An extension of Dembo-Hammer's reduction algorithm for the 0-1 knapsack problem

TL;DR

This paper introduces an extended version of Dembo-Hammer's reduction algorithm for the 0-1 knapsack problem, allowing for adjustable reduction levels and demonstrating improved computational efficiency over CPLEX in experiments.

Contribution

The paper proposes EDHR, an extension of DHR, enabling reduction to at most n^i sub-instances, providing flexible and potentially more efficient problem size reduction.

Findings

EDHR reduces search tree size more effectively than CPLEX.

The extension allows adjustable reduction levels based on parameter i.

Experimental results show improved computational performance.

Abstract

Dembo-Hammer's Reduction Algorithm (DHR) is one of the classical algorithms for the 0-1 Knapsack Problem (0-1 KP) and its variants, which reduces an instance of the 0-1 KP to a sub-instance of smaller size with reduction time complexity $O(n)$. We present an extension of DHR (abbreviated as EDHR), which reduces an instance of 0-1 KP to at most $n^i$ sub-instances for any positive integer $i$. In practice, $i$ can be set as needed. In particular, if we choose $i=1$ then EDHR is exactly DHR. Finally, computational experiments on randomly generated data instances demonstrate that EDHR substantially reduces the search tree size compared to CPLEX.