Improvement And Application Research On Multi-objective Cellular Differential Algorithm

In scientific research and engineering application,there exist a variety of multi-objective optimization problems(MOPs).Because some sub-objectives often conflict with each other,that is to say,they can not achieve best simultaneously,so the policymakers have to select compromise solutions according to the actual conditions.The multi-objective evolutionary algorithms(MOEAs)are the effective tools to solve MOPs.In recent years,all kinds of MOEAs have sprung up and been a hot research topic in scientific research and engineering application.This paper introduces the basic multi-objective cellular differential algorithm(CellDE)in detail and analyzes its deficiencies.Cell DE takes more time to maintain external population and its searching efficiency is low in earlier stage of run owing to the partial feedback mechanism.What's more,the original mutation operation exists a shortcoming that the algorithm escapes from local optimum difficultly.Hence,some improved cellular differential evolution algorithms have been proposed.Besides,they are applied to engineering optimum designs.The main contents are as follows:1.To improve the performance of CellDE on solving MOPs,a new cellular differential algorithm(NCellDE)is proposed,which is based on the complete feedback from the external population.The external population is truncated according to the rank and the distance between an individual and its k-th nearest neighbor after each generation.Then it is assigned to two-dimensional grids randomly.Furthermore,a new disturbance is introduced in the original mutation to prevent the algorithm from trapping in local optimum.Through testing 6 benchmark functions and a workshop facility layout case,the result indicates that the new algorithm is superior to the other algorithms concerning the coverage of the Pareto fronts and that the new mutation operation can improve the ability of the algorithm to escape from local optimum.2.To make further improvement the diversity and convergence of Pareto front,the feedback mechanism and maintain strategy of external population of NCellDE are adjusted.A modified cellular differential algorithm(DLCellDE)is proposed,which is based on the sufficient lead of the external population in the process of two-phase evolutionary.The NCellDE is also adopted in first stage.In second stage,the maintenance strategy of external population is replaced by that of CellDE,but the whole external population is also assigned to two-dimensional grids randomly.Through testing 15 benchmark functions and the Golinski speed reducer problem,comparative experiments show that the Pareto fronts DLCell DE obtains can distribute more uniformly and its convergence is also improved.3.Taking the multi-objective optimization design of cycloid reducer as an example,the objective functions and constraint conditions are selected and deduced,and the model established is solved by DLCellDE.DLCellDE gets better Pareto front solutions than that of CellDE and provides better design schemes than that of the routine design method.This dissertation improves the performance of CellDE mainly from three aspects: feedback mechanism of external population,diversity maintenance of external population,and way of differential mutation.The feasibility and effectiveness of the improved algorithms are verified by the optimization design examples.