Improved Artificial Bee Colony Algorithm for Multimodal Optimization Based on Crowding Method

Introduction

Evolutionary algorithms have shown to be effective and robust optimization strategies in diverse fields (Goldberg and Richardson, 1987; Clerc and Kennedy, 2002; Huang et al., 2019; Meng et al., 2021; Zaher et al., 2020; Gu et al., 2021). The bulk of EAs are built with the goal of convergent to a single global optimum. On the other hand, many issue cases in real-world optimization problems consist of many global and/or local minima. If the problem has many global optima or local optima which are good alternatives to the global optima, the evolutionary algorithm should identify all of the global optima or some local optima. Various types of classical techniques have been developed in the last decade to improve EAs’ ability to solve multimodal optimization problems, for instance clearing (Pétrowski, 1996), crowding (Pétrowski, 1996), fitness sharing (Pétrowski, 1996), speciation (Pétrowski, 1996), clustering (Yin and Germay, 1993), and restricted tournament selection (Harik et al., 1995; Stoean et al., 2010).

The artificial bee colony algorithm (Karaboga and Basturk, 2008), known as ABC, is a population-based heuristic evolutionary algorithm inspired by the honeybee swarm's intelligent foraging behaviour. According to ABC, a honey bee colony contains three types of bees: employed bee, onlooker bees, and scout bees. Employed bees are in charge of utilizing the nectar sources detected before and informing viewers inside the hive about their discoveries. In the hive, onlooker bees wait and utilize the information provided by the employed bee colony to select a food source. Scout bees choose one of the least active solutions and replace it with a randomly generated new solution. It is referred to (Karaboga and Basturk, 2008) for the specifics of the artificial bee colony. The ABC algorithm has been applied to a variety of real-world problems since its inception, including chaotic system parameter estimation (Gu et al., 2017), reconfigurable antenna array (Kala and Sundari, 2021), leaf-constrained minimum spanning tree problem (Akay et al., 2021), digital IIR filters (Karaboga, 2009; Agrawal et al., 2021), and job shop scheduling (Alzaqebah et al., 2021). Meanwhile, the ABC algorithm has been extended to address multi-objective, constrained optimization problem, and other kinds problems in various fields (Bansal et al., 2013).

In our study, we present IABC, a novel multimodal optimization algorithm that combines the crowding model with an improved artificial bee colony. First, a crowding scheme (the crowding factor set is equal to the population size) is used to extend the standard ABC algorithm to allow the artificial bee colony, tackling multimodal optimization. Second, to improve exploitation ability, an exploration search approach based on two novel search schemes is developed to increase population diversity in IABC and explore new search spaces. Experiments were carried out on 14 benchmark functions selected based on prior researches. The results of our experiments demonstrate that our method is both effective and efficient. In terms of the quality of the success rate, the average number of optima identified, success performance, and the maximum peak ratio, IABC performs better, or at least comparable, to other state-of-the-art approaches.

The next sections of this paper are organized as follows: in section 2, we will go through the ABC in great depth. The improved ABC is proposed in section 3. Benchmark problems and experimental results are included in section 4. In the conclusion, we conclude this article and make some recommendations for further research.