# Analysing convergence, consistency and trajectory of Artificial Bee Colony Algorithm

Bansal, Jagdish Chand and Gopal, Anshul and Nagar, Atulya K. (2018) Analysing convergence, consistency and trajectory of Artificial Bee Colony Algorithm. IEEE Access. ISSN 2169-3536

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Convergence of ABC.pdf - Accepted Version

Official URL: https://ieeexplore.ieee.org/document/8554261

## Abstract

Recently, swarm intelligence based algorithms gained attention of the researchers due to their wide applicability and ease of implementation. However, much research has been made on the development of swarm intelligence algorithms but theoretical analysis of these algorithms is still a less explored area of the research. Theoretical analyses of trajectory and convergence of potential solutions towards the equilibrium point in the search space can help the researchers to understand the iteration-wise behaviour of the algorithms which can further help in making them efficient. Artificial Bee Colony (ABC) optimization algorithm is swarm intelligence based algorithm. This paper presents the convergence analysis of ABC algorithm by using results from the theory of dynamical system and convergent boundaries for the parameters $\phi$ and $\psi$ is proposed. Also the trajectory of potential solutions in the search space is analysed by obtaining a partial differential equation corresponding to the position update equation of ABC algorithm. The analysis reveals that the ABC algorithm performs better/efficiently when parameters $\phi$ and $\psi$ are in the convergent region and potential solutions movement follows 1-Dimensional advection equation.

Item Type: Article Copyright(c) 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Artificial Bee Colony (ABC) Algorithm, advection equation, convergence analysis, finite difference scheme, swarm intelligence. Faculty of Science > Mathematics and Computer Science Atulya Nagar 04 Dec 2018 14:15 04 Dec 2018 14:15 http://hira.hope.ac.uk/id/eprint/2695

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