The Bees Algorithm and Its Applications

2013

A supply chain is a complex network which involves the products, services and information flows between suppliers and customers. A typical supply chain is composed of different levels, hence, there is a need to optimize the supply chain by finding the optimum configuration of the network in order to get a good compromise between the multi-objectives such as cost minimization and lead-time minimization. There are several multi-objective optimization methods which have been applied to find the optimum solutions set based on the Pareto front line. In this study, a swarm-based optimization method, namely, the bees algorithm is proposed in dealing with the multi-objective supply chain model to find the optimum configuration of a given supply chain problem which minimizes the total cost and the total lead-time. The supply chain problem utilized in this study is taken from literature and several experiments have been conducted in order to show the performance of the proposed model; in addition, the results have been compared to those achieved by the ant colony optimization method. The results show that the proposed bees algorithm is able to achieve better Pareto solutions for the supply chain problem.

Optimization algorithms are search methods where the goal is to find an optimal solution to a problem, in order to satisfy one or more objective functions, possibly subject to a set of constraints. Studies of social animals and social insects have resulted in a number of computational models of swarm intelligence. Within these swarms their collective behavior is usually very complex. The collective behavior of a swarm of social organisms emerges from the behaviors of the individuals of that swarm. Researchers have developed computational optimization methods based on biology such as Genetic Algorithms, Particle Swarm Optimization, and Ant Colony. The aim of this paper is to describe an optimization algorithm called the Bees Algorithm, inspired from the natural foraging behavior of honey bees, to find the optimal solution. The algorithm performs both an exploitative neighborhood search combined with random explorative search. In this paper, after an explanation of the natural foraging behavior of honey bees, the basic Bees Algorithm and its improved versions are described and are implemented in order to optimize several benchmark functions, and the results are compared with those obtained with different optimization algorithms. The results show that the Bees Algorithm offering some advantage over other optimization methods according to the nature of the problem.

A new population-based search algorithm called the Bees Algorithm (BA) is presented. The algorithm mimics the food foraging behaviour of swarms of honey bees. In its basic version, the algorithm performs a kind of neighbourhood search combined with random search and can be used for both combinatorial optimisation and functional optimisation. This paper focuses on the latter. Following a description of the algorithm, the paper gives the results obtained for a number of benchmark problems demonstrating the efficiency and robustness of the new algorithm.

Yugoslav Journal of Operations Research, 2014

This paper is an extensive survey of the Bee Colony Optimization (BCO) algorithm, proposed for the first time in 2001. BCO and its numerous variants belong to a class of nature-inspired meta-heuristic methods, based on the foraging habits of honeybees. Our main goal is to promote it among the wide operations research community. BCO is a simple, but efficient meta-heuristic technique that has been successfully applied to many optimization problems, mostly in transport, location and scheduling fields. Firstly, we shall give a brief overview of the other meta-heuristics inspired by bees? foraging principles pointing out the differences between them. Then, we shall provide the detailed description of the BCO algorithm and its modifications, including the strategies for BCO parallelization, and giving the preliminary results regarding its convergence. The application survey is elaborated in Part II of our paper.

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2009

The Bees Algorithm models the foraging behaviour of honeybees in order to solve optimization problems. The algorithm performs a kind of exploitative neighbourhood search combined with random explorative search. This article describes the Bees Algorithm in its basic formulation, and two recently introduced procedures that increase the speed and accuracy of the search. A critical review of the related swarm intelligence literature is presented. The effectiveness of the proposed method is compared to that of three state-of-the-art biologically inspired search methods. The four algorithms were tested on a range of well-known benchmark function optimization problems of different degrees of complexity. The experimental results proved the reliability of the bees foraging metaphor. The Bees Algorithm performed optimally, or near optimally, in almost all the tests. Compared to the three control algorithms, the Bees Algorithm was highly competitive in terms of learning accuracy and speed. The experimental tests helped also to shed further light on the search mechanisms of the Bees Algorithm and the three control methods, and to highlight their differences, strengths, and weaknesses.

