Research On Discrete Differential Evolution And Its Engineering Application

Differential evolution(DE) is a global optimization algorithm,first proposed by Kennedy Price and Rainer Storn in 1997. As a bionic algorithm,differential evolution is a simulation of Darwinism theory,that is survival of the fitness,and the inheritance-mutation principles by Mendel. Differential evolution is real-coded and therefore is quite simple in encoding.The evolutional operations of DE include merely mutation,crossover and selection.Only three parameters,namely the swarm size,scale factor,and the crossover rate are required in running the algorithm. And DE is repeatedly proved of an extremely fast convergence speed and a high robustness.All these strengths make DE an extensively popular algorithm ever since it was first proposed. Yet due to its unique mutation operation, DE is limited to the continuous problems and not applicable to the discrete problems,which however exist in great amounts in engineering practice. Inspired by its excellent performances in continuous problems,growing interests in the research of applying DE directly to discrete problems has arisen in recent years. This paper aims at putting forward a discrete version of DE,based on a thorough study of recent advances in this field. This paper is consisted of the following segments.A review is presented of the state-of-the-art developments and major applications of DE. A classification of these studies is drawn and the insufficiency of discrete DE and theoretical studies are pointed out.A comprehensive introduction of the principles of DE is provided and the spatial implication of evolutionary operations is explained in details and a flow chart of the standard DE is given. Variant schemas of DE are introduced and the rules in setting controlling parameters are also expounded.Considering the similarity between genetic algorithm(GA) and DE,a comparison of their evolution principles is conducted. Differences in inheritance operation and mutation operation are discussed. A conclusion is drawn that DE is more powerful in exploitation of local optima while GA is more suitable in global exploration,which is confirmed by a following numerical experiment.A research into the mutation operation of DE is made and the mutation is essentially a random search in the hyper-spherical space,with its center at the point depended on the base vector and its radius defined by the greatest difference of individuals in the swarm. Based on such knowledge a new mutation operation is raised to replace the original mutation operation and a discrete version of DE is put forward to operate directly in discrete space. Three schemas are also raised,depending on the different strategies adopted in the selection of base vectors. According to the performance assessment rules for heuristic algorithms,ten standard test functions are chosen to measure the feasibility and the effectness of the new DE. The optimizations produced by the new DE are compared against the results already available in current publication by PSOs and it is found that the accuracies and stability of solutions by the new DE out-performed the many discrete PSOs over several test functions.The Markov chain theory is used in analyzing the convergence of the proposed discrete DE. Based on the Markov chain theory and random mathematics the chain of the new DE is established. Due to the characteristics of the mutation operation,the swarm stops evolution when the swarm enters a steady Markov state,namely the Markov chain is stuck in a self-absorbing state,resulting in a failure to find the global optimum with probability 1.In order to test the performance of the proposed discrete DE in solving engineering problems,the optimization of structural designs of bridge cranes is chosen and optimized using the proposed DE. To better serve the design of bridge cranes,a software system for the design and optimization of crane structures is built,based on the proposed DE algorithm. Genetic algorithm,standard different evolution and fruitfly optimization algorithm are also included in the system for comparison purpose. The structure of a typical bridge crane was designed and optimized using the aboved algorithms and the results proved again the superiority of the proposed discrete DE in finding more accurate and more stable a solution.