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A modiﬁed Artiﬁcial Bee Colony algorithm for real-parameter optimization Bahriye Akay *, Dervis Karaboga
Department of Computer Engineering, Erciyes University, 38039 Melikgazi, Kayseri, Turkey
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Swarm intelligence is a research ﬁeld that models the collective intelligence in swarms of insects or animals. Many algorithms that simulates these models have been proposed in order to solve a wide range of problems. The Artiﬁcial Bee Colony algorithm is one of the most recent swarm intelligence based algorithms which simulates the foraging behaviour of honey bee colonies. In this work, modiﬁed versions of the Artiﬁcial Bee Colony algorithm are introduced and applied for efﬁciently solving real-parameter optimization problems. Ó 2010 Elsevier Inc. All rights reserved.
Article history: Available online 27 July 2010 Keywords: Swarm intelligence Self-organization Artiﬁcial Bee Colony algorithm Real-parameter optimization
1. Introduction The collective intelligent behaviour of insect or animal groups in nature such as ﬂocks of birds, colonies of ants, schools of ﬁsh, swarms of bees, and termites have attracted the attention of researchers. The aggregate behaviour of insects or animals is called swarm behaviour. Entomologists have studied this collective behaviour to model biological swarms, and engineers applied these models as a framework for solving complex real-world problems. This branch of artiﬁcial intelligence which deals with the collective behaviour of swarms through complex interaction of individuals without supervision, is referred to as swarm intelligence. Bonabeau deﬁned swarm intelligence as ‘‘any attempt to design algorithms or distributed problemsolving devices inspired by the collective behaviour of the social insect colonies and other animal societies” . Swarm intelligence has some advantages such as scalability, fault tolerance, adaptation, speed, modularity, autonomy, and parallelism . The key components of swarm intelligence are self-organization and division of labour. In a self-organising system, each of the covered units may respond to local stimuli individually and act together to accomplish a global task via division of labour without a centralized supervision. The entire system can adapt to internal and external changes efﬁciently. Bonabeau et al. have characterized four basic properties on which self-organization relies: positive feedback, negative feedback, ﬂuctuations and multiple interactions . Positive feedback means that an individual recruits other individuals by some directive, such as dancing of bees in order to lead some other bees onto a speciﬁc food source site. Negative feedback avoids all individuals accumulating on the same task by counterbalancing the attraction negatively, such as abandoning the exhausted food source. Fluctuations are random behaviours of individuals in order to explore new states, such as random ﬂights of scouts in a bee swarm. Multiple interactions are the basis of the tasks to be carried out by certain rules. Bee swarms exhibit many intelligent behaviours in their tasks such as nest site building, marriage, foraging, navigation and task selection. There is an efﬁcient task selection mechanism in a bee swarm that can be adaptively changed by the state of the hive and the environment. Foraging is another crucial task for bees. Forage selection depends on recruitment for and abandonment of food sources. There are three types of bees associated with the foraging task with respect to their selection mechanisms. Employed bees ﬂy onto the sources which they are exploiting; onlooker bees choose the sources by watching
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