In multiparty multiobjective optimization problems, solution sets are usually evaluated using classical performance metrics, aggregated across DMs. However, such mean-based evaluations may be unfair by favoring certain parties, as they assume identical geometric approximation quality to each party's PF carries comparable evaluative significance. Moreover, prevailing notions of MPMOP optimal solutions are restricted to strictly common Pareto optimal solutions, representing a narrow form of cooperation in multiparty decision making scenarios. These limitations obscure whether a solution set reflects balanced relative gains or meaningful consensus among heterogeneous DMs. To address these issues, this paper develops a fairness-aware performance evaluation framework grounded in a generalized notion of consensus solutions. From a cooperative game-theoretic perspective, we formalize four axioms that a fairness-aware evaluation function for MPMOPs should satisfy. By introducing a concession rate vector to quantify acceptable compromises by individual DMs, we generalize the classical definition of MPMOP optimal solutions and embed classical performance metrics into a Nash-product-based evaluation framework, which is theoretically shown to satisfy all axioms. To support empirical validation, we further construct benchmark problems that extend existing MPMOP suites by incorporating consensus-deficient negotiation structures. Experimental results demonstrate that the proposed evaluation framework is able to distinguish algorithmic performance in a manner consistent with consensus-aware fairness considerations. Specifically, algorithms converging toward strictly common solutions are assigned higher evaluation scores when such solutions exist, whereas in the absence of strictly common solutions, algorithms that effectively cover the commonly acceptable region are more favorably evaluated.

翻译：在多参与方多目标优化问题中，解决方案集通常使用经典性能指标进行评估，这些指标在多个决策者之间进行聚合。然而，此类基于均值的评估可能因偏袒某些参与方而不公平，因为它们假设对每个参与方的帕累托前沿具有相同的几何逼近质量具有可比较的评估意义。此外，当前关于多方多目标优化最优解的主流概念仅限于严格公共帕累托最优解，这代表了多方决策场景中一种狭隘的合作形式。这些局限性模糊了解决方案集是否反映异质决策者之间平衡的相对收益或有意义的共识。为解决这些问题，本文基于广义共识解的概念，开发了一个公平性感知的性能评估框架。从合作博弈论的视角，我们形式化了多方多目标优化公平性评估函数应满足的四条公理。通过引入让步率向量来量化个体决策者可接受的妥协程度，我们推广了多方多目标优化最优解的经典定义，并将经典性能指标嵌入到基于纳什积的评估框架中，该框架在理论上被证明满足所有公理。为支持实证验证，我们进一步构建了基准问题，通过纳入共识缺失的协商结构来扩展现有的多方多目标优化测试集。实验结果表明，所提出的评估框架能够以符合共识感知公平性考量的方式区分算法性能。具体而言，当严格公共解存在时，收敛于严格公共解的算法被赋予更高的评估分数；而在缺乏严格公共解的情况下，能有效覆盖共同可接受区域的算法则获得更有利的评估。