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An interactive algorithm to find the most preferred solution of multi-objective integer programs

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Abstract

In this paper, we develop an interactive algorithm that finds the most preferred solution of a decision maker (DM) for multi-objective integer programming problems. We assume that the DM’s preferences are consistent with a quasiconcave value function unknown to us. Based on the properties of quasiconcave value functions and pairwise preference information obtained from the DM, we generate constraints to restrict the implied inferior regions. The algorithm continues iteratively and guarantees to find the most preferred solution for integer programs. We test the performance of the algorithm on multi-objective assignment, knapsack, and shortest path problems and show that it works well.

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Acknowledgments

Pekka Korhonen and Jyrki Wallenius acknowledge the research support by the Academy of Finland Grant Numbers 133387 and 253583.

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Authors and Affiliations

  1. Department of Industrial Engineering, TED University, 06420, Ankara, Turkey

    Banu Lokman

  2. Department of Industrial Engineering, Middle East Technical University, 06531, Ankara, Turkey

    Murat Köksalan

  3. Department of Information and Service Economy, School of Business, Aalto University, Helsinki, Finland

    Pekka J. Korhonen & Jyrki Wallenius

Authors
  1. Banu Lokman
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  2. Murat Köksalan
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  3. Pekka J. Korhonen
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  4. Jyrki Wallenius
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Correspondence to Banu Lokman.

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Lokman, B., Köksalan, M., Korhonen, P.J. et al. An interactive algorithm to find the most preferred solution of multi-objective integer programs. Ann Oper Res 245, 67–95 (2016). https://doi.org/10.1007/s10479-014-1545-2

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