Separation Heuristic for the Rank-1 Chvatal-Gomory Inequalities for the Binary Knapsack Problem

Abstract

An efficient separation heuristic for the rank-1 Chvatal-Gomory cuts for the binary knapsack problem is proposed. The proposed heuristic is based on the decomposition property of the separation problem for the fixedcharge 0-1 knapsack problem characterized by Park and Lee [14]. Computational tests on the benchmark instances of the generalized assignment problem show that the proposed heuristic procedure can generate strong rank-1 C-G cuts more efficiently than the exact rank-1 C-G cut separation and the exact knapsack facet generation.

Lifting the knapsack cover inequalities for the knapsack polytope

“…Most of these focus on lifted cover inequalities (e.g., [2,3,8,12,13,15,16,18,23,26]), but there are a few papers on other families of inequalities. These include weight inequalities [22], lifted pack inequalities [1,16], Chvátal-Gomory cuts [17], Fenchel cuts [4], and the inequalities in [5], which are (somewhat confusingly) called knapsack cover inequalities. These last inequalities have received very little attention in the literature, and have not been analysed from a polyhedral point of view.…”