Hybrid Artificial Bee Colony algorithm with Differential Evolution
Graphical abstract
Introduction
Swarm intelligence has emerged as an effective tool for numerical optimization, which runs over the collaborative trial and error method. The popular techniques based on swarm intelligence are Particle Swarm Optimization (PSO) [27], Biogeographic based optimization (BBO) [40], Bacterial foraging optimization (BFO) [35], Firefly algorithm [30], Ant colony optimization (ACO) [12] and Spider monkey optimization [8]. The work proposed in the articles [12], [27], [37], [43] provides the evidence of its efficiency to find the solution of optimization problems of typical characteristics like nonlinearity, nonconvexity, and discrete search space. Artificial Bee Colony (ABC) [23] is well known optimization algorithm in this category.
ABC algorithm is a simulation of a particular behavior of honey bees known as foraging behavior (a search for food). It is easy to implement population-based optimization algorithm with very few number of parameters. Here the population includes possible solutions as food sources for honey bees. The food source's fitness is proportional to the nectar amount that it contains. In ABC, each bee moves to other food sources through position update Eq. (2) in Section 2 which is a linear combination of position of its current food source and position of a randomly selected food source with a random coefficient ϕ as step size. Due to the involvement of these random quantities, ABC is found to be good at exploration and with the lack of exploitation, i.e., incapable of applying available information to find better solution [48]. Researchers in [25], [28] also analyzed this fact and found that it will ultimately affect the ABC algorithm's convergence rate. Li et al. [29] also found that ABC suffers from convergence speed when we are dealing with some complex problems. These drawbacks may be dealt by modifying existing position update equation and/or by hybridizing another fast optimization algorithm with ABC. The articles [7], [16], [26], [48] worked to improve exploitation in ABC by modifying its position update equation while previous research in [13], [29], [34], [47] have also shown that hybrid ABC with different algorithms can perform better by integrating the respective advantages of the independent algorithms. Jadon et al. [21] modified position update equation of basic ABC algorithm. In this modification, fitness of randomly selected solution directs the sign of step size to be added in the current position to generate its neighborhood solution in employed and onlooker bee phases. Li et al. [29] proposed a hybrid version of ABC and DE algorithms and applied it to optimal reactive power flow. Amir et al. [6] hybridized DE in ABC to create new solutions for both employed and onlooker bees for unconstrained optimization problems. Alizadegan et al. [6] proposed a hybrid ABC and DE (ABC–DE) in which DE is incorporated in employed and onlooker phases. Ali et al. [47] also introduced a novel hybrid optimization method (HRABC) consisting of ABC and Taguchi method for structural design optimization. Duan et al. [13] hybridized ABC into Quantum Evolutionary Algorithm (QEA) where ABC is adopted to enhance the local exploitation capacity and randomness of the QEA populations. Abraham et al. [2] also incorporated DE process after each ABC iteration. In [34], Levenberq–Marquardt (LM) strategy is also hybridized with ABC and tested to train neural networks. In DEBCO [1], employed bee of ABC finds the neighborhood solutions through DE. Thammano et al. [42] hybridized five distinct search techniques at various levels of the ABC to solve job shop scheduling problem. Here, harmony search algorithm is used for initialization of the population. The iterated local search scheme, the scatter search method, and the filter and fan techniques are applied to search neighborhood solutions. The simulated annealing algorithm is also hybridized and applied to get a solution out of local optimum. Kang et al. [22] hybridized basic ABC with Hooke-Jeeves based local search method [19] known as HJABC. In HJABC, a selection pressure and solution ranking are used to calculate fitness function.
This paper proposes a hybrid version of ABC and DE, which also incorporates the modification in the position update equation of ABC. The proposed hybrid algorithm is named as HABCDE. In HABCDE, the employed, onlooker and scout bee phases of ABC are modified. In employed bee phase, a bee moves to other food source not only based on a randomly selected food source but also based on the current best food source. Gbest-guided ABC [48] has already applied the best solution information to update the position of any bee. In onlooker bee phase, it updates the bee's position through evolutionary operations of Differential Evolution (DE/best/1/bin) algorithmic process. The number of scouts is increased in scout phase to give a chance to re-initialize themselves to all those bees who are not being updated to a predefined number of times.
The organization for the rest in this article is as follows: Standard ABC is explained in Section 2. Section 3 reports classical DE algorithm. Section 4 details the proposed hybrid ABC (HABCDE). In Section 5, the performance of the proposed scheme is examined and measured with recent variants of ABC. Comparison is also done with some state-of-the-art algorithms and with hybrid versions of ABC. Finally, paper is concluded in Section 6.
Section snippets
Artificial Bee Colony (ABC) algorithm
The ABC algorithm was developed by Karaboga which is a simulation of food foraging behavior of real honey bees. In ABC, the food source for bees are called as solutions. ABC is composed of three types of bees namely, the employed, the onlooker and the scout. ABC colony consists equal number of employed and onlooker bees. Employed bees explore the food source in the surroundings of their hive and store the related information in their memories. Onlooker bees collect the information from employed
Differential Evolution
DE is a population-based optimization algorithm, where members of the population are potential solutions which collaboratively search solutions. DE has both the evolutionary and swarm intelligence based features as it includes evolutionary operators like mutation, crossover, selection and swarm intelligence concept like distance and direction of the individual solutions to guide the search process further. DE has different formats to apply to solve the optimization problem, e.g., it has various
Hybrid Artificial Bee Colony with Differential Evolution algorithm
As mentioned in Section 1, ABC algorithm may be improved by modifying its position update equation and/or by hybridizing it with other promising optimization algorithms. In this article, both the concepts are applied to improve basic ABC's efficiency. The proposed algorithm is a hybridization of ABC with DE algorithm and named as Hybrid Artificial Bee Colony with Differential Evolution (HABCDE) Algorithm. In HABCDE, three modifications, one in each phase of ABC, are proposed as follows:
- 1
Employed
Experimental results and discussion
According to famous No Free Lunch Theorem (NFL) [46], designing a single algorithm which is better than all other algorithms, is not possible provided it is tested over a sufficient number of problems. However, the authors are not claiming that the proposed algorithm HABCDE is superior than other algorithms for all kind of problems; the experimental results have been carried out below over a set of benchmark optimization problems and a set of real-world optimization problems to show its wider
Conclusion
Artificial Bee Colony algorithm is simple swarm intelligence based algorithm with few parameters but with drawbacks, like slow convergence and poor balance between exploration and exploitation. Differential Evolution, on the other hand, exhibits relatively faster convergence. Therefore, in this paper, ABC and DE have hybridized and a new hybrid algorithm, HABCDE is proposed. In this HABCDE, all three phases of ABC have been modified. Employed bee phase is modified by incorporating the Gbest
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