A Multiobjective Evolutionary Algorithm Based On Weighted Sum Method And Uniform Design

Many real-life decision making problems must consider optimizing a number of objectives simultaneously, and these objectives often conflict with each other.The goal of multiobjective optimization algorithms is to find a set of the most reasonable and most reliable solutions from all possible solutions. There are two main challenges for multiobjective optimization algorithms:1) How to find out more nondominated solutions in the sparse regions of nondominated frontier in order to obtain a uniformly distributed solutions along the nondominated frontier.2) How to find out nondominated solutions which are nearest to the true Pareto frontier in order to obtain high quality nondominated solutions. In this thesis, a new multiobjective evolutionary algorithm based on weighted sum method and uniform design is proposed. Its main works include:1. A new crossover operator is designed, in which two cases are considered and in each case, an efficient scheme is used to generate potential offspring. First, considering the case that solutions in some part of the nondominated frontier may be crowded and solutions in other part may be sparse, in order to get a uniformly distributed and sufficient number of solutions along the nondominated frontier, the crossover operator is designed by using uniform design and by selecting two adjacent individuals in the sparse part of the nondominated frontier as two parents. In this way of crossover, the obtained solutions will distribute more uniformly. Second, to overcome the shortcoming of weighted sum method which can not obtain the solutions on the non-convex part of the Pareto frontier, and considering the case that there may be some nondominated solutions between a pair of far away adjacent individuals in the nondominated frontier, each of these adjacent individuals and its nearest neighbor dominated solution are selected as a pair of parents to do the crossover. In this way of the crossover, it is more possible to find more nondominated solutions on the non-convex part of the nondominated frontier.2. Based on crossover designed, a new evolutionary algorithm called an multiobjective evolutionary algorithm based weighted sum and uniform design is proposed, and its global convergence is proved. The computer simulations on five test problems and the comparisons of the proposed algorithm with the well known algorithm NSGA-Ⅱvia three performance measures are made, and the results indicate the proposed algorithm is more efficient and effective.