Modified Differential Evolution Algorithms For Discrete And Continuous Optimization Problems

Evolutionary algorithms have been proved to be one kind of robust global methods for solving highly nonlinear, nondifferentiable, multimodal and multivariate optimization problems which cannot be solved by traditional gradient-based optimization techniques. Furthermore, they are suitable for problems, which are affected by noise, or their objective functions cannot be expressed in explicit mathematical forms.As a simple random heuristic search algorithm, Differential Evolution (DE) algorithm is tensively studied by scholars in various countries, due to its advantages such as stability and good global search ability. In this thesis the modified DE algorithms for integer programming, constrained optimization and unconstrained optimization problems are addressed.The main contributions of this paper are outlined as follws:For integer programming problems, a modified DE algorithm is proposed. First, in order to increase the probability for each parent to generate a better offspring, each solution is allowed to generate more than one offspring through six different mutation operators. Then a migration operation is designed to overcome premature convergence of DE. Three criteria based on feasibility are used to deal with constraints of the problem. At last, simulation results on eleven benchmark functions show that the proposed algorithm is superior to other methods in terms of convergence speed and solution quality. The algorithm can be used to solve higher dimensional problems and constrained problems.A hybrid DE algorithm for solving constrained optimization problems is proposed. By using the exact penalty method to handle the constraints, the constrained problem is transformed into an unconstrained problem. Three different mutation operators are adopted. The proposed algorithm could find the approximate optimization solution at different levels by combining estimation of distribution algorithm with DE. Finally, thirteen benchmark problems are used to illustrate its effectiveness. Simulation results show that the improved DE has global search capability, high precision and fast convergence, which is a competitive algorithm for constrained optimization.For the unconstrained optimization problems, another hybrid DE algorithm is proposed. In the algorithm, three different mutation operators are adopted. The simplex method is taken as a local search operator to improve the solution accuracy and the computational efficiency. A histogram probability model is used to generate some offspring. Finally, simulation results on eleven benchmark functions show that the proposed algorithm is efficient.