用仿生优化算法提升决策优先级计算的准确性和效率。
POO-LPSP: Parallel Osprey Optimized Least Penalty-Squared Prioritization Methods for Priority Derivation in the Analytic Hierarchy Process
- 结合改进的鹰类优化算法求解非线性优先级模型。
- 在生成式AI供应商选择中显著降低误差指标。
- 适合需要高可靠性决策支持的复杂评估场景。
成对比较（PC）通过成对互逆矩阵（PRM）是层次分析法（AHP）的核心。尽管传统特征向量法广泛应用，但其理论稳健性仍存争议。本研究在前期工作基础上，提出修正的最小惩罚平方优先化（LPSP）优化模型，包括修正的最小惩罚乘积与直接平方（LPPDS）和修正的加权平方（LPPWS），以最小化修正的均方惩罚平方变异度（RMPSV）和修正的均方惩罚加权平方变异度（RMPSWV）。然而，求解这些非线性模型对决策者而言计算复杂。为此，本文提出并行鸬鹚优化最小惩罚平方优先化（POO-LPSP）方法，融合改进的生物启发式元启发式算法——并行鸬鹚优化算法（POOA），高效求解复杂LPSP模型，从而提升优先级推导的可靠性。通过生成式人工智能（GAI）供应商选择问题的数值应用验证了该方法的实际效用与计算效率。结果表明，POO-LPSP可作为萨蒂特征系统法在AHP应用中的稳健替代方案。
原文摘要 · Abstract (English)
Pairwise comparison (PC) via pairwise reciprocal matrices (PRMs) is central to the Analytic Hierarchy Process (AHP). Although the traditional eigenvector method is widely applied to derive priorities, its theoretical robustness in reflecting true priority vectors remains debated. Building upon a previous iteration of this study, this research develops the revised Least Penalty-Squared Prioritization (LPSP) optimization models, including the revised Least Product of Penalty and Direct Squares (LPPDS) and revised Weighted Squares (LPPWS), to minimize the revised Root Mean Penalty-Squared Variance (RMPSV) and the revised Root Mean Penalty-Weighted Square Variance (RMPSWV). However, solving these non-linear formulations is computationally complex for decision-makers. To overcome these limitations, this study proposes the Parallel Osprey Optimized Least Penalty-Squared Prioritization (POO-LPSP) method. By integrating an improved bio-inspired metaheuristic Parallel Osprey Optimization Algorithm (POOA), this framework efficiently solves complex LPSP models to minimize RMPSV and RMPSWV, thereby enhancing prioritization reliability. The practical utility and computational efficiency of the POO-LPSP method are validated through a numerical application focusing on a Generative AI (GAI) vendor selection problem. To extend, POO-LPSP can serve as a robust alternative to Saaty's Eigen system method for AHP applications.
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