关键词: 进化算法，约束优化，满意度函数，罚函数

Abstract: Penalty function method is one of the most widely used methods for constrained optimization problems in evolutionary algorithms. It makes the search approach the feasible region gradually by the way to punish the infeasible solutions. hhe penalty functions are usually defined as the sum of the objective function and the penalty temps. The methods will bring two main drawbacks. Firstly, it is difficult to control penalty parameters, secondly, when the difference between the objective function value and the constrained function value is great, the algorithm can not effectively distinguish feasible from infeasible solutions, and thus can not handle the constraints effectively. To overcome the defects, two satisfaction degree functions defined by the objective function and the constraints function were designed, respectively. A new penalty function was constructed by these two satisfaction degree functions. Moreover, we designed an adaptive penalty factor which is varying with the quality of the population and the number of generations. As a result, the penalty factor can be easily controlled. hhus a new penalty function optimization model was proposed. Furthermore, a new crossover operator and a new mutation operator were designed. Based on these, a new evolutionary algorithm for constrained optimization problems was proposed. The simulations are made on six widely used benchmark problems, and the results indicate the proposed algorithm is very effective.

Key words: Evolutionary algorithm, Constrained optimization, Penalty function