Research On Evolutionary Algorithms For Many-objective Optimization Problems

In the real world,there are multiple conflicting goals that need to be optimized simultaneously.Such problems are called multi-objective optimization problems.Evolutionary algorithms are used to solve multi-objective optimization problems with remarkable results.However,when the number of objectives increases,the Pareto front is complex and the decision variables increase,the multi-objective optimization problem will be more difficult to solve.Therefore,to solve the corresponding multi-objective optimization problem,four multi-objective evolutionary algorithms are proposed in this paper.The main research contents of this paper are as follows:Aiming at the problem that multi-objective evolutionary algorithms cannot effectively balance population convergence and diversity.A multi-objective evolutionary algorithm based on vector angles and clustering is proposed.The population is divided by the environmental selection strategy,and individuals with better fitness are retained to ensure the convergence of the population.The clustering selection strategy is used to generate new classes,and the maximum vector angle is used to select and retain candidate individuals with good diversity,which balances the convergence and diversity of the population.The proposed algorithm on the DTLZ test problem is studied by simulation.The simulation results show that the convergence and diversity of the solution set obtained by the proposed algorithm are relatively well.To solving many-objective optimization problems,a scalar projection and decomposition-based evolutionary algorithm for many-objective optimization is proposed.In this algorithm,a method for estimating the shape of the Pareto front is proposed.Based on the estimated shape of the Pareto front,an appropriate individual similarity assessment method is employed.Elite individuals are retained through environmental selection strategies.Individual projections are projected onto the hyperplane through a scalar projection strategy.The similarity of individuals is effectively assessed by computing the distance between individual projected points on the hyperplane.The problem of inaccurate similarity assessment of individuals is effectively ameliorated by this strategy.The proposed algorithm on the WFG test problem is studied by simulation.The simulation results show that the shape of the Pareto front is accurately and efficiently evaluated by the proposed algorithm,and the ability of the algorithm to solve many-objective optimization problems is improved.To solve many-objective optimization problems with complex Pareto fronts,a maximum angle evolutionary selection for many-objective optimization algorithm with adaptive reference vector is proposed.Population convergence and diversity are dynamically balanced by the proposed aggregation function according to the objective and the number of evolutionary evaluations.The convergence criterion is measured by the distance between the individual and the ideal point,and the diversity criterion is measured by the vector angle between the individual and the reference vector.Elite individuals are selected as reference vectors in the algorithm,and are adaptively maintained and updated with the evolution process.The complex Pareto fronts in optimization problems are well accommodated by the algorithm.The proposed algorithm is simulated on various complex Pareto front DTLZ,WFG and Ma F test problems.The performance and stability of the proposed algorithm are significantly better than the other five many-objective evolutionary algorithms,which are verified by simulation tests.It shows that the ability of the algorithm to solve complex Pareto frontier many-objective optimization problems is effectively improved by the aggregation function and reference vector adaptive strategy.To solve multi-objective optimization problems with a large number of decision variables,a problem transformation-based and decomposition-based evolutionary algorithm for large-scale multi-objective optimization is proposed.The bidirectional reference vector generation strategy is adopted in the decision space,which adaptively guides the evolution of the population and enhances the diversity of the population.The dimension of the decision space in the original large-scale multi-objective optimization problem is reduced by the proposed algorithm.The difficulty of large-scale multi-objective optimization problems is reduced and the computational efficiency is improved.The proposed algorithm on the LSMOPs test problem is investigated by simulation tests.The convergence of the proposed algorithm is significantly better than that of the other five large-scale multi-objective evolutionary algorithms,which are verified by the simulation tests.It shows that the ability of the algorithm to solve large-scale multi-objective optimization problems is effectively improved by the bidirectional reference vector generation strategy and the problem transformation method.