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

• URL: http://arxiv.org/abs/2607.07313v1
• Date: Wed, 08 Jul 2026 11:54:59 GMT
• Title: POO-LPSP: Parallel Osprey Optimized Least Penalty-Squared Prioritization Methods for Priority Derivation in the Analytic Hierarchy Process
• Abstract summary: This study develops the revised Least Penalty-Squared Prioritization (LPSP) optimization models.<n>By integrating an improved bio-inspired metaheuristic Parallel Osprey Optimization Algorithm (POOA), this framework efficiently solves complex LPSP models.<n>The practical utility and computational efficiency of the POO-LPSP method are validated through a Generative AI (GAI) vendor selection problem.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• p-PSO: A Penalized Particle Swarm Optimization Technique for Finding D-Optimal Designs with Mixed Factors in Generalized Linear Models [0.0]
  We introduce a new, general-purpose penalty formulation for constrained optimization, named $p$-PSO.<n>Results show that the method is highly efficient, with its primary contribution being a penalty formulation that enables the direct use of an off-the-shelf PSO algorithm.
  arXiv  Detail & Related papers  (2026-06-14T18:43:29Z)
• Sequential Bayesian Optimal Experimental Design in Infinite Dimensions via Policy Gradient Reinforcement Learning [3.2580743227673694]
  High-fidelity approaches require repeated forward and adjoint PDE solves inside nested Bayesian inversion and design loops.<n>We formulate SBOED as a finite-horizon Markov decision process and learn an amortized design policy via policy-gradient reinforcement learning.<n> Numerical experiments on sequential multi-sensor placement for contaminant source tracking demonstrate approximately $100times$ speedup over high-fidelity finite element methods.
  arXiv  Detail & Related papers  (2026-01-09T15:44:49Z)
• Multi-Objective Reward and Preference Optimization: Theory and Algorithms [3.316593788543852]
  This thesis develops theoretical frameworks and algorithms that advance constrained reinforcement learning (RL) across control, preference learning, and alignment of large language models.<n>ACPO, e-COP, warmPref-PS, PSPL, and MOPO advance RL across average-cost, episodic, and preference-driven paradigms.<n> Collectively, the thesis unifies RL across average-cost, episodic, and preference-driven paradigms, delivering theoretical advances and practical tools for safe and aligned decision-making.
  arXiv  Detail & Related papers  (2025-12-11T12:51:21Z)
• Provably Mitigating Overoptimization in RLHF: Your SFT Loss is Implicitly an Adversarial Regularizer [52.09480867526656]
  We identify the source of misalignment as a form of distributional shift and uncertainty in learning human preferences.<n>To mitigate overoptimization, we first propose a theoretical algorithm that chooses the best policy for an adversarially chosen reward model.<n>Using the equivalence between reward models and the corresponding optimal policy, the algorithm features a simple objective that combines a preference optimization loss and a supervised learning loss.
  arXiv  Detail & Related papers  (2024-05-26T05:38:50Z)
• Provably Efficient UCB-type Algorithms For Learning Predictive State Representations [55.00359893021461]
  The sequential decision-making problem is statistically learnable if it admits a low-rank structure modeled by predictive state representations (PSRs) This paper proposes the first known UCB-type approach for PSRs, featuring a novel bonus term that upper bounds the total variation distance between the estimated and true models. In contrast to existing approaches for PSRs, our UCB-type algorithms enjoy computational tractability, last-iterate guaranteed near-optimal policy, and guaranteed model accuracy.
  arXiv  Detail & Related papers  (2023-07-01T18:35:21Z)
• Regularization and Variance-Weighted Regression Achieves Minimax Optimality in Linear MDPs: Theory and Practice [79.48432795639403]
  Mirror descent value iteration (MDVI) is an abstraction of Kullback-Leibler (KL) and entropy-regularized reinforcement learning (RL) We study MDVI with linear function approximation through its sample complexity required to identify an $varepsilon$-optimal policy. We present Variance-Weighted Least-Squares MDVI, the first theoretical algorithm that achieves nearly minimax optimal sample complexity for infinite-horizon linear MDPs.
  arXiv  Detail & Related papers  (2023-05-22T16:13:05Z)
• BALPA: A Balanced Primal-Dual Algorithm for Nonsmooth Optimization with Application to Distributed Optimization [39.67743321086165]
  We propose a novel primal-dual proximal splitting algorithm (PD-PSA) for the composite optimization problem with equality constraints. In BALPA, the dual update is designed as a proximal point for a time-varying quadratic function, which balances the implementation of primal and dual update. We propose a version of BALPA (S-BALPA) and apply the developed BALPA to devise a new distributed optimization algorithm.
  arXiv  Detail & Related papers  (2022-12-06T09:18:31Z)
• Asymptotically Unbiased Instance-wise Regularized Partial AUC Optimization: Theory and Algorithm [101.44676036551537]
  One-way Partial AUC (OPAUC) and Two-way Partial AUC (TPAUC) measures the average performance of a binary classifier. Most of the existing methods could only optimize PAUC approximately, leading to inevitable biases that are not controllable. We present a simpler reformulation of the PAUC problem via distributional robust optimization AUC.
  arXiv  Detail & Related papers  (2022-10-08T08:26:22Z)
• Outlier-Robust Sparse Estimation via Non-Convex Optimization [73.18654719887205]
  We explore the connection between high-dimensional statistics and non-robust optimization in the presence of sparsity constraints. We develop novel and simple optimization formulations for these problems. As a corollary, we obtain that any first-order method that efficiently converges to station yields an efficient algorithm for these tasks.
  arXiv  Detail & Related papers  (2021-09-23T17:38:24Z)
• Successive Convex Approximation Based Off-Policy Optimization for Constrained Reinforcement Learning [12.523496806744946]
  We propose a convex approximation based off-policy optimization (SCAOPO) algorithm to solve the general constrained reinforcement learning problem. In spite of the time-varying state distribution and the bias incurred by the off-policy learning, the SCAOPO with a feasible initial point can still provably converge to a Karush-Kuhn-Tucker point.
  arXiv  Detail & Related papers  (2021-05-26T13:52:39Z)
• Logistic Q-Learning [87.00813469969167]
  We propose a new reinforcement learning algorithm derived from a regularized linear-programming formulation of optimal control in MDPs. The main feature of our algorithm is a convex loss function for policy evaluation that serves as a theoretically sound alternative to the widely used squared Bellman error.
  arXiv  Detail & Related papers  (2020-10-21T17:14:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.