Research On Evolutionary Algorithms For Constrained Multi-objective Optimization Problems

Multi-objective optimization problems are common problems in the field of science and engineering applications,such as: how to plan the route to minimize the construction cost and time before subway line design;how to combine multiple investment methods in the investment field to effectively minimize the risk of investment and maximize the return on investment.This type of problem can be classified as a multi-objective optimization problem.It is widely used in scheduling,financial investment,automatic control,artificial intelligence and other fields.Therefore,the study of multi-objective optimization problems has important theoretical and practical significance.Multi-objective optimization problems include unconstrained and constrained problems.Compared with unconstrained multi-objective optimization problems.The constraints in the optimization problems make the search space of constrained multi-objective optimization problems more complicated,especially when the number of constraints is large,and the algorithm needs to balance the local search and the global search.For example,when there are many disconnected feasible spaces,the search is easy to fall into the local optimum.At the same time,as the objective space dimension increases,the constrained multi-objective optimization problem becomes a many objective optimization problem with more than three objectives.The difficulty of the problem gradually increases,and the performance of the algorithm decreases significantly.For example,the traditional Pareto dominance relationship will lose the selection pressure withe the increase of the objective space dimensionality,which leads to the failure of the algorithm using this type of relationship.In order to overcome these shortcomings,this thesis studies the constrained multi-objective optimization problem and the constrained many objective optimization problem,and proposes two types of algorithms.The main works are as follows:(1)Solv the constrained multi-objective optimization problem: 1.How to design an effective constraint handling mechanism and make good use of the valuable information of infeasible solutions.2.How to balance the convergence and the diversity of the solution set in the optimization process.Therefore,as the first research part of this thesis,a constrained multiobjective optimization algorithm based on population grouping is designed.There are two main contributions: 1.Design an adaptively grouping strategy based on non-dominated sorting to ensure the distribution of solution sets.Generate a uniform weight vector in the objective space,combine the non-dominated sorting strategy to group the population individuals,group the population with each uniform weight vector as the center,and let the population individuals evolve to PF along the weight vector to ensure the good distribution of the algorithm.2.The new evolutionary crossover operator based on elite representative points improves the search ability of the algorithm and speeds up the convergence process.In the case of population grouping,two elite representative points are found within the subpopulations.One elite representative point measures the optimal objective value,representing the individual elite in the feasible solution;the other elite representative point measures the constraint violation degree value,representing Focus on the elite individuals in the infeasible solution,and construct new crossover and selection operators based on these,so as to make full use of the valuable information of the infeasible solution and accelerate the convergence of the algorithm.(2)Solve constrained many objective optimization problems that need to be solved: 1.How to design effective methods to deal with many objective optimization problems when the selection pressure is insufficient and the PF surface is complicated and so on.2.How to balance the convergence of the algorithm and the diversity of the solution set in the highdimensional objective space.As the second research part of this article,this thesis designs an objective reduction algorithm for the problem of constrained many objective optimization containing redundant objectives.The algorithm for removing redundant objectives is based on spectral clustering,ORSC.First: sample data points.Generate evenly distributed sampling points,record the changes of the objective function value by giving the sampling points a very small increment,calculate the changes of the objective function,and obtain data points representing the changes of the objective function.Second: cluster analysis.Define the objective similarity,which is used to measure the correlation between the objective functions,and determined by the change of the objective function,and then construct the similarity matrix according to the objective similarity,and use spectral clustering to cluster and divide the objectives with high similarity cluster.Finally: find out redundant objectives.According to the results of clustering,the redundant objectives in the cluster are found,the concept of profile is defined,and a strategy for deleting redundant objectives is constructed.