An Analysis of Evolutionary Algorithms Based on Neighborhood and Step Sizes

Evolutionary algorithms (EAs) can be regarded as algorithms based on neighbourhood search, where diierent search operators (such as crossover and mutation) determine diierent neighbourhood and step sizes. This paper analyses the eeciency of various mutations in evolutionary programming (EP) by examining their neighbourhood and step sizes. It shows analytically when and why Cauchy mutation-based fast EP (FEP) 1, 2] is better than Gaussian mutation-based classical EP (CEP). It also studies the relationship between the optimality of the solution and the time used to nd the solution. Based on the theoretical analysis, an improved FEP (IFEP) is proposed, which combines the advantages of both Cauchy and Gaussian mutations in EP. Although IFEP is very simple and requires no extra parameters, it performs better than both FEP and CEP for a number of benchmark problems.