Research On Evolutionary Algorithms Based On Level Set Evolution For Global Optimization

In recent years, the global optimization problems have wide applications in many fields, such as in engineering design, decision-making and management etc, and much attention has been paid to designing simple and efficient global optimization algorithms that have no strict limitations to the problems. A theoretical model of the algorithm based on the mean function value and level set method for global optimization is proposed in [15]. This method has not strict limitations to the problems such as the requirement of convexity of the search space, differentiability of functions involved, etc. It only requires the continuity of functions involved, and this kind of theoretical algorithm is globally convergent. Evolutionary algorithms are new effective algorithms for complex nonlinear optimization problems. They do not require the differentiability and convexity of functions. To large-scale complex nonlinear optimization problem, it has more superiority over traditional algorithms. In this paper, we improve the model of the algorithm proposed in [15], and design a new evolutionary algorithm based on the improved model for unconstrained global optimization problems and constrained global optimization problems respectively. The main idea is to design an effective genetic algorithm to evolve the level set iteratively. As a result, the global optimal solution will be gradually approached. In order to make the proposed algorithm effective and efficient, we sufficiently consider the specific structure of the improved model and make use of its superiority. Moreover, we combine its superiority, evolutionary operators and constraint handling techniques with the algorithm design such that the proposed algorithm is sound.In chapter 2, a new evolutionary algorithm is proposes for the unconstrained global optimization. During the algorithm design, we adopt the real number encoding and design the crossover operator applying the idea of uniform design. To enhance the crossover operator, the local search scheme is applied after crossover operation such that the exploration ability of the crossover operator can be greatly improved. Moreover, the global convergence of the proposed algorithm is proved. The results of the numerical simulation indicate that the algorithm is effective. In chapter 3, the constrained global optimization problem is tackled. Based on the operators designed for unconstrained optimization problems in chapter 2, we design a new penalty function, a new crossover operator, a new mutation operator and a new selection operator ,respectively, and we prove the global convergence of the algorithm. At last, the results of the numerical simulations show that the proposed algorithm is effective.