Diversity And Uniformity Improving Study On Multi-objective Genetic Algorithm And Its Application

Whether in the field of scientific research or in the engineering design, there is a largenumber of multi-objective optimization problems. How to find the optimal solutions ofthese problems is one focus problem of researchers all along. But the traditionalmathematical methods have some difficulties to achieve the optimal solutions, and theemergence of multi-objective evolutionary algorithm creating a new situation to solvethese problems. Currently, the main popular multi-objective algorithms include NSGA-II,SPEA2, MOEA/D, PESA2and MOCell, et al. Among them, MOCell has got widelyattention due to good performance in terms of diversity and convergence of the algorithm.MOCell combines the cellular automata with genetic algorithm. The individuals of thepopulation are arranged in a fixed grid, each individual is limited only communicate withits neighbor individuals. To some extent, this method maintains a better populationdiversity. But, the experimental studies have found that there is still a big shortage ofMOCell in convergence and diversity of the solutions. To address this shortcoming, thispaper make some improve of MOCell algorithm from different perspective.Firstly, in order to improve population structure of MOCell, a three-dimensionaltopology population is proposed. The new structure increases the expand direction of bestindividuals of the population, making the four expand direction of two-dimensionalpopulation structure to six, improving the convergence speed of the population, andmaking the population’s diversity and convergence reach a new balance. Experimentalresults show that the performance of the improved algorithm is superior to several othercomparative algorithms.Secondly, make some improve to the crossover of the MOCell. In this paper, theorthogonal optimization experimental design idea is introduced into, and using theorthogonal table’s balanced dispersion and comparable characteristics, a orthogonalcrossover operation is designed. The significant advantage of this crossover operation isthat it can produce multiple offspring individuals simultaneously, and these individuals areevenly distributed around the parent individuals. Thus, these offspring individuals arestrong representative around parent individuals, then choose the one with best fitness fromthese individuals as the offspring individual. In order to verify the performance of the newcrossover operation, combining it with MOCell and NSGA-II respectively, and use testfunctions to test them. Experimental results show that the new crossover operation is valid. Thirdly, in order to apply MOCell to solve the multi-objective flexible job shopscheduling problems, this paper design a adaptive mechanism and a local searchmechanism to avoid the algorithm fall into premature easy. The adaptive mechanism is thatwhen the entire population has been completed one iteration, the convergence speed of thepopulation will be calculated, then automatic adjustment the shape of the populationaccording to the convergence speed, keeping the entire algorithm runs in an appropriateconvergence rate. The local search mechanism is that when the algorithm’s mutationoperation is complete, a local search carried out around the offspring individual, preventthe algorithm from falling into local optimum. Good results are obtained when using theimproved algorithm to solve the four multi-objective flexible job shop scheduling testcases, illustrating that the improved algorithm is effective.Fourthly, the two improved algorithms proposed in this paper are applied to the actualproject examples, the machine tool spindle multi-objective optimization design problemand the worm transmission multi-objective optimization design problem have been solved,and good results are achieved.