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A Criterion Space Search Algorithm for Biobjective Mixed Integer Programming: the Boxed Line Method

Tyler Perini (perinita***at***gatech.edu )
Natashia Boland (natashia.boland***at***isye.gatech.edu )
Diego Pecin (diego.pecin***at***isye.gatech.edu )
Martin Savelsbergh (martin.savelsbergh***at***isye.gatech.edu )

Abstract: Despite recent interest in multiobjective integer programming, few algorithms exist for solving biobjective mixed integer programs. We present such an algorithm: the Boxed Line Method. For one of its variants, we prove that the number of single-objective integer programs solved is bounded by a linear function of the number of nondominated line segments in the nondominated frontier; this is the first such complexity result. An extensive computational study demonstrates that the Box Line Method is also efficient in practice, and that it outperforms existing algorithms on a diverse set of instances.

Keywords: multiobjective, integer programming, criterion space search

Category 1: Applications -- OR and Management Sciences

Citation: H. Milton Stewart School of Industrial and Systems Engineering Georgia Institute of Technology, Atlanta, 09/2017.

Download: [PDF]

Entry Submitted: 09/23/2017
Entry Accepted: 09/25/2017
Entry Last Modified: 12/08/2017

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