Thus, heuristic and metaheuristic approaches have been proposed in order to achieve an approximate solution within a reasonable amount of time, but without ensuring the optimality. In other words, its exact resolution is very expensive in terms of computing time. They review and compare 11 variants of this metaheuristic approach for solving MKP.

In the same way, focused their research only on genetic algorithms. They classify and briefly discuss the existing resolution approach on this topic, especially the metaheuristics. On the other hand, are interested in multi-objective MKP. We can also mention for a recent survey of structures and algorithms of 0/1 MKP.

Furthermore, a recent survey of the most popular algorithms that have been used for solving MKP, including exact and heuristic methods, can be found in. An Elaborate literature on the MKP and its relations to different problems are published elsewhere. A comprehensive overview of practical and theoretical results for the MKP can be found in the monograph on knapsack problems by. The MKP first appeared in the context of capital budgeting. Moreover, practitioners enjoy the fact that this simple structured problem can be used as a sub-problem to solve more complicated ones or can model many industrial problems like the loading problem, cutting stock, task assignment and multiprocessor scheduling, as well as economic opportunities, such as project selection, capital budgeting, etc. On the other hand, due to its well-known NP-Hardness, many researchers choose the 0/1 MKP as a test problem for their new resolution approaches. The popularity of MKP stems from the fact that it has attracted researchers from both camps: the theoreticians as well as the practitioners enjoy the fact that this problem is a special version of the general zero-one integer programming problem. Ī study of the Stony Brook University Algorithm Repository, carried out in 1998, stipulates that the knapsack problem (especially the MKP) was the 18th most popular and the 4th most needed problem among 75 other algorithmic problems. The goal is to select a sub-set of items that maximizes the sum of their profits and keep the total weight on each dimension no more than the corresponding capacity. Moreover, the knapsack has a limited capacity on each dimension. Each item has a profit level assigned to it, and weight at each dimension. 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. 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). Finally, some synthetic remarksĪnd research directions are highlighted in the conclusion. These approaches are then quantitativelyĬompared through some indicative statistics. Important collection of recently published heuristics and metaheuristics isĬategorized and briefly reviewed. Of some important real-world applications of this problem. Give a general and comprehensive survey of the considered problem so that itĬan be useful for both researchers and practitioners. Reviews focus particularly on some specific issues. Little number of recent review papers on this problem. Leading to the maximum total profit while respecting the capacity constraints.Įven though the 0/1 MKP is well studied in the literature, we can just find a Which has to be placed into a knapsack that has a certain number of dimensions In the 0/1 MKP, a set of items is given, each with a size and value, NP-hard combinatorial optimization problem that can model a number ofĬhallenging applications in logistics, finance, telecommunications and otherįields. The 0/1 Multidimensional Knapsack Problem (0/1 MKP) is an interesting

0 1 knapsack problem