Evolutionary programming based on non-uniform mutation

Abstract

Abstract-A new evolutionary programming algorithm (NEP) using the non-uniform mutation operator instead of Gaussian or Cauchy mutation operators is proposed. NEP has the merits of "long jumps" of the Cauchy mutation operator at the early stage of the algorithm and "fine-tunings" of the Gaussian mutation operator at the later stage. Comparisons with the recently proposed sequential and parallel evolutionary algorithms are made through comprehensive experiments. NEP significantly outperforms the adaptive LEP for most of the benchmarks. NEP outperforms some parallel GAs and performs comparably to others in terms of the solution quality and algorithmic robustness. We give a detailed theoretical analysis of NEP. The probability convergence is proved. The expected step size of the non-uniform mutation is calculated. Based on this, the key property of NEP with "long jumps" at the early stage and "fine-tunings" at the later stage is proved strictly. Furthermore, the feature at the whole process of the algorithm, especially at the middle stage of it is appended.Index Terms: Evolutionary programming, genetic algorithm, non-uniform mutation, global optimization, probability convergence, theoretical analysis. I IntroductionINSPIRED by the biological evolution and natural selection, intelligent computation algorithms are proposed to provide powerful tools for solving many difficult problems. Genetic algorithms (GAs) [2,3], evolutionary strategies (ESs) [4], and the evolutionary programming (EP) [5,21] are especially noticeable among them. In GAs, the crossover operator plays the major role and the mutation is always seen as an assistant operator. In ESs and EP, however, the mutation has been considered as the main operator. GAs usually adopt a high crossover probability and a low mutation probability, while ESs and EPs * Partially supported by a National Key Basic Research Project of China and by a USA NSF grant CCR-0201253. apply mutation to every individual. In binary GAs, one, two, multi-point, or uniform crossover and uniform mutation [1,3] In this paper, a new evolutionary programming algorithm (abbr. NEP) using the non-uniform mutation instead of Gaussian or Cauchy mutations is proposed. This work is inspired by the following observations. First, Yao et al [14,15] argued that "higher probability of making longer jumps" is a key point that FEP and LEP perform better than CEP. However, "longer jumps" are detrimental if the current point is already very close to the global optimum. Second, the non-uniform mutation operator introduced in [1] has the feature of searching the space uniformly at the early stage and very locally at the later stage. In other words, the non-uniform mutation has the common merits of "higher probability of making far long jumps" at the early stage and "much better local fine-tuning ability" at the later stage. In [1], the non-uniform mutation operator is used in GAs by Michalewicz. As we mentioned before, the mutation operator is generally seen as an assistant operator in GAs. While in NEP, the m...

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