Early Estimates of the Size of Branch-and-Bound Trees

Authors:
Grard Cornujols;Miroslav Karamanov;Yanjun Li
Affiliations:
Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, and LIF, Facult des Sciences de Luminy, 13288 Marseille, France;Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213;Krannert Graduate School of Management, Purdue University, West Lafayette, Indiana 47907
Venue:
INFORMS Journal on Computing
Year:
2006

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Abstract

This paper intends to show that the time needed to solve mixed-integer-programming problems by branch and bound can be roughly predicted early in the solution process. We construct a procedure that can be implemented as part of an MIP solver. It is based on analyzing the partial tree resulting from running the algorithm for a short period of time and predicting the shape of the whole tree. The procedure is tested on instances from the literature. This work was inspired by the practical applicability of such a result.