of each subpopulation guides other solutions to search.Additionally,the convergence of the knee point approach can be exploited,and the subpopulation-based approach improves performance by improving the diversity of the evolutionary algorithm.Therefore,these advantages can make the algorithm suitable for solving MaOPs.In addition,in the test problem with dimension higher than 10,the algorithm uses a two-tier weight allocation method.Compared with the single-tier weight allocation method,it can not only make up for the problem that the number of weights is too large and the size of the population is affected,but also ensure that the algorithm can have a set of weight vectors with appropriate number and uniform distribution to control the distribution of the population when solving the high-dimensional problem.In this paper,the algorithm is tested on a series of high-dimensional test problems(DTLZ series,WFG series)and compared with the six most advanced algorithms,including SPEA2+SDE,MOEA/D,MSOPS,NSGA-III,GrEA,HypE and KnEA,under various conditions up to fifteen targets.From the experimental data,it can be seen that the proposed algorithm has strong competitiveness in high-dimensional test problems.This is mainly attributed to the fact that when querying the inflection points of subpopulations,it is necessary to calculate the hyperplanes of each subpopulation separately.These separate operations can assign different hyperplanes to different subpopulations.Therefore,after the population convergence,the solution of subpopulations can easily find a more suitable location,thus enhancing the distribution of the algorithm and improving the overall performance of the algorithm.