On tightening 0-1 programs based on extensions ofpure 0-1 knapsack and subset-sum problems

We present a framework for automatic tightening of general 0-1 programs. A givenconstraint is tightened by using its own structure as well as information from the other constraints.Our approach exploits special structures that are frequently encountered in practicalproblems, namely knapsack constraints, cliques, covers, variable covers and variable upperbounds. We consider 0-1 knapsack and subset-sum problems with clique and cover inducedconstraints. The tightening (reduction and increasing) of constraint coefficients benefits fromimplication results due to probing analysis. Some computational experience is reported onwell-known real-life problems as well as on a new set of large-scale problems from theinvestment planning sector.

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