Computational Intelligence and Neuroscience

Volume 2019, Article ID 2564754, 19 pages

https://doi.org/10.1155/2019/2564754

## A Multistrategy Artificial Bee Colony Algorithm Enlightened by Variable Neighborhood Search

^{1}School of Traffic & Transportation, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China^{2}Institute of Modern Logistics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China

Correspondence should be addressed to Wan-li Xiang; nc.ude.ujt@lwgnaix

Received 26 April 2019; Revised 13 August 2019; Accepted 11 September 2019; Published 3 November 2019

Academic Editor: Juan Carlos Fernández

Copyright © 2019 Wan-li Xiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Artificial bee colony (ABC) has a good exploration ability against its exploitation ability. For enhancing its comprehensive performance, we proposed a multistrategy artificial bee colony (ABCVNS for short) based on the variable neighborhood search method. First, a search strategy candidate pool composed of two search strategies, i.e., ABC/best/1 and ABC/rand/1, is proposed and employed in the employed bee phase and onlooker bee phase. Second, we present another search strategy candidate pool which consists of the original random search strategy and the opposition-based learning method. Then, it is used to further balance the exploration and exploitation abilities in the scout bee phase. Last but not least, motivated by the scheme of neighborhood change of variable neighborhood search, a simple yet efficient choice mechanism of search strategies is presented. Subsequently, the effectiveness of ABCVNS is carried out on two test suites composed of fifty-eight problems. Furthermore, comparisons among ABCVNS and several famous methods are also carried out. The related experimental results clearly demonstrate the effectiveness and the superiority of ABCVNS.

#### 1. Introduction

There are a vast lot of problems to be optimized in the social production and life. In order to achieve better solutions to these problems, a great number of algorithms have been developed. Owing to shortages (e.g., function’s continuity needed) of deterministic approaches, various nature-enlightened algorithms had been developed to better deal with extremely difficult optimization problems. Generally speaking, during the past four decades, various researchers have developed different nature-inspired approaches such as genetic algorithms [1, 2], particle swarm optimization [3], differential evolution (called DE) [4], and artificial bee colony [5, 6].

Among them, artificial bee colony (ABC) is a distinguished representative of population-based global optimization methods, and it was first proposed by Karaboga in 2005 [5]. After that, comparative studies were carried out by Karaboga et al. [7, 8] among ABC, PSO, DE, GA, and so on. The comparative outcomes show its superiority when compared with those competitors. In addition, it needs fewer parameters. Afterwards, a great number of researchers show a lively interest in addressing ABC. Meanwhile, a lot of enhanced variants had been presented to solve various problems such as function optimization [9–22], vehicle routing problem [23], multiobjective optimization problems [24], and others [25–27].

Besides practical applications of ABC in the research fields listed above, many researchers concentrate on improving the performance of the traditional ABC to solve function optimization problems with different characteristics of nonconvexity, noncontinuity, separability, etc. For example, Alatas [9] proposed a chaotic ABC, in which both a chaotic initialization technique and a chaotic search method are proposed. Enlightened from the search process of particle swarm optimization, Zhu and Kwong [10] designed a novel search technique for improving ABC. In the proposed GABC, the search can effectively utilize the information of the global best individual. Motivated from the search strategy of DE [4], Gao and Liu [11] creatively developed a modified artificial bee colony (named MABC), in which a new equation named ABC/best/1 is proposed. To enhance the level of information sharing among various individuals, Akay and Karaboga [12] introduced a new control parameter called modification rate. It was used to randomly change parameters. Furthermore, it effectively enhances its exploitation ability. Frequently, the ABC was hybridized with other local approaches [13] to enhance its search ability. More recently, many researchers would like to utilize hybridization of multiple search strategies to balance the exploration and exploitation abilities of ABC [18, 21]. For instance, Gao et al. [18] first constructed a strategy candidate pool composed of three search strategies with different search abilities and then proposed an adaptive selection mechanism to select a search strategy for each individual based on previous search experiences. Moreover, the proposed algorithm, namely, MuABC, had achieved a better performance when compared with the standard ABC and other state-of-the-art algorithms. Kiran et al. [21] first chose five search strategies to form a strategy candidate pool and then designed a probabilistic selection scheme for choosing a search strategy during the evolving process. Furthermore, the proposed approach, called ABCVSS for short, outperformed the basic ABC, ABC variants, and other kinds of methods in terms of solution quality for most of the cases.

