A Criterion Space Method for Biobjective Mixed Integer Programming: The Boxed Line Method

Tyler Perini (), Natashia Boland (), Diego Pecin () and Martin Savelsbergh ()
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Tyler Perini: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;
Natashia Boland: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;
Diego Pecin: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;
Martin Savelsbergh: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332

INFORMS Journal on Computing, 2020, vol. 32, issue 1, 16-39

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 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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