Abstract
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.
Highlights
The following conclusions can be drawn from the Figure 3: The heuristics are studied in 22 papers, comprising almost 20% of all references given in the Table 1, contrary to the metaheuristics that remained the most common methods for solving 0/1 Multidimensional Knapsack Problem (0/1 MKP), studied in 89 references (80% of the list)
This article aims to build a relevant survey of the most useful variants of 0/1 MKP. It attempts to highlight some real-world applications encountered in the literature
We can see that articles related to 0/1 MKP continue to be published in a large number of research journals having a different scope
Summary
The 0/1 MKP can be informally stated as the problem of packing items into a knapsack while staying within the limits of different constraints (dimensions). They can be, for example, the maximum weight that can be carried, the maximum available volume, or/and the maximum amount that can be afforded for the items. Due to its well-known NP-Hardness, many researchers choose the 0/1 MKP as a test problem for their new resolution approaches. On the other hand, [18] are interested in multi-objective MKP They classify and briefly discuss the existing resolution approach on this topic, especially the metaheuristics. Other hybrid methods can be developed by combining a heuristic/metaheuristic with another heuristic/metaheuristic [20], or by combining an exact method with another exact method [21], or by combining a heuristic/metaheuristic with an exact method [22] [23]
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