Differential Evolution Algorithm And Its Application In Mechanical Optimum Design

Evolution algorithm is a kind of random searching algorithm. It simulates biology natural selection and natural evolution, through iterating repeatedly. This kind of algorithm does not need other auxilformiary informations of the function, and can achieve very high accuracy. It is especially suitable for the complex nonlinear optimization problems. Differential evolution algorithm (DE) is one kind of evolution algorithm, which based on the population difference and proposed by Rainer Storn and Kenneth Price in 1996. It has the parallel and fast searching as well as programming easily features. It has obtained the widespread application in various fields afterwards. The work carried out in this paper includes two major contents as follows.Firstly, it is considered in this paper that the community cooperation evolution thinking cannot be manifested in the basic deferential evolution algorithm very well. Therefore, this article introduced the concept of central point of the population, and proposed a modified differential evolution algorithm, in which the central point of the population participates in competition of the optimum point of the population. Also the center differential evolution algorithm introducing the central point of the population in variation operation and a modified center differential evolution algorithm in which the central point of the population participates in variation operation and in competition of optimum point of the population are proposed. The self-adptive crossover rate is also introduced.Secondly, whereas multi-objective optimization problems widely exist in real world and its research is still a hotspot in evolutionary algorithm research, a multi-objective differential evolution optimization algorithm based on dynamic Pareto optima set and center differential evolution is brought forward. The proposed algorithm used an external archive to store nondominated solutions. Individuals in archive must be compared with each other and eliminated gradually. At last a whole Pareto optima set would be obtained. For the multi-objective optimization problems with constraint conditions, the direct solution method is used to process constraints. The simulation results of some typical test functions and results of some engineering optimization design examples in this article all proved the validity of these proposed algorithms.