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Preprocessing and cut generation techniques for multi-objective binary programming

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  • Boland, Natashia
  • Charkhgard, Hadi
  • Savelsbergh, Martin

Abstract

We present the theoretical foundations for a number of preprocessing and cut generation techniques for multi-objective binary programs. The techniques are based on a characterization of conditions under which the objective functions of a multi-objective binary program guarantee the existence of an ideal point in criterion space, i.e., the existence of a feasible solution that simultaneously minimizes all objectives. Even though few multi-objective binary programs of interest have objective functions satisfying these conditions, the conditions are likely to be satisfied for a subset of the objective functions and/or be satisfied when the objective functions are restricted to a subset of the variables. We show that recognizing whether or not this occurs is NP-hard, but can be done in pseudo-polynomial time. The preprocessing and cut generation techniques can be incorporated in any decision or criterion space search algorithm for multi-objective binary programs. Preliminary computational tests demonstrate their potential in practice.

Suggested Citation

  • Boland, Natashia & Charkhgard, Hadi & Savelsbergh, Martin, 2019. "Preprocessing and cut generation techniques for multi-objective binary programming," European Journal of Operational Research, Elsevier, vol. 274(3), pages 858-875.
    • Handle: RePEc:eee:ejores:v:274:y:2019:i:3:p:858-875
    DOI: 10.1016/j.ejor.2018.10.034
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