Research And Application Of Multi-objective Optimization Algorithms Base On Differential Evolution

In scientific research and engineering design, many specific issues can be summarized as parameter optimization problems often with multiple design objectives. These multiple objectives often conflict with each others, which means any improvement in one objective often lead to performance degradation of at least one objective. So achieving an optimum for all objectives simultaneously is very difficult. Therefore, research on multi-objective optimization algorithms becomes a hot topic both for scientific research and engineering design. Evolutionary algorithms (EAs) are intelligent heuristic optimization and search techniques inspired by nature. During the past thirty years, EAs have attracted wide attention by many researchers in solving multi-objective optimization problems. As an important component of EA community, differential evolution (DE) is a new intelligent heuristic optimization algorithm which has many merits such as it is easy to understand, it has a simple structure, there are a few control parameters and high robustness. This thesis aims at solving multi-objective optimization problems based on DE, the main contributions of which can be summarized as follows:(1) Research on solving multi-objective problems with differential evolution is conducted and a DE with clone immune multi-objective optimization algorithm is proposed. The main structure of the approach is based on DE, but makes some modifications during population initialization, DE mutation operator and selection operator. Asymmetric Latin hypercube design method is used in the initialization step to enhance the diversity of the main population. In DE mutation step, a neighborhood topology among all the individuals is defined and then a new mutation operator combining local search and global search is proposed. Crowding distance based proportional cloning operation is adapted to improve both the convergence speed and optima diversity. Experimental results on5test functions indicate that the new algorithm outperforms two state-of-the-art multi-objective evolutionary algorithms.(2) Because single strategy based selection operator easily make the search get stick at local optima, a multi-population strategy based multi-objective optimization algorithm (DEHC) is designed. In DEHC, the main population is divided into three sub-populations and each sub-population corresponds to a different selection strategy, which can combine all the advantages of each selection strategy. An external archive is introduced to store all the current non-dominated solutions and these solutions are also as the final output results. Additionally, a mutation candidate pool is established to store two commonly used strategies and then one strategy is selected when needed. Experimental results on a large number of test functions indicate that the proposed multi-population strategies are beneficial for tackling optimization problems with multiple conflict objectives.(3) Enhancing the search engine’s exploration and exploitation abilities and developing an effective constraint-handling technique are two issues in solving constrained problems, so a new hybrid differential evolution algorithm with alpha constrained domination technique (HDE-aCD) is presented. In HDE-aCD, a new hybrid operator based on DE and dynamic simplex crossover operator is designed and the new operator puts more effort on enhancing the search algorithm’ exploration at the beginning stage and enhancing the exploitation at the later stage. Furthermore, to effectively tackle the constraints, a new alpha constrained domination method is presented by incorporating fuzzy control and dominant principle. In the method, how well an individual satisfies the constraints is measured by a membership function, i.e. an individual is a feasible one with a high probability if it close to feasible domain while is an infeasible one if it is far from the feasible domain. So the dominant relationship of two individuals is modified. Experimental results indicate HDE-aCD is an effective approach to solve constrained problems.(4) To determine a set of proper control parameters for DE, a new approach which integrates self-adaptive differential evolution algorithm with epsilon constrained-domination principle is put forward, named SADE-εCD. In SADE-εCD, the trial vector generation strategies and the DE’s parameters are gradually self-adjusted adaptively based on the knowledge learnt from the previous searches in generating improved solutions. Furthermore, by incorporating domination principle into epsilon constrained method, epsilon constrained-domination principle is proposed to handle constraints in multi-objective problems. According to this principle, the pseudo feasible concept is defined for the first time and the main individuals are divided into two kinds, i.e. pseudo feasible ones and pseudo infeasible ones. SADE-sCD treats the pseudo feasible individuals as feasible ones and this highly increases the diversity of main population and finely exploits the useful information carried by some infeasible individuals. The advantageous performance of SADE-sCD is validated by comparisons with multi-objective evolutionary algorithms over fourteen test problems. The performance indicators show that SADE-εCD is an effective approach to solving constrained multi-objective problems, which is basically enabled by the integration of self-adaptive strategies and epsilon constrained-domination principle. In addition, results of solving4engineering design problems indicate the feasibility and effectiveness of SADE-εCD in solving engineering problems.(5) To solve the engineering design problems, i.e. p-Xylene oxidation reaction process and gasoline blending design problem, first these problems are converted into constrained multi-objective problems and then SADE-εCD is applied to solve these problems, Compare to using single-objective optimization, using multi-objective optimization can provide a set of trade-off Pareto optimal solutions and the performs can select a preferred solution. Experimental results indicate that SADE-εCD is a potential method to solve engineering design problems.