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Source note2 min read

POO-LPSP: Parallel Osprey Optimized Least Penalty-Squared Prioritization Methods for Priority Derivation in the Analytic Hierarchy Process

Source

arXiv

arxiv.org/abs/2607.07313v1

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Plain-Language Brief

This research introduces the Parallel Osprey Optimized Least Penalty-Squared Prioritization (POO-LPSP) method, an improvement on previous Least Penalty-Squared Prioritization (LPSP) optimization models. The POO-LPSP aims to enhance prioritization reliability by solving complex LPSP models more efficiently using the Parallel Osprey Optimization Algorithm (POOA). The method's practical utility and efficiency are demonstrated through a numerical application focused on a Generative AI vendor selection problem.

What the Document Says

  • The research presents the POO-LPSP method, an improvement of revised Least Penalty-Squared Prioritization (LPSP) optimization models.
  • The LPSP models include LPPDS and LPPWS to minimize Root Mean Penalty-Squared Variance (RMPSV) and Root Mean Penalty-Weighted Square Variance (RMPSWV).
  • The POO-LPSP method overcomes computational complexity by integrating the Parallel Osprey Optimization Algorithm (POOA).
  • The method is validated through a numerical application focused on a Generative AI vendor selection problem.
  • The research suggests that POO-LPSP can serve as a robust alternative to Saaty's Eigen system method for AHP applications.

Key Concepts Mentioned

  • Pairwise comparison
  • Analytic Hierarchy Process (AHP)
  • Least Penalty-Squared Prioritization (LPSP)
  • Parallel Osprey Optimized Least Penalty-Squared Prioritization (POO-LPSP)
  • Parallel Osprey Optimization Algorithm (POOA)
  • Root Mean Penalty-Squared Variance (RMPSV)
  • Root Mean Penalty-Weighted Square Variance (RMPSWV)
  • Generative AI (GAI)

Claims Made by the Document

  • The POO-LPSP method enhances prioritization reliability.
  • POO-LPSP can serve as a robust alternative to Saaty's Eigen system method for AHP applications.

Evidence Used

  • Development of the revised LPSP optimization models and the POO-LPSP method.
  • Numerical application focused on a Generative AI vendor selection problem.

Methods / Approach

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Limitations Stated by the Authors

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Limitations Noted by the Agent

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Open Questions

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Notes for Future Q&A

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Raw Abstract / Excerpt

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.