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Open AccessArticle

A Novel Monarch Butterfly Optimization with Global Position Updating Operator for Large-Scale 0-1 Knapsack Problems

by Yanhong Feng 1, Xu Yu 2 and Gai-Ge Wang 3,4,5,6,*
1
School of Information Engineering, Hebei GEO University, Shijiazhuang 050031, China
2
School of Information Science and Technology, Qingdao University of Science and Technology, Qingdao 266061, China
3
Department of Computer Science and Technology, Ocean University of China, Qingdao 266100, China
4
Institute of Algorithm and Big Data Analysis, Northeast Normal University, Changchun 130117, China
5
School of Computer Science and Information Technology, Northeast Normal University, Changchun 130117, China
6
Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun 130012, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1056; https://doi.org/10.3390/math7111056
Received: 18 September 2019 / Revised: 24 October 2019 / Accepted: 25 October 2019 / Published: 4 November 2019
(This article belongs to the Special Issue Evolutionary Computation)
As a significant subset of the family of discrete optimization problems, the 0-1 knapsack problem (0-1 KP) has received considerable attention among the relevant researchers. The monarch butterfly optimization (MBO) is a recent metaheuristic algorithm inspired by the migration behavior of monarch butterflies. The original MBO is proposed to solve continuous optimization problems. This paper presents a novel monarch butterfly optimization with a global position updating operator (GMBO), which can address 0-1 KP known as an NP-complete problem. The global position updating operator is incorporated to help all the monarch butterflies rapidly move towards the global best position. Moreover, a dichotomy encoding scheme is adopted to represent monarch butterflies for solving 0-1 KP. In addition, a specific two-stage repair operator is used to repair the infeasible solutions and further optimize the feasible solutions. Finally, Orthogonal Design (OD) is employed in order to find the most suitable parameters. Two sets of low-dimensional 0-1 KP instances and three kinds of 15 high-dimensional 0-1 KP instances are used to verify the ability of the proposed GMBO. An extensive comparative study of GMBO with five classical and two state-of-the-art algorithms is carried out. The experimental results clearly indicate that GMBO can achieve better solutions on almost all the 0-1 KP instances and significantly outperforms the rest.
Keywords: Monarch butterfly optimization; greedy optimization algorithm; global position updating operator; 0-1 knapsack problems Monarch butterfly optimization; greedy optimization algorithm; global position updating operator; 0-1 knapsack problems
MDPI and ACS Style

Feng, Y.; Yu, X.; Wang, G.-G. A Novel Monarch Butterfly Optimization with Global Position Updating Operator for Large-Scale 0-1 Knapsack Problems. Mathematics 2019, 7, 1056.

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