Original articles
Nature-inspired approach: An enhanced moth swarm algorithm for global optimization

https://doi.org/10.1016/j.matcom.2018.10.011Get rights and content

Abstract

The moth swarm algorithm (MSA) is a recent swarm intelligence optimization algorithm, but its convergence precision and ability can be limited in some applications. To enhance the MSA’s exploration abilities, an enhanced MSA called the elite opposition-based MSA (EOMSA) is proposed. For the EOMSA, an elite opposition-based strategy is used to enhance the diversity of the population and its exploration ability. The EOMSA was validated using 23 benchmark functions and three structure engineering design problems. The results show that the EOMSA can find a more accurate solution than other population-based algorithms, and it also has a fast convergence speed and high degree of stability.

Introduction

From a general point of view, optimization is the process of searching for the global solution of a problem under a given circumstance. The growing complexity of real-world optimization problems has motivated researchers to search for a new method. The simulation of some natural phenomena, for example, physical, chemical, evolutionary issues and biological behavioral patterns, has been used to develop new nature-inspired algorithms, which have demonstrated flexibility, efficiency, simplicity and the avoidance of local optima more than traditional methods [51]. Inspired by this idea, ant colony optimization (ACO) [42], [51], differential evolution (DE) [52], particle swarm optimization (PSO) [30], gray wolf optimization (GWO) [39], [46], self-defense mechanism of plants optimization [7] have been proposed and applied widely. In recent years, these algorithms have been applied in many fields, such as image processing [4], power systems [5], [34], data clustering [1], pattern recognition [21] and tuning of neural networks [40], bee colony optimization applied to fuzzy controller design [8] and the imperialist competitive algorithm applied to dynamic parameter optimization [3].

Moths often fly at night. Because they have a good sense of smell and hearing, they can adapt to life at night. Therefore, moths have phototaxis. From the onlooker’s point of view, it is clear that moths are attracted by light, but the facts are more specific because moths become dizzy and confused around bright objects that are circling. Moths use light as a compass to navigate, which evolved into a fixed part of the eye that accepts light. Provided the light source is far away, such as the sun or moon, moths’ eyes receive light at an angle that is almost identically parallel. Then, provided moths fly in a straight line toward the rectilinear direction, visual imaging remains unchanged. However, when the light source is very close, moths still fly straight, and the angle of the light that is received at each instant of movement changes. Therefore, to adapt to the change, moths, from the point of view of a bystander, seem to be spiraling toward the light source. Moths attempt to hide from predators in daylight, and at night they use the celestial navigation technique to orient themselves in the dark and exploit food sources. Moths fly in a straight line over a long distance by steering their locomotion at a constant angle relative to celestial far-distant point light, for example, moonlight, which is also known as the light compass reaction. Despite this, such orientation suffers from transverse direction motion because of futile spiral tracks around nearby artificial light sources [6], [16], [17], [20].

The moth swarm algorithm (MSA) [41] was proposed by Al-Attar Ali Mohamed in 2016. It is a new population-based intelligent optimization algorithm inspired by the orientation of moths in a noisy environment toward moonlight. The MSA has good performance in the field of swarm intelligence, but its convergence precision and speed can be limited in some applications. In view of this deficiency, in this paper, the original algorithm is based on the elite opposition strategy to improve the convergence speed and accuracy.

The remainder of this paper is organized as follows: In Section 2, the original MSA is briefly introduced. This is followed in Section 3 by the new elite opposition-based MSA (EOMSA). Simulation experiments and results analysis are described in Section 4. Finally, the conclusion and future works are presented in Section 5.

Section snippets

Moth swarm algorithm (MSA)

In the MSA, a possible solution of the optimization problem is represented by the position of a light source, and the fitness of this solution is considered as the luminescence intensity of the light source. These assumptions are used to approximate the characteristics of the proposed algorithm. Additionally, the moth swarm is considered to consist of three groups of moths, which are defined as follows:

Pathfinders: a small group of moths that have the ability to discover new areas over the

Elite opposition-based moth swarm algorithm (EOMSA)

The MSA (Al-Attar Ali Mohamed, 2016) can easily solve low-dimensional unimodal optimization problems and high-dimensional multimodal optimization problems. To speed up the convergence speed and convergence accuracy of the MSA, we add an elite strategy to improve the performance of the algorithm.

The added elite reverse mechanism increases the exchange of information between moth individuals and elite moth individuals. To a certain extent, the elite reverse strategy enlarges the search space

Simulation experiments and result analysis

In this section, 23 benchmark functions [22], [53] are applied to evaluate the optimal performance of the EOMSA. These 23 benchmark functions (shown in Table 1) have been widely used in the literature. The EOMSA is compared with four state-of-the-art metaheuristic algorithms: bat algorithm (BA) [55], LMFO [32], GWO [39], PSO-GSA [38] and MSA [41]. The space dimension, scope, optimal value and iterations of the 23 functions are shown in Table 1. The remainder of this section is organized as

Conclusions

In this paper, to overcome the disadvantage of standard MSA, an optimization strategy was incorporated into the MSA to generate the EOMSA for function optimization and structure engineering design problems. Global elite opposition-based learning enhances the diversity of the population, which helps to improve its exploration ability. From the results of the 23 benchmark functions and three engineering design problems, the performance of the EOMSA was better than, or at least comparable with,

Acknowledgments

Funding: This work was supported by the National Science Foundation of China [grant numbers 61563008, 61463007]; and the Project of Guangxi University for Nationalities Science Foundation, China [grant numbers2016GXNSFAA380264, 2018GXNSFAA138146]. We thank Maxine Garcia, Ph.D., from Liwen Bianji, Edanz Group China (www.liwenbianji.cn/ac) for editing the English text of a draft of this manuscript.

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