Evolutionary Algorithms For Multi-Objective Optimization Without Preferences And Their Applications

Arising from practical problems, multi-objective optimization plays a significant role in economy, military and other high-tech research fields.Multi-objective optimization often involves incommensurable and competing objectives, and the number of its Pareto optimal solutions is usually infinite, thus how to find a sufficient number of uniformly distributed and representative Pareto optimal solutions for the decision maker is very important.In this thesis, the basic concepts, theories and frames of the evolutionary algorithm and multi-objective optimization are systematically introduced firstly. Then a new model of multi-objective optimization based on the ideal variance of the population rank and the variance of the population density is proposed, among which the ideal variance of the population rank is a measure of the quality of solutions obtained on Pareto front, and the variance of the population density is a measure of the uniformity of the distribution of solutions obtained on Pareto front. Using these two measures as two objective functions, the multi-objective optimization problem is finally converted into a bi-objective optimization problem. For the transformed problem, a novel multi-objective genetic algorithm (a rank and density multi-objective evolutionary algorithm: RDMOEA) is proposed and the convergence of RDMOEA is proved. The computer simulations demonstrate the effectiveness of the proposed algorithm.Furthermore, a new multi-objective genetic algorithm is presented to solve the nonlinear constrained programming problem. The problem is firstly converted into a two-objective optimization. For the transformed problem, a novel multi-objective genetic algorithm (NMGA) is proposed and the global convergence is proved. The numerical experiments show that NMGA is effective in dealing with the nonlinear constrained programming problem.