A Research Of Population Ordering Strategies And Gravitational Grouping Model Based Evolutionary Algorithms

Global optimization problems exist in various areas such as scientific research, engineering,and economic management, etc. It is a series of problems with theoretical significances andpractical application values to be studied. As one type of the distinguished optimization methods,Evolutionary Algorithms have great advantages in solving problems of difficulty, such asnondifferentiable, nonlinear, and multivariable problems. This paper studies the EvolutionaryAlgorithms as the object to be improved, and the improvements includ accuracies of results,convergence speed and robustness.First, a basic research of improving the structure of population in Differential Evolution iscarried out and the population ordering strategy is proposed, based on which, DifferentialEvolution based on Ordering of individuals (ODE) is proposed. Then individual-sampling andbinary-differential strategies are introduced, and two other variants are proposed, i.e., DifferentialEvolution based on Individual-Sorting and Individual-Sampling strategies (ISSDE) and Binary-Differential Evolution based on Ordering of individuals (OBDE). The experimental results showthat these proposed algorithms have great improvement than Differential Evolution, especially forsolving low-dimensional problems.Second, the physics universal gravitation model is introduced into algorithms and the Elitismand Gravitational Evolution based CoEvolutionary (EGCE) is proposed. The population is dividedinto two sub-populations, i.e. the elite sub-population and the common sub-population via elitegrouping strategy. Then, several random factors are introduced to keep the good genes of elite sub-population and to maintain a diversity of common sub-population. The two groups of benchmarkfunctions including both high-dimensional and low-dimensional are used to test the performance ofEGCE, compared with Maximal Gravitation Optimization Algorithm and M-Elite CoEvolutionaryAlgorithm. The results show EGCE performs better in accuracies of results, and have fasterconvergence speed and better robustness.Last, the proposed EGCE is combined with Opposition-Based Differential Evolution, to finishthe optimization work together, and the Gravitational Evolution and Opposition-basedCoEvolutionary (GOCE) is proposed，which shows the expansibility and transferability of EGCE.The experimental results show GOCE obtains a much better accuracies of results, but much slower convergence speed. It indicates GOCE is appropriate for the problems that require high accuracybut ignore the time-consuming processes.The proposed strategies and parameters of algorithms are detailed illustrated and studied byexperiments in this paper. The vast data of trail-and-error study results show the proposedalgorithms are not sensitive to vary of parameters, which indicates the algorithms are suitable formany applications and easy to realize. The convergence of algorithms are proved via the conditionsof random algorithms convergence and Markov chains theory, which show that all the proposedalgorithms converge at the global optimum in probability1.