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Discrete Representation of the Non-dominated Set for Multi-objective Multi-party Negotiation Problems

Author

Listed:
  • Lizhen Shao

    (University of Science and Technology Beijing)

  • Jieyuan Guo

    (University of Science and Technology Beijing)

  • Quanxiu Lv

    (Guangxi Beitou IT Innovation Technology Investment Group CO., LTD)

  • Shu Liang

    (Tongji University)

Abstract

In a multi-party negotiation problem, there does not exist an agreement that maximizes the interests of all the negotiators, which leads to a multi-objective optimization problem in nature. For negotiation decision support purposes, Pareto optimal solutions are often obtained to assist the negotiation process. In this paper, we focus on generation of Pareto optimal solutions from the objective space as negotiators are assumed to be interested in making decisions based on the objective values. For a convex multi-objective multi-party negotiation problem with a mediator involved, we propose an objective space projection method to generate Pareto optimal solutions so that their corresponding non-dominated points in the objective space are evenly distributed. The set of the obtained non-dominated points is a discrete representation of the non-dominated set (Pareto frontier). We prove that a certain coverage error and uniformity level of the discrete representation can be guaranteed. Experimental results show that the proposed method can obtain better discrete representations than other methods and it will be beneficial for assisting the negotiation process.

Suggested Citation

  • Lizhen Shao & Jieyuan Guo & Quanxiu Lv & Shu Liang, 2025. "Discrete Representation of the Non-dominated Set for Multi-objective Multi-party Negotiation Problems," Group Decision and Negotiation, Springer, vol. 34(3), pages 623-642, June.
    • Handle: RePEc:spr:grdene:v:34:y:2025:i:3:d:10.1007_s10726-025-09927-y
    DOI: 10.1007/s10726-025-09927-y
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    References listed on IDEAS

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    1. Shao, Lizhen & Ehrgott, Matthias, 2016. "Discrete representation of non-dominated sets in multi-objective linear programming," European Journal of Operational Research, Elsevier, vol. 255(3), pages 687-698.
    2. Lou, Youcheng & Wang, Shouyang, 2016. "Approximate representation of the Pareto frontier in multiparty negotiations: Decentralized methods and privacy preservation," European Journal of Operational Research, Elsevier, vol. 254(3), pages 968-976.
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