This dissertation is composed of three parts. In the first part, the background of our research is introduced, and the developments of evolutionary algorithm and the future prosperity are reviewed. In the second part, a brief introduction to evolutionary algorithm, including the basic concepts in evolutionary algorithm, the key elements of evolutionary algorithm, some existed improved evolutionary algorithm and its mathematical basics are discussed. In the third part, an improved evolutionary algorithm based on law of conservation of entropy called ECEA is presented. In the fourth part, precise optimal solutions of the constrained problems are gotten by using this algorithm. Compared with other methods, the experimental results of the new algorithm show the advantages of the convergence and accuracy.The main research work and innovation of this work are as follows:(1) ECEA is proposed in this thesis, which simulates the law of conservation of entropy in the universe system to coordinate the contradictions between the elitist strategy and population diversity. The value range of entropy of population fitness (hereinafter referred to as population entropy) is mapped to [0, 1], which represents the diversity of population. In order that it can be with the elitist entropy (elite selection rate) to constitute the equation of conservation of entropy. So the elitist can be chosen adaptively according to the diversity of population. In the initial stage of evolutionary, the solution search area is increased by reducing the choice of the elitist. With the iterative generation increasing, the number of the elite is greatly increased dynamically to accelerate the convergence speed of the algorithm.(2) A semi-consistent-crossover-operator is proposed, which can changes the crossover operator adaptively according to the diversity of population. So the population diversity can be improved at the first half time in population evolving, and semi-consistent-crossover-operator can speed up the convergence to the optimal value at the second half time. And then a non-uniform mutation rate based on the population entropy changing is proposed, its value is so small at the first half time in population evolving in order that the fine individuals not be destroyed easily, while in the second half time the value has been increased, in order to reduce the capability of converging to a local optimal solution at a certain extent.(3) ECEA is feasibility and efficiency through theoretical proofing and examples contrasting. At the first, theoretical analysis of convergence and the computing performance of ECEA based on the Markov chain are presented, then ECEA is applied to solve the optimization of some benchmark constrained functions. And the results of the experiments show that ECEA, compared with other optimal methods, has faster convergence and solutions with high precision. |