Solving 0–1 knapsack problems by chaotic monarch butterfly optimization algorithm with Gaussian mutation

• Published in: Memetic computing Vol. 10; no. 2; pp. 135 - 150
• Main Authors: Feng, Yanhong, Yang, Juan, Wu, Congcong, Lu, Mei, Zhao, Xiang-Jun
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2018; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Artificial Intelligence; Bioinformatics; Butterflies & moths; Chaos theory; Complex Systems; Control; Engineering; Gaussian process; Global optimization; Heuristic methods; Mathematical and Computational Engineering; Mechatronics; Migration; Optimization algorithms; Regular Research Paper; Robotics; Monarch butterfly optimization; 0–1 Knapsack problems; Gaussian mutation operator; Chaotic maps
• ISSN: 1865-9284; 1865-9292
• DOI: 10.1007/s12293-016-0211-4

Recently, inspired by the migration behavior of monarch butterflies in nature, a metaheuristic optimization algorithm, called monarch butterfly optimization (MBO), was proposed. In the present study, a novel chaotic MBO algorithm (CMBO) is proposed, in which chaos theory is introduced in order to enhance its global optimization ability. Here, 12 one-dimensional classical chaotic maps are used to tune two main migration processes of monarch butterflies. Meanwhile, applying Gaussian mutation operator to some worst individuals can effectively prevent premature convergence of the optimization process. The performance of CMBO is verified and analyzed by three groups of large-scale 0–1 knapsack problems instances. The results show that the introduction of appropriate chaotic map and Gaussian perturbation can significantly improve the solution quality together with the overall performance of the proposed CMBO algorithm. The proposed CMBO can outperform the standard MBO and other eight state-of-the-art canonical algorithms.