A Bibliographical Survey On Some Well-Known Non-Standard Knapsack Problems

Abstract

Knapsack problem and its generalizations have been intensively studied during the last three decades with a rich literature of research reports. Over the years, surveys and reviews have been conducted mostly on the standard knapsack problems, namely, the single-constraint linear model. This paper reports the solution approaches developed for some non-standard knapsack problems with wide range of applications through a bibliographical review. The non-standard knapsack problems reviewed in this paper include the multidimensional knapsack problem, the multiple-choice knapsack problem, the 0–1 multiple knapsack problem, the quadratic knapsack problem, the maximin knapsack problem and the collapsing knapsack problem. Features of the solution approaches for each type of these non-standard knapsack problems and the computational experience as reported in the literature are summarized into several concise tables to provide a quick and broad reference for future researches.