# SASS: slicing with adaptive steps search method for finding the non-dominated points of tri-objective mixed-integer linear programming problems

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## Abstract

Multi-objective optimization problems (MOOP) reflect the complexity of many real-world decision problems where objectives are conflicting. The presence of more than one criterion makes finding the non-dominated (ND) points a crucial issue in the decision making process. Tri-objective mixed-integer linear programs (TOMILP) are an important subclass of MOOPs that are applicable to many problems in economics, business, science, and engineering including sustainable systems that must consider economic, environmental, and social concerns simultaneously. The literature on finding the ND points of TOMILPs is limited; there are only a few algorithms published in the literature that do not guarantee generating the entire ND points of TOMILPs. We present a new method, the Slicing with Adaptive Steps Search (SASS), to generate the ND points of TOMILPs. The result of SASS is primarily a superset of the set of ND points in the form of (partially) ND faces. We then perform a post-processing to eliminate the dominated parts of the partially ND faces. We provide a theoretical analysis of SASS and illustrate its effectiveness on a large set of instances.

## Keywords

Tri-objective programming Mixed-integer linear programming Non-dominated points Lexicographic optimization Exact method Non-dominated faces## Notes

### Acknowledgements

We gratefully acknowledge the computational infrastructure support provided by the IBM Corporation through the IBM SUR award. We also acknowledge valuable comments and suggestions provided by Emre Alper Yıldırım, Emre Mengi, Matthias Ehrgott, Annals of OR and MOPGP 2017 conference referees. Funding was provided by TUPRAS (OS.00054).

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