A Binary differential search algorithm for the 0-1 multidimensional knapsack problem

The multidimensional knapsack problem (MKP) is known to be NP-hard in operations research and it has a wide range of applications in engineering and management. In this study, we propose a binary differential search method to solve 0-1 MKPs where the stochastic search is guided by a Brownian motion-...

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Main Authors: Liu, J., Wu, Changzhi, Cao, J., Wang, X., Teo, K.
Format: Journal Article
Published: Elsevier 2014
Online Access:http://purl.org/au-research/grants/arc/LP140100873
http://hdl.handle.net/20.500.11937/27975
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author Liu, J.
Wu, Changzhi
Cao, J.
Wang, X.
Teo, K.
author_facet Liu, J.
Wu, Changzhi
Cao, J.
Wang, X.
Teo, K.
author_sort Liu, J.
building Curtin Institutional Repository
collection Online Access
description The multidimensional knapsack problem (MKP) is known to be NP-hard in operations research and it has a wide range of applications in engineering and management. In this study, we propose a binary differential search method to solve 0-1 MKPs where the stochastic search is guided by a Brownian motion-like random walk. Our proposed method comprises two main operations: discrete solution generation and feasible solution production. Discrete solutions are generated by integrating Brownian motion-like random search with an integer-rounding operation. However, the rounded discrete variables may violate the constraints. Thus, a feasible solution production strategy is used to maintain the feasibility of the rounded discrete variables. To demonstrate the efficiency of our proposed algorithm, we solved various 0-1 MKPs using our proposed algorithm as well as some existing meta-heuristic methods. The numerical results obtained demonstrated that our algorithm performs better than existing meta-heuristic methods. Furthermore, our algorithm has the capacity to solve large-scale 0-1 MKPs.
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institution Curtin University Malaysia
institution_category Local University
last_indexed 2025-11-14T08:08:12Z
publishDate 2014
publisher Elsevier
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spelling curtin-20.500.11937-279752022-11-23T03:27:38Z A Binary differential search algorithm for the 0-1 multidimensional knapsack problem Liu, J. Wu, Changzhi Cao, J. Wang, X. Teo, K. The multidimensional knapsack problem (MKP) is known to be NP-hard in operations research and it has a wide range of applications in engineering and management. In this study, we propose a binary differential search method to solve 0-1 MKPs where the stochastic search is guided by a Brownian motion-like random walk. Our proposed method comprises two main operations: discrete solution generation and feasible solution production. Discrete solutions are generated by integrating Brownian motion-like random search with an integer-rounding operation. However, the rounded discrete variables may violate the constraints. Thus, a feasible solution production strategy is used to maintain the feasibility of the rounded discrete variables. To demonstrate the efficiency of our proposed algorithm, we solved various 0-1 MKPs using our proposed algorithm as well as some existing meta-heuristic methods. The numerical results obtained demonstrated that our algorithm performs better than existing meta-heuristic methods. Furthermore, our algorithm has the capacity to solve large-scale 0-1 MKPs. 2014 Journal Article http://hdl.handle.net/20.500.11937/27975 10.1016/j.apm.2016.06.002 http://purl.org/au-research/grants/arc/LP140100873 Elsevier fulltext
spellingShingle Liu, J.
Wu, Changzhi
Cao, J.
Wang, X.
Teo, K.
A Binary differential search algorithm for the 0-1 multidimensional knapsack problem
title A Binary differential search algorithm for the 0-1 multidimensional knapsack problem
title_full A Binary differential search algorithm for the 0-1 multidimensional knapsack problem
title_fullStr A Binary differential search algorithm for the 0-1 multidimensional knapsack problem
title_full_unstemmed A Binary differential search algorithm for the 0-1 multidimensional knapsack problem
title_short A Binary differential search algorithm for the 0-1 multidimensional knapsack problem
title_sort binary differential search algorithm for the 0-1 multidimensional knapsack problem
url http://purl.org/au-research/grants/arc/LP140100873
http://hdl.handle.net/20.500.11937/27975