Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem

Silvano Martello, David Pisinger, Paolo Toth
1999 Management science  
T wo new algorithms recently proved to outperform all previous methods for the exact solution of the 0-1 Knapsack Problem. This paper presents a combination of such approaches, where, in addition, valid inequalities are generated and surrogate relaxed, and a new initial core problem is adopted. The algorithm is able to solve all classical test instances, with up to 10,000 variables, in less than 0.2 seconds on a HP9000-735/99 computer. The C language implementation of the algorithm is available
more » ... on the internet. (Knapsack Problem; Dynamic Programming; Branch-and-Bound; Surrogate Relaxation)
doi:10.1287/mnsc.45.3.414 fatcat:jmxmjvttw5bvtpejkg23mrozly