Improvements of real coded genetic algorithms based on differential operators preventing premature convergence

Abstract

This paper presents several types of evolutionary algorithms (EAs) used for global optimization on real domains. The interest has been focused on multimodal problems, where the difficulties of a premature convergence usually occurs. First the standard genetic algorithm (SGA) using binary encoding of real values and its unsatisfactory behavior with multimodal problems is briefly reviewed together with some improvements of fighting premature convergence. Two types of real encoded methods based on differential operators are examined in detail: the differential evolution (DE), a very modern and effective method firstly published by R. Storn and K. Price [17], and the simplified real-coded differential genetic algorithm SADE proposed by the authors [11]. In addition, an improvement of the SADE method, called CERAF technology, enabling the population of solutions to escape from local extremes, is examined. All methods are tested on an identical set of objective functions and a systematic comparison based on a reliable methodology [1] is presented. It is confirmed that real coded methods generally exhibit better behavior on real domains than the binary algorithms, even when extended by several improvements. Furthermore, the positive influence of the differential operators due to their possibility of self-adaptation is demonstrated. From the reliability point of view, it seems that the real encoded differential algorithm, improved by the technology described in this paper, is a universal and reliable method capable of solving all proposed test problems.

Incremental evolution strategy for function optimization

“…With regard to the algorithms in comparison, the settings for their specific parameters follow the same settings as described in the original papers [22][2] [21], as shown in Table 1. In this problem, the Griewangk function is scalable and the interactions among variables are nonlinear.…”

“…Simplified Atavistic Differential Evolution (SADE) combines the features of differential evolution (DE) with those of traditional genetic algorithms [21]. DE is a modern and efficient optimization method essentially relying on so-called differential operator, which was invented as the solution method for the Chebychev trial polynomial problem by Stone and Price [20].…”

“…CERAF is a technology enabling the population of solutions to escape from local extremes, which aims to improve the performance of SADE by preventing premature convergence [21].…”

“…The PSO program and the SADE program were downloaded respectively from their creator's homepages. And the SADE program was combined with the CERAF technology based on the concept from [21].…”

Ecological relationships, thresholds and time-lags determining phytoplankton community dynamics of Lake Kinneret, Israel elucidated by evolutionary computation and wavelets

“…It, therefore, does not depend on additional probability distributions as common for conventional optimization algorithms but makes it a self-organizing scheme. According to Hrstka and Kucerová (2004) DE outperforms other optimization methods in terms of convergence speed and robustness.…”