International journal of engineering business management, 2016

This article proposes a bees algorithm for solving a mathematical model of strategic supply chains planning and design in the globalization context. The model, taken from the literature, involves a multi-echelon, multi-facility and multi-product supply chain in a dynamic environment. Our bees algorithm, the first to be applied to this kind of problem, was adapted specifically to the optimization problem, and its performance was benchmarked against the genetic algorithm (GA) provided by commercial optimization software MATLAB R2011b. This is in order to test its effectiveness in an already known supply chain design problem, which has not been solved yet in optimized way. Several configurations of the algorithm were tested and analysed; the bees algorithm performs better of 10% in quality of solution respect to the GA with equivalent calculation time. The better quality of their solutions and the good calculation time performances have encouraged towards more accurate studies on tuning parameters and an extended utilization of the methodology on problems of logistic systems configuration and supply chain design.

International Journal of Applied Metaheuristic Computing, 2013

Nowadays computers are used to solve a variety and multitude of complex problems facing in every sphere of peoples’ life. However, many of the problems are intractable in nature exact algorithm might need centuries to manage with formidable challenges. In such cases heuristic or in a broader sense meta-heuristic algorithms that find an approximate solution but have acceptable time and space complexity play indispensable role. In this article, the authors present a state-of-the-art review on meta-heuristic algorithm popularly known as artificial bee colony (ABC) inspired by honey bees. Moreover, the ABC algorithm for solving single and multi-objective optimization problems have been studied. A few potential application areas of ABC are highlighted as an end note of this article.

—In this paper an overview of the areas where the Bee Colony Optimization (BCO) and its variants are applied have been given. Bee System was identified by Sato and Hagiwara in 1997 and the Bee Colony Optimization (BCO) was identified by Lucic and Teodorovic in 2001. BCO has emerged as a specialized class of Swarm Intelligence with bees as agents. It is an emerging field for researchers in the field of optimization problems because it provides immense problem solving scope for combinatorial and NP-hard problems. BCO is one of the benchmark systems portraying team work, collaborative work. BCO is a bottom-up approach of modeling where agents form global solution by optimizing the local solution.

Artificial Intelligence Review, 2016

The Bees Algorithm (BA) is a bee swarm intelligence-based metaheuristic algorithm that is inspired by the natural behavior of honeybees when foraging for food. BA can be divided into four parts: parameter tuning, initialization, local search, and global search. Since its invention, several studies have sought to enhance the performance of BA by improving some of its parts. Thus, more than one version of the algorithm has been proposed. However, upon searching for the basic version of BA in the literature, unclear and contradictory information can be found. By reviewing the literature and conducting some experiments on a set of standard benchmark functions, three main implementations of the algorithm that researchers should be aware of while working on improving the BA are uncovered. These implementations are Basic BA, Shrinking-based BA and Standard BA. Shrinking-based BA employs a shrinking procedure, and Standard BA uses a site abandonment approach in addition to the shrinking procedure. Thus, various implementations of the shrinking and site-abandonment procedures are explored and incorporated into BA to constitute different BA implementations. This paper proposes a framework of the main implementations of BA, including Basic BA and Standard BA, to give a clear picture of these implementations and the relationships among them. Additionally, the experiments show no significant differences among most of the shrinking implementations. Furthermore, this paper reviews the improvements to BA, which are improvements in the parameter tuning, population initialization, local search and global search. It is hoped that this paper will provide researchers who are working on improving the BA with valuable references and guidance.

2012

Swarm Intelligence is the most studied area by several researchers it is the part of AI based on the study of actions of individuals in various decentralized system. The BCO metaheuristics has been introduced fairly recently as a new direction in the field of Swarm Intelligence. Artificial Bee represents agents which collaboratively solve complex combinatorial optimization problem. It was introduced in 2005 and has been applied to solve different optimization problems in various areas. BCO is a benchmark system which shows the team work and applied in various optimization problem. Keywords—Swarm Intelligence (SI), Bee Colony Optimization (BCO), Artificial Bee Colony (ABC).