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Article

The Importance of Transfer Function in Solving Set-Union Knapsack Problem Based on Discrete Moth Search Algorithm

by 1,2,3, 1,2,* and 1,2
1
School of Economics and Management, China University of Geosciences, Beijing 100083, China
2
Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Natural Resources, Beijing 100083, China
3
School of Information Engineering, Hebei GEO University, Shijiazhuang 050031, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(1), 17; https://doi.org/10.3390/math7010017
Received: 1 September 2018 / Revised: 10 December 2018 / Accepted: 10 December 2018 / Published: 24 December 2018
(This article belongs to the Special Issue Evolutionary Computation)
Moth search (MS) algorithm, originally proposed to solve continuous optimization problems, is a novel bio-inspired metaheuristic algorithm. At present, there seems to be little concern about using MS to solve discrete optimization problems. One of the most common and efficient ways to discretize MS is to use a transfer function, which is in charge of mapping a continuous search space to a discrete search space. In this paper, twelve transfer functions divided into three families, S-shaped (named S1, S2, S3, and S4), V-shaped (named V1, V2, V3, and V4), and other shapes (named O1, O2, O3, and O4), are combined with MS, and then twelve discrete versions MS algorithms are proposed for solving set-union knapsack problem (SUKP). Three groups of fifteen SUKP instances are employed to evaluate the importance of these transfer functions. The results show that O4 is the best transfer function when combined with MS to solve SUKP. Meanwhile, the importance of the transfer function in terms of improving the quality of solutions and convergence rate is demonstrated as well. View Full-Text
Keywords: set-union knapsack problem; moth search algorithm; transfer function; discrete algorithm set-union knapsack problem; moth search algorithm; transfer function; discrete algorithm
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MDPI and ACS Style

Feng, Y.; An, H.; Gao, X. The Importance of Transfer Function in Solving Set-Union Knapsack Problem Based on Discrete Moth Search Algorithm. Mathematics 2019, 7, 17. https://doi.org/10.3390/math7010017

AMA Style

Feng Y, An H, Gao X. The Importance of Transfer Function in Solving Set-Union Knapsack Problem Based on Discrete Moth Search Algorithm. Mathematics. 2019; 7(1):17. https://doi.org/10.3390/math7010017

Chicago/Turabian Style

Feng, Yanhong; An, Haizhong; Gao, Xiangyun. 2019. "The Importance of Transfer Function in Solving Set-Union Knapsack Problem Based on Discrete Moth Search Algorithm" Mathematics 7, no. 1: 17. https://doi.org/10.3390/math7010017

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