Research On Evolutionary Algorithms For Constrained Optimization And Multiobjective Optimization

It is common to face a number of optimization problems in many areas of the real world, especially in the science and engineering fields. However, these problems are often constrained, and sometimes the optimizing objective number is more than one. Because of the different features of these problems, the traditional methods in Operational Research are hard to solve these problems effectively. As robust population-based global search methods, Evolutionary Algorithms (EAs) are very promising to solve the constrained optimization problems and the multiobjective optimization problems. Therefore, the research of evolutionary optimization has received more and more attentions, and has become a hot research field in Evolutionary Computation.The aim of this dissertation is to explore the theories and mechanisms of EAs and to design effective algorithms and strategies for Single-objective Constrained Optimization, Multiobjective Optimization and Multiobjective Constrained Optimization, and to do the corresponding theoretic and experimental analyses. The main research works in this dissertation consist of the following aspects.(1) For Single-objective Constrained Optimization, in order to improve the explicit search biases ability in feasible regions, three preconditions of explicit search biases are presented, and then a novel search biases selection strategy is proposed by using stochastic ranking and is implemented within the framework of Evolution Strategy (ES). In order to effectively locate the feasible global optimum, how much attention should be paid to the promising infeasible solutions is investigated. Then with the analyses of the influence of the comparison probability in stochastic ranking on the final position of the feasible solution after ranking, a novel dynamic stochastic selection strategy is put forward within the framework of multimember differential evolution and the dynamic settings of the comparison probability are also discussed. Experimental results on common benchmark functions demonstrate the effectiveness of the two strategies, respectively.(2) For Multiobjective Optimization, by the comparisons and analyses of the simulated binary crossover (SBX) and mutation operator in ES, a novel normal distribution crossover (NDX) is designed for the steady-state multiobjective evolutionary algorithm (MOEA)ε-MOEA with the introduction of discrete recombination operator in ES. So the NDX not only has the equal exploitation ability with the SBX, but also has more effective exploration ability. And the experimental results show that the NDX significantly improve the quality of the obtained non-dominated solutions by the algorithmε-MOEA. Based on the analyses of the relationship between the value of the parameterεand the maximum number of the non-dominated solutions, a novel self-adaption strategy for the parameterεinε-MOEA is proposed. Then this novel strategy is applied in the algorithmε-MOEA, and the experimental results on 10 benchmark functions demonstrate that even if without the good initial value for the parameterε, the algorithm is able to approximately obtain the expected number of non-dominated solutions, which are very close to and uniformly distributed on the Pareto-optimal front. Furthermore, the genetic drift phenomenon arose by the self-adaption strategy is discussed. Two cases of genetic drifts are pointed out, and the (possible) corresponding solutions are provided. By the introduction of the archive set, a steady-stateε-MOEA with the self-adaption of the parameterεis proposed and the steady-sate characteristic is also proved theoretically. In order to reduce the computational amount, an approximate steady state algorithm is designed in the experiments by setting the upper limit and adopting the FIFO (First In, First Out) updating strategy for the archive set, and the comparison experiments on common test functions are also done.(3) For Multiobjective Constrained Optimization, in order to enhance the boundary search ability, two schemes of selecting the current best solutions for multiobjective differential evolution are proposed. And in order to obtain more complete Pareto front, a hybrid approach named DE-MOEA based on genetic algorithm and multiobjective differential evolution is given within the (N+N) framework by the reference of the search biases strategy suggested by Runarsson and Yao, i.e., the two schemes are used in the evolutionary multiobjective constrained optimization. Then the hybrid algorithm DE-MOEA is compared with the current state-of-the-art algorithm CNSGA-II on 12 common test functions, and the experimental results show that the hybrid algorithm has better performance, especially in the distribution of the obtained Pareto front. In addition, the parameter settings in the hybrid algorithm DE-MOEA are also analyzed and discussed.In this dissertation, with the studies in evolutionary constrained optimization and evolutionary multiobjective optimization, a novel search biases selection strategy and a novel dynamic stochastic selection strategy are designed for Single-objective Constrained Optimization, a novel normal distribution crossover, a novel self-adaption strategy for the parameterεand a steady-stateε-MOEA with the self-adaption of the parameterεare proposed for Multiobjective Optimization, and a hybrid algorithm based on genetic algorithm and multiobjective differential evolution is suggested for Multiobjective constrained optimization. The works in this dissertation are very important to the research of the evolutionary optimization and the optimization applications of EAs in the real world.