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Neural Computing and Applications

, Volume 28, Issue 7, pp 1619–1634 | Cite as

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

  • Yanhong Feng
  • Gai-Ge Wang
  • Suash Deb
  • Mei Lu
  • Xiang-Jun Zhao
Original Article

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.

Keywords

Evolutionary computation Monarch butterfly optimization Knapsack problems Greedy optimization algorithm 

Notes

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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Copyright information

© The Natural Computing Applications Forum 2015

Authors and Affiliations

  • Yanhong Feng
    • 1
  • Gai-Ge Wang
    • 2
    • 3
    • 4
  • Suash Deb
    • 5
  • Mei Lu
    • 2
  • Xiang-Jun Zhao
    • 2
  1. 1.School of Information EngineeringShijiazhuang University of EconomicsShijiazhuangChina
  2. 2.School of Computer Science and TechnologyJiangsu Normal UniversityXuzhouChina
  3. 3.Institute of Algorithm and Big Data AnalysisNortheast Normal UniversityChangchunChina
  4. 4.School of Computer Science and Information TechnologyNortheast Normal UniversityChangchunChina
  5. 5.IT & Educational ConsultantRanchiIndia

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