The 0/1 Multidimensional Knapsack Problem and Its Variants: A Survey of Practical Models and Heuristic Approaches

• 作者: Boujemaa Achchab Hassan El Amri Mohamed Naimi Soukaina Laabadi
• 来源期刊: 美国运筹学期刊(英文)
• 学科: 医学
• 关键词: 0/1 MULTIDIMENSIONAL KNAPSACK PROBLEM SURVEY Real-World Applications HEURISTICS Metaheuristics
• 年，卷（期）: 2018,（5）
• 页码范围: 395-439
• 页数: 45页
• 分类号: R73

摘要

The 0/1 Multidimensional Knapsack Problem (0/1 MKP) is an interesting NP-hard combinatorial optimization problem that can model a number of challenging applications in logistics, finance, telecommunications and other fields. In the 0/1 MKP, a set of items is given, each with a size and value, which has to be placed into a knapsack that has a certain number of dimensions having each a limited capacity. The goal is to find a subset of items leading to the maximum total profit while respecting the capacity constraints. Even though the 0/1 MKP is well studied in the literature, we can just find a little number of recent review papers on this problem. Furthermore, the existing reviews focus particularly on some specific issues. This paper aims to give a general and comprehensive survey of the considered problem so that it can be useful for both researchers and practitioners. Indeed, we first describe the 0/1 MKP and its relevant variants. Then, we present the detailed models of some important real-world applications of this problem. Moreover, an important collection of recently published heuristics and metaheuristics is categorized and briefly reviewed. These approaches are then quantitatively compared through some indicative statistics. Finally, some synthetic remarks and research directions are highlighted in the conclusion.