The Research On Constrained Multi-objective Optimization Problem Based On Evolutionary Algorithms

In daily lives,there are a considerable number of multi-objective optimization problems,in which multiple objectives are required to be optimized simultaneously,along with many different constraints.Among the many algorithms,which can solve this problem,multi-objective evolutionary algorithms are widely used due to its strong robustness and global searching ability.Therefore,it has attracted more and more scholars to study on it.Due to the existence of constraints,in order to avoid being trapped in local optimum,as well as get the better result of convergence and distribution,the evolutionary algorithm needs to make rational use of the information of feasible and infeasible solutions generated in the evolution process and guide the population to skip the infeasible domain to reach the optimal frontier.Therefore,based on the evolutionary algorithm,we select two representative constraint processing techniques to study the convergence and distribution of the algorithm.The main research contents are summarized as follows:Firstly,a self-tuning operator and adaptive ? truncated NSGA-II algorithm are proposed for the problem of convergence and distribution imbalance in the process of population optimization.Different from the classical crossover operator,the normaldistribution crossover operator is adopted in this method,which enables the algorithm to obtain the probability of more uniform sub-generation values based on a wider search space.At the same time,it greatly reduces the situation which the algorithm being trapped in local optimum,therefore,it can play a role in improving the population diversity.Then,through the adaptive mutation operator,the relation between the mutation value and the value of the objective function is established,and the mutation rate is adjusted according to the degree of evolution to improve the convergence of the algorithm.Finally,through the adaptive ? truncation strategy,the infeasible solution with less constraint violation degree are introduced in the early stage of the algorithm to increase the diversity of the population.In the later stage of the algorithm,the ? value reduces to 0.At this moment,all the individuals in the population are feasible,which promotes the convergence of the population.In this way,the convergence and distribution of the algorithm are effectively adjusted by this method.Secondly,in order to solve the problem which is that the previous constrained optimization algorithms adopted the same strategy for the superior solution and inferior solution and leads to poor performance of the algorithm,a two-stage three-archive set constraint optimization algorithm is proposed.Three different archive sets are used to preserve the non-dominated solutions,dominating solutions and non-dominated feasible solutions,which are all generated during evolution.By adopting different optimization strategies for each archive set,this method enables each archive set to achieve optimal search efficiency and to reduce the algorithm for unnecessary crossover and mutation.Moreover,this method effectively takes the information provided by the optimal infeasible solution as the evolutionary direction and serves as the guiding indicator of the algorithm.The feasibility and effectiveness of the algorithm are verified by experiments on different constraint test functions.Third,the proposed algorithm is applied to the traveling salesman problem and vehicle routing problem.For the traveling salesman problem,the classical singleobjective problem with shortest path is extended to the multi-objective problem with shortest path and lowest cost.Meanwhile,the soft time window constraint is also added to develop a new model of multi-objective traveling salesman problem.Combining with the two-stage three-archive set constraint optimization algorithm proposed in this thesis,the method is verified with the Solomon standard test set,and it shows good performance of the algorithm.As for the vehicle routing problem,based on the actual situation,the established model is designed as a multi-objective multi-vehicle path model.Based on the constraints of the soft time window,the vehicle overweight limit and the vehicle expenditure cost limit were added.Combining with the self-tuning operator and adaptive ? truncated NSGA-II algorithm proposed in this thesis,shows the effectiveness when it is used to solve the vehicle routing problem.