The Cooperative Co-evolutionary Differential Evolution Algorithms To Optimize High-Dimension Function

Co-evolution algorithm(proposed by Hillis firstly in 1991)has been developed as a kind of new evolution algorithm extensively on the base of co-evolution theory.The difference between co-evolution algorithm and traditional evolution algorithm is that co-evolution algorithm takes the adjustment of populations as well as that of populations and environment into account in evolving process.For the advantages of co-evolution algorithm,more and more scholars contribute to this field,which makes it a hotspot in evolution computation.Moreover,DE is proposed by Storn and Price in 1995,which is a stochastic,population-based,and relatively unknown evolutionary algorithm for global optimization that has recently been successfully applied to many optimization problems.This dissertation focuses on how to apply DE and co-evolution to complex functions optimization,including the following contributions:(1)A cooperative co-evolutionary differential evolution(called CCDE)was proposed based on DE and the framework of cooperative co-evolutionary approach.CCDE partitions a high-dimensional complex search space by splitting the solution vectors into smaller vectors,then uses multiple cooperating subpopulations(or smaller vectors)to co-evolve subcomponents of a solution.Additionally,in order to research the effect of experiment result on complex functions optimization when we choose different cooperators,two algorithms including CCDE-1(choose the best cooperators)and CCDE-2(Each individual in a subpopulation is evaluated by combining it with the best known individual from each of the other species and with a random selection of individuals from each of the other species.The two resulting vectors are then applied to the target function and the better of the two values is returned as the offspring's fitness)were set in this dissertation.Then three benchmark functions were tested with these two algorithms.The experimental results showed that CCDE-2 is better than CCDE-1 and GA.CCDE-2 performed as well as CCDE-1 on the non-interacting variable problem and CCDE-2 performed much better on interacting variable problems than CCDE-1.(2)A cooperative hybrid genetic differential evolution algorithm(CGDE)was proposed based on CCDE,which employs a Gauss mutation operator to enhance its exploring ability.Firstly, CGDE generates new individual using mutation and crossover operators of DE.Sub-sequentially, this new individual is changed by Gauss mutation of genetic algorithms to keep the diversity of population.Thirdly,a better individual is selected using selection operator of DE to form a new population.Finally,a loop using the above steps is taken to evolve.Eleven benchmark functions were tested by CGDE in this dissertation.The experimental results showed that CGDE is better than CCDE,DE and GA on convergence,the best fitness found and the number of function evaluations.