A Dynamic Programming Approach to Evader Pathfinding in Static Pursuit Scenarios

TL;DR

The paper tackles evader pathfinding under a static defender deployment by reframing the problem as a risk-weighted shortest path. It introduces DPERO, which converts the multiplicative survival objective $S(P)=\prod_{v\in P}(1-p_c(v))$ into an additive cost using $w(v)=-\log(1-p_c(v))$ and solves the resulting problem with value-iteration-based dynamic programming. Key contributions include a formal static pursuit-evasion formulation, the DPERO algorithm, and experimental evidence showing superior evader survival compared to a naive shortest-path baseline, especially as defender density grows. This work provides a computationally tractable tool for vulnerability analysis and strategic planning in security-sensitive urban networks, with extensions to stochastic timing and multi-objective trade-offs to be explored in future work.

Abstract

The interdiction of escaping adversaries in urban networks is a critical security challenge. State-of-the-art game-theoretic models, such as the Escape Interdiction Game (EIG), provide comprehensive frameworks but assume a highly dynamic interaction and entail significant computational complexity, which can be prohibitive for real-time applications. This paper investigates a crucial sub-problem: an evader's optimal pathfinding calculus when faced with a static or pre-determined defender deployment. We propose the Dynamic Programming for Evader Route Optimization (DPERO) algorithm, which models the environment as a graph with probabilistic risks at various nodes. By transforming the multiplicative survival objective into an additive cost function using logarithms, we frame the task as a shortest path problem solvable with value iteration. This approach allows for the efficient computation of a path that optimally balances safety and distance. Experimental results on simulated grid networks demonstrate that DPERO identifies routes with significantly higher survival probabilities compared to naive shortest-path baselines, validating its efficacy as a practical tool for vulnerability analysis and strategic planning.