A Multi-objective Genetic Algorithm Based On A New Model

Many real world problems are usually composed of multi-objective problems. Generally, these objects are conflict and the number of Pareto optimal solutions is usually infinite. How to find a sufficient number of uniformly and widely distributed representative Pareto optimal solutions for the decision maker is very important.Many problems which often depend on the mathematical characteristics of the objective functions can not be solved satisfactorily by the traditional approaches. Genetic algorithms have been proved efficient to many hard engineering optimization problems due to its global searching ability. Over the last 10 years, there has been an increasing interest in applying genetic algorithm to multi-objective optimization problems, and many work have been done in this field.In this thesis, the basic concepts, theories and frames of the evolutionary algorithm and the multi-objective optimization are systematically introduced firstly. Then a new measure called S-measure for the broadness of the non-dominated solution range in the objective space based on the orthogonal design is proposed. Through the introduction of the concepts of the rank variance, density variance and S-measure variance based on the rank, density and distribution of the solutions, the multi-objective optimization problem is converted into a three-objective optimization problem. For the transformed problem, a two-phase multi-objective genetic algorithm (TPMOGA) is proposed. See wheather the maximum archive number tends to M and whether the density variance and S-measure variance tends to zero as the end conditions, the algorithm tends to find good quality non-dominated solutions. In the end the convergence of TPMOGA is proved. The computer simulations demonstrate that TPMOGA can find a large number of uniformly and widely distributed Pareto-optimal solutions.