Solving the 0-1 Multidimensional Knapsack Problem with Resolution Search
Sylvain Boussier (LIA), Michel Vasquez (LGI2P, EMA), Yannick Vimont, (LGI2P), Said Hanafi (LAMIH), Philippe Michelon (LIA)
TL;DR
This paper introduces an exact algorithm combining resolution search and branch & bound techniques to solve large-scale 0-1 Multidimensional Knapsack Problems, revealing optimal values for previously unsolved instances.
Contribution
The paper presents a novel hybrid algorithm that effectively solves large, complex multidimensional knapsack problems and uncovers optimal solutions for previously unresolved instances.
Findings
Successfully solved 10-constraint, 500-variable instances from OR-Library
Proved optimal values for large-scale, strongly correlated instances
Demonstrated the algorithm's effectiveness on previously unsolved problems
Abstract
We propose an exact method which combines the resolution search and branch & bound algorithms for solving the 0?1 Multidimensional Knapsack Problem. This algorithm is able to prove large?scale strong correlated instances. The optimal values of the 10 constraint, 500 variable instances of the OR-Library are exposed. These values were previously unknown.
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Taxonomy
TopicsOptimization and Packing Problems · Optimization and Search Problems · Advanced Manufacturing and Logistics Optimization