Research On Multi-objective Evolutionary Algorithms In Low And High Dimensional Objective Space

In the real world,most of the optimization problems have at least two or more objectives to be optimized,which are generally called the multi-objective optimization problems.After more than 20 years' developing,the multi-objective evolutionary algorithms should be one of the most popular ways to handle the multi-objective optimization problems.This dissertation focuses on the different technical difficulties of the multi-objective evolutionary algorithms in both low(2 or 3 objectives)and high(more than 3 objectives)dimensional objective space.Moreover,this dissertation has proposed three different multi-objective evolutionary algorithms,specially designed for tackling the low dimensional,high dimensional,and both low and high dimensional objective space cases,respectively.The main research work of this dissertation is outlined as follows.1)Concerning the diversity maintaining issue of the multi-objective evolutionary algorithms in the low dimensional objective space,this dissertation studies the related works of the decomposition based multi-objective evolutionary algorithms,and proposes a multi-objective evolutionary algorithm based on hierarchical decomposition,named MOEA/HD.MOEA/HD adopts the concept of hierarchy,and builds a subordinate-superior hierarchical relationship between each two subproblems,thus connecting all the subproblems as a self-organized map and self-adaptively adapting the evolutionary directions and behaviors.According to the related experiments of this dissertation,MOEA/HD performs better than the other comparison algorithms on most test instances in bi-and tri-objective space.In particular,MOEA/HD maintains better diversity and uniformity of the population in objective space,when tackling complex and irregular Pareto fronts.2)Concerning the lack of convergence for the multi-objective evolutionary algorithms in the high dimensional objective space,this dissertation studies the related works of the distance based evolutionary algorithms,and proposes a Minkowski distance based evolutionary algorithm,named MDEA.MDEA adopts the concept of Minkowski distance,and dynamically estimates the general curvature of the targeted Pareto front,thereby self-adaptively choosing the most proper order of the Minkowski distance to measure the convergence degree of each solution,providing an extra selection pressure on the population evolution.According to the related experiments of this dissertation,MDEA performs better than the other comparison algorithms on most test instances in 5-and 10-objective space.In addition,this dissertation also studies the integration of the Minkowski distance method in MDEA with two other classic distance based evolutionary algorithms.The empirical results indicate that the integrated algorithms perform generally better than their original versions,which also confirms the efficiency and universality of the proposed Minkowski distance method.3)Concerning the difficulty of simultaneously adapting to the different convergence and diversity demands in the low and the high dimensional objective space for the multi-objective evolutionary algorithms,this dissertation studies the related works of the indicator based evolutionary algorithms,and proposes a polar metric based evolutionary algorithm,named PMEA.PMEA adopts the concept of polar metric,and combines the techniques of both the weight vector and the distance,under a comprehensive consideration of both diversity and convergence.According to the related experiments of this dissertation,PMEA performs better than the other comparison algorithms on most test instances in 3-,5-and 10-objective space,which satisfies the designing target of balancing the diversity and convergence in both low and high dimensional objective space to some extent.In addition,this dissertation also studies the performance of PMEA on a real-world test instance.The empirical results indicate that PMEA still performs the best,which demonstrates the universality and generality of PMEA.In general,this dissertation mainly studies the different requirements for diversity and cornvergence in low and high dimensional objective space,and have proposed corresponding solutions and algorithms.Numerous comparison experiments have proved the efficiency,as well as the guiding significance and application value,of the proposed solutions and algorithms,to push forward the research of multi-objective evolutionary algorithms in low and high dimensional objective space.