A Two-Stage Reactive Auction Framework for the Multi-Depot Rural Postman Problem with Dynamic Vehicle Failures

TL;DR

This study tackles the MD-RPP-RRV under stochastic vehicle failures, a dynamic, NP-hard arc-routing problem with multiple depots and battery constraints. It introduces a two-stage reactive framework that first applies a fast Centralized Auction to reallocate failed trips, then refines the plan with a Peer Auction and a Magnetic Field Router for local schedule repair, all while providing a worst-case additive bound on rescheduling penalty. The approach achieves dramatic runtime reductions (over 95%) and maintains high-quality solutions across 257 failure scenarios, often outperforming reactive Simulated Annealing while scaling to large networks. These results support real-time mission continuity in autonomous fleets by balancing speed and solution quality through principled auction-based reallocation and localized optimization.

Abstract

Although unmanned vehicle fleets offer efficiency in transportation, logistics and inspection, their susceptibility to failures poses a significant challenge to mission continuity. We study the Multi-Depot Rural Postman Problem with Rechargeable and Reusable Vehicles (MD-RPP-RRV) with vehicle failures, where unmanned rechargeable vehicles placed at multiple depots with capacity constraints may fail while serving arc-based demands. To address unexpected vehicle breakdowns during operation, we propose a two-stage real-time rescheduling framework. First, a centralized auction quickly generates a feasible rescheduling solution; for this stage, we derive a theoretical additive bound that establishes an analytical guarantee on the worst-case rescheduling penalty. Second, a peer auction refines this baseline through a problem-specific magnetic field router for local schedule repair, utilizing parameters calibrated via sensitivity analysis to ensure controlled computational growth. We benchmark this approach against a simulated annealing metaheuristic to evaluate solution quality and execution speed. Experimental results on 257 diverse failure scenarios demonstrate that the framework achieves an average runtime reduction of over 95\% relative to the metaheuristic baseline, cutting rescheduling times from hours to seconds while maintaining high solution quality. The two-stage framework excels on large-scale instances, surpassing the centralized auction in nearly 80\% of scenarios with an average solution improvement exceeding 12\%. Moreover, it outperforms the simulated annealing mean and best results in 59\% and 28\% of scenarios, respectively, offering the robust speed-quality trade-off required for real-time mission continuity.

Figures (17)

• Figure 1: (a) Initial two-vehicle plan, (b) dynamic failure of $V_2$ on a required edge, and (c) rescheduled $V_1$ route covering the unserved required edge.
• Figure 2: Flowchart of the proposed reactive framework. The process begins with failure detection and task filtering, followed by a rapid Centralized Auction for feasibility and a Peer Auction refinement phase for solution quality.
• Figure 3: MD-RPP-RRV Candidate Search procedure: (a) Initial setup. (b) First search iteration with small radius yields no results. (c) Second iteration with expanded radius identifies Vehicle 1 as a candidate.
• Figure 4: Example of Trip Insertion: (a) Initial routes of $V_1$ and $V_2$. (b) $V_2$'s failed trip is inserted into $V_1$'s route at depot $d_2$, creating a valid sub-tour.
• Figure 5: Step-by-step construction of a single trip by the Magnetic Field Router. (a) Instance topology showing depots (red) and required edges (blue). (b) The resulting trip path. Note the vehicle visits depot 1 mid-trip but continues to service edges 5-4. (c) Evolution of the decision forces. The vehicle continues servicing edges as long as the Required Edge Attraction (blue) dominates. The trip terminates only when the Depot Attraction (red) overtakes the edge attraction due to depleting capacity.