Solving 0–1 knapsack problem by a novel binary monarch butterfly optimization

• Published in: Neural computing & applications Vol. 28; no. 7; pp. 1619 - 1634
• Main Authors: Feng, Yanhong, Wang, Gai-Ge, Deb, Suash, Lu, Mei, Zhao, Xiang-Jun
• Format: Journal Article
• Language: English
• Published: London Springer London 01.07.2017; Springer Nature B.V
• Subjects: Accuracy; Artificial Intelligence; Branch & bound algorithms; Computational Biology/Bioinformatics; Computational Science and Engineering; Computer Science; Data Mining and Knowledge Discovery; Dimensional stability; Image Processing and Computer Vision; Knapsack problem; Optimization; Original Article; Probability and Statistics in Computer Science; Solution space; Vectors (mathematics); Monarch butterfly optimization; Knapsack problems; Evolutionary computation; Greedy optimization algorithm
• ISSN: 0941-0643; 1433-3058
• DOI: 10.1007/s00521-015-2135-1

This paper presents a novel binary monarch butterfly optimization (BMBO) method, intended for addressing the 0–1 knapsack problem (0–1 KP). Two tuples, consisting of real-valued vectors and binary vectors, are used to represent the monarch butterfly individuals in BMBO. Real-valued vectors constitute the search space, whereas binary vectors form the solution space. In other words, monarch butterfly optimization works directly on real-valued vectors, while solutions are represented by binary vectors. Three kinds of individual allocation schemes are tested in order to achieve better performance. Toward revising the infeasible solutions and optimizing the feasible ones, a novel repair operator, based on greedy strategy, is employed. Comprehensive numerical experimentations on three types of 0–1 KP instances are carried out. The comparative study of the BMBO with four state-of-the-art classical algorithms clearly points toward the superiority of the former in terms of search accuracy, convergent capability and stability in solving the 0–1 KP, especially for the high-dimensional instances.