Optimal threshold resetting in collective diffusive search

2026-03-26

AI Summary

This work addresses the inefficiency of conventional stochastic resetting strategies, which rely on external timers and fail to align with the intrinsic dynamics of multi-agent diffusive search. The authors propose a threshold-triggered, event-driven resetting mechanism: in a one-dimensional domain, N non-interacting diffusive searchers are deployed, and a global reset is initiated whenever any searcher reaches a predefined threshold, aiming to minimize the mean first-passage time. By combining continuous diffusion modeling, first-passage time analysis, and scale-invariant threshold parametrization, the study uncovers a cooperative optimization principle between group size and threshold location. Notably, the mean first-passage time exhibits a non-monotonic dependence on N, revealing both a critical population size \(N_c(u)\) and an optimal number of searchers \(N_{\text{opt}}(u)\), thereby significantly enhancing search efficiency while remaining practically implementable.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Web Mining and Content Analysis: Content-based information diffusion
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Stochastic resetting has attracted significant attention in recent years due to its wide-ranging applications across physics, biology, and search processes. In most existing studies, however, resetting events are governed by an external timer and remain decoupled from the system's intrinsic dynamics. In a recent Letter by Biswas et al, we introduced threshold resetting (TR) as an alternative, event-driven optimization strategy for target search problems. Under TR, the entire process is reset whenever any searcher reaches a prescribed threshold, thereby coupling the resetting mechanism directly to the internal dynamics. In this work, we study TR-enabled search by $N$ non-interacting diffusive searchers in a one-dimensional box $[0,L]$, with the target at the origin and the threshold at $L$. By optimally tuning the scaled threshold distance $u = x_0/L$, the mean first-passage time can be significantly reduced for $N \geq 2$. We identify a critical population size $N_c(u)$ below which TR outperforms reset-free dynamics. Furthermore, for fixed $u$, the mean first-passage time depends non-monotonically on $N$, attaining a minimum at $N_{\mathrm{opt}}(u)$. We also quantify the achievable speed-up and analyze the operational cost of TR, revealing a nontrivial optimization landscape. These findings highlight threshold resetting as an efficient and realistic optimization mechanism for complex stochastic search processes.

Problem

• stochastic resetting
• threshold resetting
• collective search
• diffusive searchers
• first-passage time

Innovation

• threshold resetting
• collective search
• diffusive dynamics
• mean first-passage time
• stochastic optimization