Academic journal article Journal of Digital Information Management

Differential Evolution Enhanced with Composite Population Information Based Mutation Operators

Academic journal article Journal of Digital Information Management

Differential Evolution Enhanced with Composite Population Information Based Mutation Operators

Article excerpt

1. Introduction

Differential evolution (DE), proposed by Storn and Price [1], is a simple yet powerful evolutionary algorithm for global numerical optimization. It has many attractive characteristics, such as ease to use, simple structure, speediness and robustness. Due to these merits, DE has been extended to handle multi-objective, constrained, large-scale, dynamic, and uncertain optimization problems [2]. Furthermore, DE has been successfully used in diverse fields [2-4], such as chemical engineering, engineering design, pattern recognition, and so on.

In DE, there exist two main factors which significantly influence the performance of DE. The first one is the control parameters, i.e., population size NP, scaling factor F, and crossover rate CR, and the second one is the evolutionary operators, i.e., mutation, crossover and selection. In the literature about DE, there are many improved DE variants proposed during the last decade. Based on the reference [5], these advanced DE variants can be divided into two categories, DE with the additional components and DE with a modified structure. Modifications on DE in these variants mainly focus on introducing the self-adaptive strategies for the control parameters [6-9], devising the new mutation operators [10-13], developing the ensemble strategies [6][14-15], proposing the hybrid DE with other optimization algorithms [16] and population topology (multi or parallel population) [17], etc.

In the mutation operator of most DE variants, a mutant vector can be treated as the lead individual to explore the search space and generated by adding a difference vector to a base vector. We have observed, however, that these two vectors (i.e., base and difference vectors) in most of DE are usually selected randomly, which does not fully utilize the useful population information to guide the search.

In order to alleviate these drawbacks and enhance the performance of DE, we propose a new DE framework with Composite Population Information based mutation operator (DE-CPI). In DE-CPI, a ring topology is firstly employed to obtain the neighborhood information by defining the neighbors for each individual. Then, the neighbors of each individual are partitioned into the better and worse groups according to their fitness values compared to that of it. After that, with respect to the base vector selected from the neighborhood of the current vector, the direction information is introduced into the mutation operator by selecting the vectors from the better and worse groups respectively to construct the difference vector. In this way, DE-CPI not only utilizes the information of neighboring individuals to exploit the regions of minima and accelerate convergence, but also incorporates the direction information of population to move the individuals to a promising area. Therefore, the composite population information, i.e., neighborhood and direction information, can be fully and simultaneously utilized in DE-CPI to guide the search of DE.

To evaluate the effectiveness of the proposed method, DECPI is applied to six original DE algorithms, as well as several advanced DE variants. Extensive experiments have been carried out on a set of benchmark functions. Through the extensive experimental study, the results show that DE-CPI is able to enhance the performance of most of the DE algorithms studied.

The main contributions of this study include the following:

* Both neighborhood and direction information, as the composite population information, are utilized fully and simultaneously to select the base and difference vectors for mutation, which is beneficial to guide the search of DE.

* DE-CPI provides a simple and effective way for enhancing the exploration ability of DE by combining the neighborhood and direction information of population.

* By keeping the simple structure of DE, DE-CPI is very simple and can be easily applied to other advanced DE variants. …

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