انتخاب بهترین دور در الگوریتم مصنوعی کلونی زنبور عسل

The Artificial Bee Colony (ABC) algorithm is inspired by the behavior of honey bees. The algorithm is one of the Swarm Intelligence algorithms explored in recent literature. ABC is an optimization technique, which is used in finding the best solution from all feasible solutions. However, ABC can sometimes be slow to converge. In order to improve the algorithm performance, we present a modified method for solution update of the onlooker bees in this paper. In our method, the best feasible solutions found so far are shared globally among the entire population. Thus, the new candidate solutions are more likely to be close to the current best solution. In other words, we bias the solution direction toward the best-so-far position. Moreover, in each iteration, we adjust the radius of the search for new candidates using a larger radius earlier in the search process and then reduce the radius as the process comes closer to converging. Finally, we use a more robust calculation to determine and compare the quality of alternative solutions. We empirically assess the performance of our proposed method on two sets of problems: numerical benchmark functions and image registration applications. The results demonstrate that the proposed method is able to produce higher quality solutions with faster convergence than either the original ABC or the current state-of-the-art ABC-based algorithm.

Swarm Intelligence is a meta-heuristic method in the field of artificial intelligence that is used to solve optimization problems. It is based on the collective behavior of social insects, flocks of birds, or schools of fish. These animals can solve complex tasks without centralized control. Researchers have analyzed such behaviors and designed algorithms that can be used to solve combinatorial and numerical optimization problems in many science and engineering domains. Previous research [1], [2], [3] and [4] has shown that algorithms based on Swarm Intelligence have great potential. The algorithms that have emerged in recent years include Ant Colony Optimization (ACO) [5] based on the foraging behavior of ants, and Particle Swarm Optimization (PSO) [6] based on the behaviors of bird flocks and fish schools. Exploration and exploitation are the important mechanisms in a robust search process. While exploration process is related on the independent search for an optimal solution, exploitation uses existing knowledge to bias the search. In the recent years, there are a few algorithms based on bee foraging behavior developed to improve both exploration and exploitation for solving the numerical optimization problems. The Artificial Bee Colony (ABC) algorithm introduced by D. Karaboga [7] is one approach that has been used to find an optimal solution in numerical optimization problems. This algorithm is inspired by the behavior of honey bees when seeking a quality food source. The performance of ABC algorithm has been compared with other optimization methods such as Genetic Algorithm (GA), Differential Evolution algorithm (DE), Evolution Strategies (ES), Particle Swarm Optimization, and Particle Swarm Inspired Evolutionary Algorithm (PS-EA) [8], [9] and [10]. The comparisons were made based on various numerical benchmark functions, which consist of unimodal and multimodal distributions. The comparison results showed that ABC can produce a more optimal solution and thus is more effective than the other methods in several optimization problems [11], [12] and [13]. Yang [14] introduced an algorithm called the Virtual Bee Algorithm (VBA) for solving engineering optimizations that have multi-peaked functions. In the VBA algorithm, the objectives or optimization functions are encoded as virtual foods. Virtual bees are used to search for virtual foods in the search space. The position of each virtual bee is updated via the virtual pheromone from the neighboring bees. The food with largest number of virtual bees or intensity of visiting bees corresponds to the optimal solution. However, the VBA algorithm was only tested using two-dimension functions. An optimization algorithm inspired by the honey bee foraging behavior based on the elite bee method was proposed by Sundareswaran [15]. The bee whose solution is the best possible solution in each simulation iteration is considered to be the elite bee. A probabilistic approach is used to control the movement of the other bees, so majority of bees will follow the elite bee's direction while a few bees may fly to other directions. This approach improves the capability of convergence to a global optimum. To improve the exploration and exploitation of foraging behavior of honey bees for numerical function optimization, Akbari et al. [16] presented an algorithm called Bee Swarm Optimization (BSO). In this method, the bees of the swarm are sorted according to the fitness values of the most recently visited food source and these sorted bees are divided into three types. The bees that have worst fitness are classified as scout bees, while the rest of bees are divided equally as experienced foragers and onlookers. Different flying patterns were introduced for each type of bee to balance the exploration and exploitation in this algorithm. The experimental results from these algorithms show that the algorithms based on bee foraging behavior can successfully solve numerical optimization problems. However, in some cases the convergence speed can be an issue. This paper introduces a modified version of ABC in order to improve the algorithm's performance. First, we test our modified algorithm using the same benchmarks as the previously cited research including the original ABC and the BSO algorithm. Then, we apply our method to optimize the mutual information value in order to measure similarity in an image registration process. We compare the registration results between the original ABC and our best-so-far method. The paper is organized as follows. Section 2 describes the original ABC algorithm. Section 3 presents our best-so-far method. Section 4 describes the automated image registration problem. Section 5 presents the experiments. Section 6 compares and discusses the performance results of the best-so-far method with the original method and BSO algorithm. Finally, Section 7 offers our conclusions.

In this paper, a best-so-far method for solution updates in the Artificial Bee Colony algorithm was proposed. We have replaced the neighboring solutions-based approach with the best-so-far technique in order to increase the local search ability of the onlooker bees. The searching method based on a dynamic adjustment of search range depending on the iteration was introduced for scout bees. The comparison and the selection of the new solution were changed from a fitness-based comparison to an objective-value-based comparison that can help to resolve round up issues in the computation of the floating point “goodness” value. In our best-so-far method, onlooker bees compare the information from all employed bees to select the best-so-far candidate food source. This will bias the solution handled by onlooker bees towards the optimal solution. Moreover, if the solution appears to stagnate in a local optimum, the scout bee can randomly generate a new position in order to maintain the diversity of new food sources. The performance of the best-so-far ABC method was then compared with the original ABC algorithm and the BSO algorithm using a set of benchmark functions. The computational complexity and the rate of convergence on both best-so-far ABC method and the original ABC method were addressed. The results from the experiments provide evidence that the best-so-far ABC outperforms all the mentioned algorithms in both quality and convergence rate. We further applied the best-so-far method to optimize the mutual information in an image registration application. Several image pairs were used in the experiments. The results showed that our algorithm can arrive at the convergence state more quickly. Lastly, the mutual information value produced by the best-so-far method is higher implying that the registration quality is also enhanced. Thus, we can conclude that our best-so-far ABC is efficient from both the perspective of solution quality and algorithm performance. The algorithm can serve as an alternative in several application domains in the future.