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Mathematical Problems in Engineering
Volume 2013, Article ID 948303, 22 pages
Research Article

A Swarm Optimization Algorithm for Multimodal Functions and Its Application in Multicircle Detection

Departamento de Ciencias Computacionales, Universidad de Guadalajara, CUCEI, Avenida Revolución 1500, C.P 44430, Guadalajara, Jal, Mexico

Received 3 September 2012; Accepted 25 December 2012

Academic Editor: Baozhen Yao

Copyright © 2013 Erik Cuevas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In engineering problems due to physical and cost constraints, the best results, obtained by a global optimization algorithm, cannot be realized always. Under such conditions, if multiple solutions (local and global) are known, the implementation can be quickly switched to another solution without much interrupting the design process. This paper presents a new swarm multimodal optimization algorithm named as the collective animal behavior (CAB). Animal groups, such as schools of fish, flocks of birds, swarms of locusts, and herds of wildebeest, exhibit a variety of behaviors including swarming about a food source, milling around a central location, or migrating over large distances in aligned groups. These collective behaviors are often advantageous to groups, allowing them to increase their harvesting efficiency to follow better migration routes, to improve their aerodynamic, and to avoid predation. In the proposed algorithm, searcher agents emulate a group of animals which interact with each other based on simple biological laws that are modeled as evolutionary operators. Numerical experiments are conducted to compare the proposed method with the state-of-the-art methods on benchmark functions. The proposed algorithm has been also applied to the engineering problem of multi-circle detection, achieving satisfactory results.