Abstract-Differential evolution (DE) is well known as a simple and efficient scheme for global optimization over continuous spaces. It has reportedly outperformed a few evolutionary algorithms (EAs) and other search heuristics like the particle swarm optimization (PSO) when tested over both benchmark and realworld problems. DE, however, is not completely free from the problems of slow and/or premature convergence. This paper describes a family of improved variants of the DE/target-tobest/1/bin scheme, which utilizes the concept of the neighborhood of each population member. The idea of small neighborhoods, defined over the index-graph of parameter vectors, draws inspiration from the community of the PSO algorithms. The proposed schemes balance the exploration and exploitation abilities of DE without imposing serious additional burdens in terms of function evaluations. They are shown to be statistically significantly better than or at least comparable to several existing DE variants as well as a few other significant evolutionary computing techniques over a test suite of 24 benchmark functions. The paper also investigates the applications of the new DE variants to two reallife problems concerning parameter estimation for frequency modulated sound waves and spread spectrum radar poly-phase code design.
Differential evolution (DE) is one of the most powerful stochastic real parameter optimizers of current interest. In this paper, we propose a new mutation strategy, a fitness-induced parent selection scheme for the binomial crossover of DE, and a simple but effective scheme of adapting two of its most important control parameters with an objective of achieving improved performance. The new mutation operator, which we call DE/current-to-gr_best/1, is a variant of the classical DE/current-to-best/1 scheme. It uses the best of a group (whose size is q% of the population size) of randomly selected solutions from current generation to perturb the parent (target) vector, unlike DE/current-to-best/1 that always picks the best vector of the entire population to perturb the target vector. In our modified framework of recombination, a biased parent selection scheme has been incorporated by letting each mutant undergo the usual binomial crossover with one of the p top-ranked individuals from the current population and not with the target vector with the same index as used in all variants of DE. A DE variant obtained by integrating the proposed mutation, crossover, and parameter adaptation strategies with the classical DE framework (developed in 1995) is compared with two classical and four state-of-the-art adaptive DE variants over 25 standard numerical benchmarks taken from the IEEE Congress on Evolutionary Computation 2005 competition and special session on real parameter optimization. Our comparative study indicates that the proposed schemes improve the performance of DE by a large magnitude such that it becomes capable of enjoying statistical superiority over the state-of-the-art DE variants for a wide variety of test problems. Finally, we experimentally demonstrate that, if one or more of our proposed strategies are integrated with existing powerful DE variants such as jDE and JADE, their performances can also be enhanced.
Differential evolution (DE) is well known as a simple and efficient scheme for global optimization over continuous spaces. In this paper we present two new, improved variants of DE. Performance comparisons of the two proposed methods are provided against (a) the original DE, (b) the canonical particle swarm optimization (PSO), and (c) two PSO-variants. The new DE-variants are shown to be statistically significantly better on a seven-function test bed for the following performance measures: solution quality, time to find the solution, frequency of finding the solution, and scalability.
Summary.Since the beginning of the nineteenth century, a significant evolution in optimization theory has been noticed. Classical linear programming and traditional non-linear optimization techniques such as Lagrange's Multiplier, Bellman's principle and Pontyagrin's principle were prevalent until this century. Unfortunately, these derivative based optimization techniques can no longer be used to determine the optima on rough non-linear surfaces. One solution to this problem has already been put forward by the evolutionary algorithms research community. Genetic algorithm (GA), enunciated by Holland, is one such popular algorithm. This chapter provides two recent algorithms for evolutionary optimization -well known as particle swarm optimization (PSO) and differential evolution (DE). The algorithms are inspired by biological and sociological motivations and can take care of optimality on rough, discontinuous and multimodal surfaces. The chapter explores several schemes for controlling the convergence behaviors of PSO and DE by a judicious selection of their parameters. Special emphasis is given on the hybridizations of PSO and DE algorithms with other soft computing tools. The article finally discusses the mutual synergy of PSO with DE leading to a more powerful global search algorithm and its practical applications.
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