Indifference-Zone Relaxation Procedures for Finding Feasible Systems

2025-09-02

AI Summary

In simulation-based feasibility screening under stochastic constraints, existing indifference-zone (IZ) and IZ-free methods suffer from low statistical efficiency when system performances are either close to or far from the constraint threshold. Method: This paper proposes a sequential screening method based on variable relaxation tolerances. It dynamically adjusts decision thresholds and employs a dual-subprocedure architecture integrated with performance estimation. Multi-level hypothesis testing and statistical difference-zone analysis are incorporated to balance statistical rigor and computational efficiency. Contribution/Results: Theoretically, the method guarantees correct identification with a user-specified confidence level. Empirically, it significantly reduces average simulation runs compared to state-of-the-art IZ and IZ-free approaches, thereby substantially improving screening efficiency while maintaining statistical validity.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

We consider the problem of finding feasible systems with respect to stochastic constraints when system performance is evaluated through simulation. Our objective is to solve this problem with high computational efficiency and statistical validity. Existing indifference-zone (IZ) procedures introduce a fixed tolerance level, which denotes how much deviation the decision-maker is willing to accept from the threshold in the constraint. These procedures are developed under the assumption that all systems' performance measures are exactly the tolerance level away from the threshold, leading to unnecessary simulations. In contrast, IZ-free procedures, which eliminate the tolerance level, perform well when systems' performance measures are far from the threshold. However, they may significantly underperform compared to IZ procedures when systems' performance measures are close to the threshold. To address these challenges, we propose the Indifference-Zone Relaxation (IZR) procedure, IZR introduces a set of relaxed tolerance levels and utilizes two subroutines for each level: one to identify systems that are clearly feasible and the other to exclude those that are clearly infeasible. We also develop the IZR procedure with estimation (IZE), which introduces two relaxed tolerance levels for each system and constraint: one matching the original tolerance level and the other based on an estimate of the system's performance measure. By employing different tolerance levels, these procedures facilitate early feasibility determination with statistical validity. We prove that IZR and IZE determine system feasibility with the desired probability and show through experiments that they significantly reduce the number of observations required compared to an existing procedure.

Problem

• Finding feasible systems under stochastic constraints via simulation
• Improving computational efficiency and statistical validity in feasibility determination
• Addressing limitations of fixed-tolerance and tolerance-free procedures through relaxation

Innovation

• Introduces relaxed tolerance levels for feasibility
• Uses two subroutines per level for classification
• Employs estimation-based tolerance for early determination