Representing the nondominated set with a small subset in multi-objective mixed integer programs

Doğan, Ilgın
Multi-Objective Mixed Integer Programs (MOMIPs) have a wide variety of application areas in real-life decision making problems. Since the number of nondominated points grows exponentially with the problem size and finding all nondominated points is typically hard and impractical in MOMIPs, generating a subset having “desired properties” rises as an important problem. Motivated with this fact, we observe that the distribution of nondominated points may be critical in defining the desired properties of the representative subset to be generated. Based on our observations, we develop algorithms to generate a small subset of nondominated points that represents the nondominated set with a prespecified coverage gap. Our computational experiments show that our algorithms outperform the existing algorithms in terms of the cardinality of the generated representative set and the solution time.


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In this thesis, we study generating a subset of all nondominated points of multi-objective integer programs in order to represent the nondominated frontier. Our motivation is based on the fact that generating all nondominated points of a multi-objective integer program is neither practical nor useful. The computational burden could be prohibitive and the resulting set could be huge. Instead of finding all nondominated points, we develop algorithms to generate a small representative subset of nondominated po...
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Citation Formats
I. Doğan, “Representing the nondominated set with a small subset in multi-objective mixed integer programs,” M.S. - Master of Science, Middle East Technical University, 2018.