Research And Application Of Evolutionary Algorithms For Solving Constrained Multi-objective Optimization Problem

Multi-objective optimization problems(MOPs)are widely used in scientific research and engineering applications and have become a hot and difficult research area in the field of intelligent optimization.Thanks to the advantages of parallelism and high robustness as well as good performance in handling MOPs,evolutionary algorithms have received more and more attention from researchers in solving MOPs.A constrained many-objective optimization problem(CMa OP)is a MOP with more than three objectives and with constraints.Although multi-objective evolutionary algorithms(MOEAs)have become the mainstream method for solving MOPs,the numerous objectives and complex constraints make it difficult to cope with the discrete high-dimensional search space when solving CMa OPs,and the population is easily trapped in the local optimum or local feasible region.Therefore,a many-objective evolutionary algorithm(Ma OEA)based on twostage and a many-objective evolutionary algorithm based on dual-population are proposed for CMa OPs and both are applied to real-world problems.The work in this paper is divided into three parts as follows.(1)To address the problems that populations are easily blocked by infeasible regions and poor population diversity,a two-stage search strategy with the combined operator is proposed and implemented on AGE-MOEA to form TSCOEA.TSCOEA deals with the constraints in two stages.In the first stage,the algorithm optimizes only the objective function and the population is not constrained to rapidly approach in the direction of the Pareto front;in the second stage,the constraint violation degree is treated as a new objective function to solve the original constraint problem.A combined operator consisting of a simulated binary crossover operator,polynomial mutation operator,and DE/current-to-pbest/1 operator is used in the search process to generate offspring with excellent convergence and diversity.Experiments with four Ma OEAs on the C-DTLZ,DC-DTLZ,and MW test suites show that TSCOEA has significant advantages in IGD indicator and HV indicator.(2)To address the difficulty of balancing constraints and objectives simultaneously for a single population,a dual-population-based strategy is proposed and implemented on NSGA-III to form DP-NSGA-III.Two populations of DP-NSGA-III interact by sharing offspring.The main population of DP-NSGA-III is based on NSGA-III and aims to solve the original CMa OPs;the auxiliary population ignores the constraints and uses Minkowski distance to select the best individuals and aims to solve the unconstrained Ma OPs with less evolutionary pressure.To take better advantage of the two-population and further exploit the infeasible solution,an ε-constrained handling method is designed for the main population.The ε-constrained bound of this method is monotonically decreasing to 0.Experiments show that the IGD indicator and HV indicator of DP-NSGA-III on the C-DTLZ,DC-DTLZ,and MW test suites are significantly better than peer algorithms.(3)Engineering problems have complex objective functions and constraints.To verify the value of the proposed algorithms in real-world problems,the above two evolutionary algorithms are used in the optimization of a 5-objective precipitation drainage system with 7 constraints.Both the objective function and the constraints of this problem are nonlinear.The experiments show that the two evolutionary algorithms proposed in this paper have certain advantages in HV indicator.Considering the realistic situation,five non-dominated feasible solutions of TSCOEA are given in this paper.This experiment further validates the value of this paper’s research in real-world engineering problems.