To better enhance the basic ABCs performance, a multistrategy ABC is proposed enlightened from the variable neighborhood search technique [28–30]. For convenience, it was named after ABCVNS, where both ABC/best/1 and ABC/rand/1 are used to construct the first search strategy candidate pool. It is utilized both in the first stage and in the second stage. Furthermore, the second search strategy candidate pool is employed in the scout bee phase, and it consists of an original random search strategy and an opposition-based learning method. Then, a novel mechanism of choice of search strategies is proposed inspired by the variable neighborhood search method. In addition, an opposition-based learning method is employed to initially generate a population with better diversities. To comprehensively show the advantage of ABCVNS, a few experiments on a large number of benchmark problems are conducted. Comparisons of ABCVNS and many other famous methods are also provided. The related comparative results demonstrate that the proposed ABCVNS can be regarded as a competitive method.

The remainder of the work is organized as follows. Section 2 briefly describes the basic ABC. Next, a novel multistrategy ABC is proposed and described in detail in Section 3. In Section 4, a few comparative experiments are carried out and the comparative results are provided and discussed in detail. Finally, Section 5 concludes the work and puts forward a few future research directions.

#### 2. Classical ABC

Enlightened from the collective intelligence behaviors of bee swarm [5], Karaboga developed ABC in 2005. In ABC, the bee swarm is divided into three groups. They are employed bees, onlooker bees, and scout bees, respectively. Among them, employed bees stand half of the swarm and onlooker bees form another half. As far as labor division of honey bees is concerned, the task of exploring nectar sources is undertaken by the employed bees. After that, they would pass the information of nectar amount onto onlooker bees. On the basis of the shared information, a food source is selected and exploited by an onlooker bee in turn with a certain percentage. If one employed bee or one onlooker bee exhausts a food source, then the corresponding bee would play a role of a scout bee, which will perform a random search to get out of a local trap.

Generally, by imitating the foraging behavior of artificial bee colony, the ABC is made up of four sequential phases. They are the initialization, employed bee, onlooker bee, and scout bee phases, respectively.

Before gathering the nectar of honey bees, a population of artificial individuals is randomly generated according to the following equation to denote real-world honey bees:where ; and represent the upper and lower bounds of the component *j*, respectively; and *ξ* is a random number in the range of [0,1). Randomly generated *D*-dimensional vector of indicates an artificial agent. Meanwhile, we should predefine a suitable stopping criterion and the parameter *limit* employed for controlling appearances of scout bees.

Following the initialization phase, employed bees begin to explore food sources successively in the light of the following equation:where and together with are randomly produced by a uniform distribution. In addition, *k* has to be different from *i*. is a randomly generated number between .

Next, fitness values of artificial individuals are calculated as follows:where and indicate the cost value and the fitness value of the *i*-th artificial individual, respectively.

At the beginning of the second stage, probability values are calculated according to the following formula:where denotes the probability of the *i*-th artificial food source chosen by onlooker bees. It depends on nectar amounts of the corresponding food source. That is, the higher the is, the higher the chance of choosing the *i*-th food source is. In this context, employed bees pass information on to onlooker bees.

Based on equation (2), each onlooker bee chooses a food source in turn. Then, it begins to exploit around the corresponding food source.

Next, a predetermined parameter *limit* is employed to decide whether or not a scout bee occurs. Concretely speaking, provided that a bee continuously performs *limit* searches around the same food source, and it fails to achieve a better one, then the bee will become a scout bee. That is, it will randomly search for a new food source to jump out of a local trap in the light of the following equation:where . Besides, the other parameters are the same settings as those of equation (1).

During the foraging processes of the honey bee colony, they may cross some borders. That is, the artificial individuals/solutions may violate boundary constraints. To make solutions feasible, the following equation is employed to repair those infeasible solutions:

To summarize, after initializing a population, other stages of ABC are executed repeatedly until one halt condition is encountered.

#### 3. A Multistrategy Artificial Bee Colony Algorithm

##### 3.1. Initialize a Population in View of Opposition-Based Learning

First of all, a population of artificial individuals is randomly produced according to equation (1). Based on the initial artificial individuals/solutions, some opposite solutions are generated to improve population diversities. That is, an opposition-based learning (OBL) method [31] is used to construct these opposite solutions. Since 2008, the OBL method has been widely applied in many population-based algorithms such as DE [32, 33] and ABC [11]. More concretely, equation (7) is employed here to produce oppositional vectors :where . The rest of the parameters are the same settings as those of equation (1).

By integrating the OBL and the random initialization approaches, the corresponding integrated initialization approach can be listed in Algorithm 1.