A comprehensive empirical demonstration of the impact of choice constraints on solving generalizations of the 0–1 knapsack problem using the integer programming option of CPLEX®

Abstract

This paper provides comprehensive empirical and analytical evidence of the impact of choice constraints on two important categories of knapsack problems by using the integer programming option of CPLEX®. Specifically, if choice constraints are added to the 270 multidimensional knapsack problems (MKPs) in Beasley's OR-Library (used widely for comparing MKP heuristics), then the time needed to solve these problems with CPLEX® version 12 is reduced by more than 99.97%. Similar results are demonstrated for the 810 multi-demand multidimensional knapsack problems (MDMKPs) in Beasley's OR-Library. Additionally, using these 270 MKP and 810 MDMKP problem instances, it is shown that even if only some of the variables have choice constraints imposed on them, the CPLEX solution times are drastically reduced. These results provide motivation for operations research practitioners to check whether choice constraints are applicable (even if only on some of the variables) when solving real-world problems involving generalizations of the 0–1 knapsack problem.