Interpolation Based Mutation Variants of Differential Evolution

Differential evolution algorithm (DE) is an efficient and versatile population-based search technique for global optimization. In this paper, two novel mutation variants for DE are presented. These mutation variants are based on interpolation rules; first variant is based on Inverse Quadratic Interpolation called IQI-DE and the second variant is based on sequential parabolic interpolation called SPI-DE. Both variants aim at efficiently generating the base vector in the mutation phase of DE. The performance of proposed variants is implemented on 12 benchmark problems and compares with basic DE and five other enhanced versions of DE such as DERL, ODE, jDE, JADE, and LeDE. Experimental results show that the proposed variants are significantly better or at least comparable to other variants in term of convergence speed and solution accuracy. DOI: 10.4018/jaec.2012100103 International Journal of Applied Evolutionary Computation, 3(4), 34-50, October-December 2012 35 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. In order to improve the performance of DE, several versions of DE variants have been proposed by many researchers over the last few decades. Some of the recent modified variants of DE are given in Section 3. In basic DE, the base vector is either randomly selected (DE/rand/bin) or is selected ‘greedily.’ In this paper we have proposed two new mutation schemes for DE. The first scheme is Inverse Quadratic Interpolation (IQI) scheme and the second one is named Sequential Parabolic Interpolation (SPI). The corresponding DE variants are named as IQI-DE and SPI-DE. Both schemes aim at efficiently generating the base vector in the mutation phase of DE. The only difference to DE and both proposed algorithms at base vector in mutation operation. The significance of selecting efficient base vector is discussed later in the paper. Here we would like to mention that in this paper we are presenting the extended work of our previous study about IQI-DE and SPI-DE, given in Kumar et al. (2011). The rest of the paper is organized as follows: The basic DE is given in Section 2. A brief literature review is given in Section 3. Section 4 discusses the proposed SPI-DE and IQI-DE algorithms. In Section 5 experimental settings are given. In Section 6, numerical results are discussed; finally the paper concludes with Section 7.