The Research On Constrained Multi-Objective Evolutionary Algorithm Based On Population State Detection

Multiobjective Optimization Problems(MOPs)bring great challenges to the optimization process because there are multiple objective functions to be optimized,which may conflict with each other.Multi-objective optimization problems in actual production and life are difficult to avoid the limitations of various constraints,and a proper constraint function can represent each constraint.These existing multi-objective optimization problems restricted by constraints are defined as Constraint Multi-Objective Optimization Problems(CMOPs).By directly adding consideration to the constraints based on the classic Multi-objective Evolutionary Algorithms(MOEAs),although it can make the final feasible solutions,it is usually impossible to solve the problem that the optimization results fall into the local optimum;thus,the problem is challenging to get the genuinely optimal feasible solution.For example,the classic NSGA-IICDP based on Pareto Dominance and the efficient CMOEAD based on the MOEA/D decomposition framework are all due to overemphasizing the feasibility of the solution,and it is effortless to fall into the excellent local result in the search process.Later,the newly proposed algorithms to strengthen the convergence of the algorithm in the objective space,such as PPS,MOEAD-Epsilon,and other algorithms,even if they can search for the optimal feasible region,they still cannot search for all the optimal feasible regions,and the solution set has poor distribution on the Pareto Front(PF).This is because CMOPs are restricted by constraints,which will make Constraint Multi-objective Optimization Evolutionary Algorithms(CMOEAs)constrain the algorithm to search for other possible feasible regions while optimizing the convergence of feasible solutions,limiting the algorithm distribution.Therefore,it is the key to restricting the performance of CMOEAs to ensure the convergence of the algorithm solution,the distribution of the solution set in all optimal feasible regions,and the complete PF under many constraints,and it is also the main content of the work of this paper.This paper proposes two-phased optimization CMOEAs based on population status detection and a new dominance principle to solve CMOPs.One is to detect the search state of the population in the target space during the evolution process to determine what evolution strategy adjustment mechanism should be adopted for this state so that the algorithm can exert the best search effect.We named this CMOEA as a constrained multi-objective evolutionary strategy based on population state detection(PSDS);the other method is based on the traditional decomposition framework,based on the evolution of the algorithm.The actual situation in the process invokes the newly defined dominance relationship to select the next generation of individuals.This new dominance relationship can realize the exploration of feasible regions that are not dominated by each other,thereby optimizing the distribution of the algorithm.We call this CMOEA a staged temporary dual-population evolutionary algorithm with staged temporary dual-population based on a novel dominance principle(CMOEA-NDP).To enable CMOEAs to meet the requirements of converging to the optimal feasible region and all discretely distributed feasible regions when solving CMOPs,the two methods proposed in this paper adopt a staged optimization process through state detection but improve search diversity.The methods used are not the same.The former is alternately used through constrained and unconstrained evolution mechanisms to evolve to the optimal feasible region.The reinitialization method ensures that the population evolution process will not get into trouble.The latter mainly uses a temporary second population to search for non-dominated solutions that may exist in other feasible areas to improve the diversity of the main population.Both strategies use archive sets independent of the population to save each generation’s feasible solutions and screen the feasible solutions.At the same time,the output solution sets of the two methods use Pareto dominance to achieve iterative updates.PSDS uses accurate state detection strategies to determine the next stage of evolution mechanism,whether to consider the switching of constraint conditions and reinitialize the population to achieve convergence and The balance of distribution.CMOEA-NDP opens up auxiliary populations to search for diversity at a suitable stage based on the detection of population status.The main population can obtain better convergence and distribution with temporary auxiliary population information.The two evolutionary strategies in this article and a variety of advanced C-MOEAs(NSGA-II-CDP,CMOEAD,To P,PPS,C-TAEA,etc.)are carried out on the CDTLZ series,MW series,LIR-CMOP series,and DASCMOP series test suites Experiments and comparisons,and according to the different characteristics of PSDS and CMOEA-NDP,PSDS and MOEADDAE other than the above-mentioned advanced CMOEAs are also separately compared,and CMOEA-NDP is separately compared with CCMO.By comparing the experimental results of the IGD and HV evaluation indicators of each algorithm on many test problems,the two algorithms proposed in this paper are universally competitive in solving CMOPs and can achieve good results better than most cash algorithms.