Active-constraint variable ordering for faster feasibility of mixed integer linear programs

Authors:
Jagat Patel;John W. Chinneck
Affiliations:
Nortel Networks, 3500 Carling Avenue, K2H 8E9, Ottawa, Ontario, Canada;Carleton University, Systems and Computer Engineering, 3500 Carling Avenue, K1S 5B6, Ottawa, Ontario, Canada
Venue:
Mathematical Programming: Series A and B
Year:
2007

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Abstract

The selection of the branching variable can greatly affect the speed of the branch and bound solution of a mixed-integer or integer linear program. Traditional approaches to branching variable selection rely on estimating the effect of the candidate variables on the objective function. We present a new approach that relies on estimating the impact of the candidate variables on the active constraints in the current LP relaxation. We apply this method to the problem of finding the first feasible solution as quickly as possible. Empirical experiments demonstrate a significant improvement compared to a state-of-the art commercial MIP solver.