A theoretical and empirical investigation on the Lagrangian capacities of the 0-1 multidimensional knapsack problem

► We formally reintroduce Lagrangian capacity suitable to the 0-1 MKP. ► We present its new geometric equivalent condition including an associated property. ► We propose a novel Lagrangian heuristic FPLS for the 0-1 MKP. ► We verify the advantage of FPLS through various experiments on benchmark data...

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Bibliographic Details
Published in:European journal of operational research Vol. 218; no. 2; pp. 366 - 376
Main Authors: Yoon, Yourim, Kim, Yong-Hyuk, Moon, Byung-Ro
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 16.04.2012
Elsevier
Elsevier Sequoia S.A
Subjects:
0-1 Multidimensional knapsack problem
Applied sciences
Exact sciences and technology
Flows in networks. Combinatorial problems
Heuristic
Integer programming
Knapsack problem
Lagrange multiplier
Lagrangian capacity
Lagrangian method
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization algorithms
Studies
Integer programming
Lagrangian capacity
0-1 Multidimensional knapsack problem
Lagrangian method
Lagrangian
Empirical method
Knapsack problem
Lagrange multiplier
Zero one programming
Integer programming 0-1 Multidimensional knapsack problem
Heuristic method
Relaxation method
Capacity constraint
Large scale
Multidimensional system
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:► We formally reintroduce Lagrangian capacity suitable to the 0-1 MKP. ► We present its new geometric equivalent condition including an associated property. ► We propose a novel Lagrangian heuristic FPLS for the 0-1 MKP. ► We verify the advantage of FPLS through various experiments on benchmark data. We present a novel Lagrangian method to find good feasible solutions in theoretical and empirical aspects. After investigating the concept of Lagrangian capacity, which is the value of the capacity constraint that Lagrangian relaxation can find an optimal solution, we formally reintroduce Lagrangian capacity suitable to the 0-1 multidimensional knapsack problem and present its new geometric equivalent condition including a new associated property. Based on the property, we propose a new Lagrangian heuristic that finds high-quality feasible solutions of the 0-1 multidimensional knapsack problem. We verify the advantage of the proposed heuristic by experiments. We make comparisons with existing Lagrangian approaches on benchmark data and show that the proposed method performs well on large-scale data.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2011.11.011