Original articlesNature-inspired approach: An enhanced moth swarm algorithm for global optimization
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.
References (56)
- et al.
Efficient protocol for data clustering by fuzzy Cuckoo Optimization Algorithm
Appl. Soft Comput.
(2016) - et al.
Weighted Superposition Attraction (WSA): A swarm intelligence algorithm for optimization problems–Part 2: Constrained optimization
Appl. Soft Comput.
(2015) - et al.
Imperialist competitive algorithm with dynamic parameter adaptation using fuzzy logic applied to the optimization of mathematical functions
Algorithms
(2017) - et al.
Optimal sub-band adaptive thresholding based edge preserved satellite image denoising using adaptive differential evolution algorithm
Neurocomputing
(2016) - et al.
Optimal power flow using an improved colliding bodies optimization algorithm
Appl. Soft Comput.
(2016) Moth and candle: the candle flame as a sexual mimic of the coded infrared wavelengths from a moth sex scent (pheromone)
Appl. Opt.
(1977)- et al.
A new optimization meta-heuristic algorithm based on self-defense mechanism of the plants with three reproduction operators
Soft Comput.
(2018) - et al.
A generalized type-2 fuzzy logic approach for dynamic parameter adaptation in bee colony optimization applied to fuzzy controller design
Inform. Sci.
(2018) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art
Comput. Methods Appl. Mech. Engrg.
(2002)- et al.
Constraint-handling in genetic algorithms through the use of dominance-based tournament selection
Adv. Eng. Inform.
(2002)
Learning, odour preference and flower foraging in moths
J. Exp. Biol.
Optimal design of a welded beam via genetic algorithms
AIAA J.
Water cycle algorithm-anovel metaheuristic optimization method for solving constrained engineering optimization problems
Comput. Struct.
Behavioural analysis of olfactory conditioning in the moth spodoptera littoralis
J. Exp. Biol.
Accurate algorithm for numerical simulation of Levy stable stochastic processes
Phys. Rev. E
Impact of outdoor lighting on moths: an assessment
J. Lepidopterists’ Soc.
Effects of artificial night lighting on moths
A study on the use of nonparametric tests for analyzing the evolutionary algorithms’behaviour: A case study on the CEC’2005 speciael session on real parameter optimization
J. Heuristics
A hybrid PSO-GA algorithm for constrained optimization problems
Appl. Math. Comput.
The ecological impacts of nighttime light pollution: a mechanistic appraisal
Biol. Rev.
Fuzzy logic in the gravitational search algorithm for the optimization of modular neural networks in pattern recognition
Expert Syst. Appl.
Real-Parameter Black-Box Optimization Benchmarking 2009 Experimental Setup, Institute National de Recherche en Informatique et en Automatique (INRIA)Rapports de Recherche RR-6828, Mar. 20
An effective co-evolutionary particle swarm optimization for constrained engineering design problems
Eng. Appl. Artif. Intell.
A bacterial gene recombination algorithm for solving constrained optimization problems
Appl. Math. Comput.
An effective co-evolutionary differential evolution for constrained optimization
Appl. Math. Comput.
An augmented lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design
J. Mech. Des.
Water Evaporation Optimization: A novel physically inspired optimization algorithm
Comput. Struct.
A new meta-heuristic method: ray optimization
Comput. Struct.
Cited by (24)
Snow avalanches algorithm (SAA): A new optimization algorithm for engineering applications
2023, Alexandria Engineering JournalA modified seahorse optimization algorithm based on chaotic maps for solving global optimization and engineering problems
2023, Engineering Science and Technology, an International JournalAn improved whale optimization algorithm based on multi-population evolution for global optimization and engineering design problems
2023, Expert Systems with ApplicationsCitation Excerpt :As shown in Table 17, MEWOA obtains similar solutions to ALO, CS, MBA, and ISA and outperforms ABC, GA, and ALM. We evaluate the optimization results of MEWOA in the pressure vessel design problem by selecting thirteen algorithms from the literature (Long, Wu, Liang, & Xu, 2019), (Nadimi-Shahraki et al., 2021), and (Luo et al., 2019) for comparison. As shown in Table 18, We can see that MEWOA achieves the best optimization results compared to other algorithms.
Improved Harris hawks optimization for non-convex function optimization and design optimization problems
2023, Mathematics and Computers in SimulationCitation Excerpt :Result of average ranking value is shown in Fig. 9. To verify the generalizability and effectiveness of the proposed algorithm, HHOBM is applied to solve two engineering design problems: Pressure vessel design problem [56] and Cantilever beam design problem [33]. The HHO algorithm is a population-based meta heuristic algorithm with a simple structure and fast convergence, and it does not require a lot of user input parameters.
Quadratic interpolation boosted black widow spider-inspired optimization algorithm with wavelet mutation
2022, Mathematics and Computers in SimulationCitation Excerpt :On the other hand, there are lots of strategies to improve the global exploration capabilities of algorithms. An elite opposition-based strategy was used to enhance the diversity of the population of the original moth swarm algorithm [31]. Results showed that the improved algorithm can find more accurate solutions than other MAs.
Improved Lévy flight distribution algorithm with FDB-based guiding mechanism for AVR system optimal design
2022, Computers and Industrial EngineeringCitation Excerpt :On the other hand, metaheuristic methods can produce effective solutions for large-scale and complex problems by actively and efficiently exploring the search space. These methods can be applied to different problems regardless of their mathematical models and can produce near-optimal solutions (Duman et al., 2021; Aras et al., 2021; Luo et al., 2019). The search-process lifecycle steps are executed in the second part of the optimization process.