New Evolutionary Algorithms For Multiobjective Optimization Problems

Multiobjective optimization problem has a wide range of applications in the real world. It is different from the single objective optimization. It often involves incommensurable and competing objectives, and the number of its Pareto optimal solutions is usually infinite. Therefore, it is very important to design new algorithms which can find well distributed and close-to-Pareto-optimal solutions.In this thesis, the basic concepts, theories and frames of the evolutionary algorithm and multi-objective optimization are reviewed and analyzed systematically first. Then an improved multiobjective evolutionary algorithm (LEMOEA) is proposed which is based on NSGA-II. It uses distribution function to limit the number of individuals chosen by elitist scheme, and a good diversity of solutions can be kept. Moreover, the single-compound crossover operator is designed and it can increase the search ability of the algorithm. Experimental results show that the improved algorithm has faster convergent speed and can find the better diversity of solutions than NSGA-II.Furthermore, a multiobjective particle swarm algorithm based on the crowding distance is proposed. The crowing distance proposed in NSGA-II is adopted to calculate the crowing degree of the nondominated solutions in the external archive in this paper. The globally optimal position of each particle is predicted according to tournament selection scheme, and each particle is then guided to a sparse region of nondominated solutions. As a result, it is helpful for an algorithm to find a better distribution of the nondominated solutions. Moreover, the adoption of the dynamic mutation operator is beneficial to avoid the premature convergence. The results indicate the proposed algorithm is better than the compared algorithms on solution quality and distribution.