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

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Abstract

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.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (Nos. 61272297, 61402207, 61503165), Jiangsu Province Science Foundation for Youths (No. BK20150239) and R&D Program for Science and Technology of Shijiazhuang (No. 155790215).

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Authors and Affiliations

  1. School of Information Engineering, Shijiazhuang University of Economics, Shijiazhuang, 050031, Hebei, China

    Yanhong Feng

  2. School of Computer Science and Technology, Jiangsu Normal University, Xuzhou, 221116, Jiangsu, China

    Gai-Ge Wang, Mei Lu & Xiang-Jun Zhao

  3. Institute of Algorithm and Big Data Analysis, Northeast Normal University, Changchun, 130117, China

    Gai-Ge Wang

  4. School of Computer Science and Information Technology, Northeast Normal University, Changchun, 130117, China

    Gai-Ge Wang

  5. IT & Educational Consultant, Ranchi, Jharkhand, India

    Suash Deb

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  1. Yanhong Feng
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Correspondence to Gai-Ge Wang.

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Feng, Y., Wang, GG., Deb, S. et al. Solving 0–1 knapsack problem by a novel binary monarch butterfly optimization. Neural Comput & Applic 28, 1619–1634 (2017). https://doi.org/10.1007/s00521-015-2135-1

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