Study On Evolutionary Algorithms For Many-Objective Optimization Problems

With a wide range application of multi-objective optimization problems in the fields of engineering and practice,the research of multi-objective optimization problems has become a hot research topic. As a population-based intelligent search method, evolutionary algorithms have been able to successfully solve multi-objective optimization problems with two or three objectives currently. However, for many objective optimization problems(i.e., for the problems with four or more objectives), evolutionary algorithms based on Pareto dominance will face huge challenges in search ability, computation cost and visualization etc. Therefore, the research on many-objective evolutionary algorithms has become one of the key issues in the field of evolutionary algorithms.Many-objective optimization problems can be divided into two categories according to actual dimension(i.e., the number of independent objective functions) of the Pareto front. One is the problem in which the actual dimension of the Pareto front is less than the number of the objective functions, and this kind of many objective optimization problems contains redundant objectives which can be removed. The other is the problem in which the actual dimension of the Pareto front equals to the number of the objective functions, and this kind of the problems does not contain redundant objectives. The aim of this dissertation is to design some efficient many-objective evolutionary algorithms to solve the two kinds of many-objective optimization problems. The main contributions of this dissertation consist of the following aspects.1. For many-objective optimization problems containing redundant objectives, two novel objective reduction algorithms are proposed in this dissertation. One is a novel objective reduction evolutionary algorithm based on Pareto representative solutions, under the premise of keeping the Pareto dominance relationship between solutions. First, in order to obtain the entire conflicting information on the whole Pareto front, a set of representative non-dominated solutions widely distributed on the approximately Pareto front are generated by using a decomposition based multi-objective evolutionary algorithm. Then, a fast objective reduction algorithm is proposed after analyzing conflicting objectives of the representative non-dominated solutions. The other objective reduction algorithm is based on objective clustering by analyzing the relationship between objectives. Different from the existing works, a novel metric: inter-dependence coefficient, which uses the union of mutual information of objectives and correlation coefficient, is introduced. This metric can represent the non-linear relationship among objectives. In order to remove redundant objectives, PAM clustering algorithm is employed to merge the less conflict objectives into the same cluster and assign the more conflict objectives to different clusters. Afterwards, the cluster which has the least conflict is chosen and some of the objectives in it are removed to make the objective reduction. Finally, numerical experiments are conducted and the results indicate the effectiveness of the two proposed algorithms.2. For many-objective optimization problems without any redundant objective, two modified decomposition based multi-objective evolutionary algorithms are developed from two different perspectives. In detail, from the perspective of designing weight vectors, a novel adaptive weight vector decomposition based many-objective evolutionary algorithm is proposed. The proposed algorithm can dynamically adjust the distribution of the weight vectors according to the shape of the Pareto front using uniform design, meanwhile, a preprocessing method in the initialization period, which assigns the best weight vector for each initial solution, is also proposed. Besides, from the perspective of hybrid evolution modes, a hybrid decomposition evolutionary algorithm based on a new dominance relation between individuals is proposed. In order to increase the selection pressure and improve the diversity, the subpopulation evolutionary model is adopted in the proposed algorithm, and a new dominance relation based on efficiency order is designed to compare and update individuals inside each subpopulation. Besides, for the purpose of improving the performance of local search, Powell search scheme is used as the local search operator in the proposed evolutionary algorithm. The experiment results for standard test problems show that the proposed two algorithms have advantages over the compared algorithms in convergence and diversity.3. For the distribution programming problems in the field of logistics, firstly,a method for quantitative calculation of the logistics service level based on commodity processing ability is proposed. Second, a multi-objective optimization model with three objectives is developed for the logistics distribution programming problems. The three objectives are the minimization of the total expense, the maximization of the logistics service level based on distribution time, and the maximization of the logistics service level based on commodity processing ability, respectively. Third, we propose a preference based multi-objective evolutionary algorithm to solve the model. Finally, an example of logistics distribution planning is simulated with ten non-dominated solutions obtained within the scope of the subjective preference and provide scientific basis for decision makers.