Technology Category
Reasoning under Uncertainty: Stochastic OptimizationPlanning, Routing, and Scheduling: Planning under UncertaintyConstraint Satisfaction and Optimization: Distributed CSP/Optimization
Solving the Constrained Random Disambiguation Path Problem via Lagrangian Relaxation and Graph Reduction
🤖 AI Summary
This paper addresses the resource-constrained Stochastic Obstacle Disambiguation Path Planning (RDP) problem—an extension of the Stochastic Obstacle Sensing (SOS) problem—where agents must jointly decide *when* to disambiguate probabilistic obstacles and *how* to plan paths under a global disambiguation budget in uncertain environments. We propose COLOGR, a novel algorithmic framework that integrates Lagrangian relaxation with a two-stage vertex elimination scheme to achieve efficient pruning with zero duality gap. Furthermore, we introduce a risk-aware edge cost model that unifies probabilistic obstacle blocking probabilities and traversal penalties. Experiments demonstrate that COLOGR significantly outperforms greedy baselines across diverse scenarios involving varying obstacle density, sensor accuracy, and risk preferences, closely approximating offline optimal solutions while reducing computational complexity by an order of magnitude.
Technology Category
Application Category
📝 Abstract
We study a resource-constrained variant of the Random Disambiguation Path (RDP) problem, a generalization of the Stochastic Obstacle Scene (SOS) problem, in which a navigating agent must reach a target in a spatial environment populated with uncertain obstacles. Each ambiguous obstacle may be disambiguated at a (possibly) heterogeneous resource cost, subject to a global disambiguation budget. We formulate this constrained planning problem as a Weight-Constrained Shortest Path Problem (WCSPP) with risk-adjusted edge costs that incorporate probabilistic blockage and traversal penalties. To solve it, we propose a novel algorithmic framework-COLOGR-combining Lagrangian relaxation with a two-phase vertex elimination (TPVE) procedure. The method prunes infeasible and suboptimal paths while provably preserving the optimal solution, and leverages dual bounds to guide efficient search. We establish correctness, feasibility guarantees, and surrogate optimality under mild assumptions. Our analysis also demonstrates that COLOGR frequently achieves zero duality gap and offers improved computational complexity over prior constrained path-planning methods. Extensive simulation experiments validate the algorithm's robustness across varying obstacle densities, sensor accuracies, and risk models, consistently outperforming greedy baselines and approaching offline-optimal benchmarks. The proposed framework is broadly applicable to stochastic network design, mobility planning, and constrained decision-making under uncertainty.
Problem
Research questions and friction points this paper is trying to address.
Resource-constrained path planning with uncertain obstacles
Optimizing disambiguation costs under a global budget
Risk-adjusted shortest path with probabilistic blockage penalties
Innovation
Methods, ideas, or system contributions that make the work stand out.
Lagrangian relaxation for constrained path planning
Two-phase vertex elimination for optimal pruning
Risk-adjusted edge costs in WCSPP formulation
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