Interpolation Based Mutation Variants of Differential Evolution

Interpolation Based Mutation Variants of Differential Evolution

Pravesh Kumar (Department of Applied Science and Engineering, Indian Institute of Technology, Roorkee, Roorkee, India), Sushil Kumar (Department of Applied Science and Engineering, Indian Institute of Technology, Roorkee, Roorkee, India), Millie Pant (Department of Applied Science and Engineering, Indian Institute of Technology, Roorkee, Roorkee, India) and V.P. Singh (Stallion College for Engineering and Technology, Saharanpur, India)
Copyright: © 2012 |Pages: 17
DOI: 10.4018/jaec.2012100103
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Abstract

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.
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2. The Basic De

Differential evolution algorithm a simple, powerful and iteration based search technique for global optimization. It starts with a set of solution, which is randomly generated when no preliminary knowledge about the solution space is available. This set of solution is called population. Let PG={XiG, i=1,2,...NP} be the population at any generation G which contain NP individuals and an individual XiG can be defined as a D dimensional vector i.e., XiG =(x1,iG,, x2,iG…, xD,iG). For basic DE (DE/rand/1/bin) mutation, crossover and selection operations are defined as:

  • Mutation: For each target vector Xi,G mutant vector ViG is defined by:

    (1)

Some other mutation variants are given as:

(2)

Where are randomly chosen integers, distinct from each other and also different from the running index i. F is a real and constant factor having value between [0, 2] and controls the amplification of differential variation (Xr2G – Xr3G).

  • Crossover: Crossover is introduced to increase the diversity of perturbed parameter vectors ViG ={v1,iG, v2,iGvD,iG}.

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