Fairness-Aware Performance Evaluation for Multi-Party Multi-Objective Optimization
Zifan Zhao, Peilan Xu, Wenjian Luo
TL;DR
The paper tackles fairness in evaluating solutions for multiparty multiobjective optimization by moving beyond mean-based metrics that can bias toward certain DMs. It introduces a fairness-aware Nash-product-based evaluation, $\Psi_{\mathrm{NP}}(P)=\prod_{m=1}^M u_m(P)$ with $u_m(P)=C-L_m(P)$, and a concession-rate framework that defines a mutually acceptable consensus region $\mathcal{A}$, augmented by a penalty $L_m^{\mathrm{pen}}(P)$ for violations. The framework is shown to satisfy four axioms (Pareto Monotonicity, Symmetry, Balance Preference, Acceptability Monotonicity) and is validated on extended MPMOP and MPDMP benchmarks, including a PF-free UAV case, demonstrating improved discrimination of fairness-driven performance over meanIGD. Results reveal that $\Psi_{\mathrm{NP}}$ prioritizes balanced relative gains and consensus, especially when strictly common Pareto-optimal solutions are scarce, underscoring the practical impact of incorporating fairness into algorithm evaluation and design. The work provides a principled, algorithm-independent fairness measure with potential to guide fairness-aware optimization in complex, heterogeneous DM settings.
Abstract
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.