A practical approach for dealing with hard knapsack problems using general‐purpose integer programming software

Abstract

Several articles dealing with the generation of hard 0‐1 knapsack problems (KPs) have given rise to 13,940 KP instances being made available for empirical testing. These KPs are typically solved using algorithms specifically designed to solve hard KPs. The goal of this paper is to demonstrate that two general‐purpose integer programming software packages using default parameter settings and a standard PC can successfully be used to generate optimal or guaranteed near‐optimal solutions for these 13,940 KP instances. Over 97% of the 13,940 instances have solutions generated that are guaranteed to be within 0.01% of optimum in less than 1 minute and a practical strategy for dealing with the other 3% is presented. Additionally, 3240 of the most difficult KPs were generated based on 6 parameters. Statistical analyses for predicting which values for these six parameters result in difficult‐to‐solve KPs based on the software used will be discussed. These results will be of particular interest to operations research practitioners who need to efficiently solve hard KPs related to real‐world applications.