Finding and exploring promising search space for The 0–1 Multidimensional Knapsack Problem

The 0–1, Multidimensional Knapsack Problem (MKP) is a classical NP-hard combinatorial optimization problem with many engineering applications. In this paper, we propose a novel algorithm combining evolutionary computation with the exact algorithm to solve the 0–1 MKP. It maintains a set of solutions...

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Bibliographic Details
Published in:Applied soft computing Vol. 164; p. 111934
Main Authors: Xu, Jitao, Li, Hongbo, Yin, Minghao
Format: Journal Article
Language:English
Published: Elsevier B.V 01.10.2024
Subjects:
0–1 Multidimensional Knapsack Problem
Evolutionary computation
Exact algorithm
Heuristic
Large Neighborhood Search
0–1 Multidimensional Knapsack Problem
Exact algorithm
Large Neighborhood Search
Evolutionary computation
Heuristic
ISSN:1568-4946
Online Access:Get full text
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Summary:The 0–1, Multidimensional Knapsack Problem (MKP) is a classical NP-hard combinatorial optimization problem with many engineering applications. In this paper, we propose a novel algorithm combining evolutionary computation with the exact algorithm to solve the 0–1 MKP. It maintains a set of solutions and utilizes the information from the population to extract good partial assignments. To find high-quality solutions, an exact algorithm is applied to explore the promising search space specified by the good partial assignments. The new solutions are used to update the population. Thus, the good partial assignments evolve towards a better direction with the improvement of the population. Extensive experimentation with commonly used benchmark sets shows that our algorithm outperforms the state-of-the-art heuristic algorithms, TPTEA and DQPSO, as well as the commercial solver CPlex. It finds better solutions than the existing algorithms and provides new lower bounds for 10 large and hard instances. •We propose an efficient and practical algorithm for solving the 0–1 Multidimensional Knapsack Problem in this paper.•The algorithm takes advantages of Evolutionary Computation and Large Neighborhood Search.•It works well in solving the large and hard 0–1 MKP instances.•We provide new lower bounds (best known results) for 10 large and hard instances from the commonly used benchmark set.
ISSN:1568-4946
DOI:10.1016/j.asoc.2024.111934