Solution Methods for the Multiple-Choice Knapsack Problem and Their Applications

Abstract

The Knapsack Problem belongs to the best-studied classical problems in combinatorial optimization. The Multiple-choice Knapsack Problem (MCKP) represents a generalization of the problem, with various application fields such as industry, transportation, telecommunication, national defense, bioinformatics, finance, and life. We found a lack of survey papers on MCKP. This paper overviews MCKP and presents its variants, solution methods, and applications. Traditional operational research methods solving the knapsack problem, such as dynamic programming, greedy heuristics, and branch-and-bound algorithms, can be adapted to MCKP. Only a few algorithms appear to have solved the problem in recent years. We found various related problems during the literature study and explored the broad spectrum of application areas. We intend to inspire research into MCKP algorithms and motivate experts from different domains to apply MCKP.