Single-objective And Multi-objective Optimization Evolutionary Algorithms And Their Application

In many fields of science and technology, industries and practice etc, there are a lot of problems can be converted into the kind of mathematical model about certain function optimization.Evolutionary algorithms are one of the effective algorithms for hard optimization and multiobjective optimization problcms, which are attached more and more importance to. This paper studies evolutionary algorithms for single objective and multiobjective optimization.A novel constrain handling algorithm is proposed. This algorithm use infeasible individuals to increase search space and avoid to choose penalty factor. It has two populations, which are feasible population and infeasible population. This method searches the solution space through the mixture crossover of feasible and infeasible solutions, and does the selection operation on feasible and infeasible populations, respectively. Selection operation evaluates fitness function of individuals and it converges to optimum solution according to evolution theory of "survival of the fittest".It avoids the difficulty of selecting the penalty factor in penalty strategy and makes the handling constrain simplify. This paper chooses ten problems from benchmark problems.The problems have been solved by new algorithm and the results have been campared with other algorithms.The results indicate the proposed algorithm is better than others and it has a certain stability.A multiobjective evolutionary algorithm is improved in this paper.New algorithm have two improvements. At first, it uses new method which is proposed in this paper to handle constrain. Second, it introduces dynamics population strategy and eliminates crowded comparison opterator. The function of crowded comparsion operator in NSGA-II is that select some individuals from non-dominated set F_i to keep a determined population in parent generation. It uses the dynamic population strategy, so cowded comparsion operator is not need. Because the variables perturbations cannot be avoided in practice, practitioners are interested in finding the so-called robust solutions which are less sensitive to small changes in variables. To the MEMS designing problems, this paper use an improved NSGA-II algorithm to search robust solutions. The results of resonators' parameters indicate the proposed algorithm is feasible.