Bird swarm algorithms with chaotic mapping

Abstract

Swarm intelligence based optimization methods have been proposed by observing the movements of alive swarms such as bees, birds, cats, and fish in order to obtain a global solution in a reasonable time when mathematical models cannot be formed. However, many swarm intelligence algorithms suffer premature convergence and they may stumble in local optima. Bird swarm algorithm (BSA) is one of the most recent swarm-based methods that suffers the same problems in some situations. In order to obtain a faster convergence with high accuracy from the swarm based optimization algorithms, different methods have been utilized for balancing the exploitation and exploration. In this paper, chaos has been integrated into the standard BSA, for the first time, in order to enhance the global convergence feature by preventing premature convergence and stumbling in the local solutions. Furthermore, a new research area has been introduced for chaotic dynamics. The standard BSA and the chaotic BSAs proposed in this paper have been tested on unimodal and multimodal unconstrained benchmark functions, and on constrained real-life engineering design problems. Generally, the obtained results from the proposed novel chaotic BSAs with an appropriate chaotic map can outperform the standard BSA on benchmark functions and engineering design problems. The proposed chaotic BSAs are expected to be used effectively in many complex problems in future by integrating enhanced multi-dimensional chaotic maps, time-continuous chaotic systems, and hybrid multi-dimensional maps.