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

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.