Anytime Metaheuristic Framework for Global Route Optimization in Expected-Time Mobile Search

TL;DR

This work tackles global route optimization for Expected-Time Mobile Search (ETS) in static continuous 2D environments by reframing ETS as a Minimum Latency Problem on a fixed graph. A decoupling scheme reduces ETS to a discrete sensing problem (D-ETS), which Milaps then solves via a graph-search with turning (GSPT) formulation using an anytime Ms-GVNS metaheuristic; multiple static weight schemes and a replanning option are explored to approximate dynamic detection probabilities. The authors introduce disjoint weight-defining regions to better capture spatial probability mass, and present Milaps with several variants (DisSplit, DisMaxW, DisGreedy, with or without replanning) that substantially outperform utility-greedy baselines on a new large-scale 240-instance D-ETS dataset. Quantitative results show Milaps-DisGreedy achieves near-perfect solutions with significant runtime efficiency, while qualitative studies demonstrate framework flexibility under varying footprint radii, turning costs, and object distributions. The work advances scalable ETS optimization and sets the stage for online/adaptive, multi-agent extensions and fully coupled guard-generation and route-planning approaches.

Abstract

Expected-time mobile search (ETS) is a fundamental robotics task where a mobile sensor navigates an environment to minimize the expected time required to locate a hidden object. Global route optimization for ETS in static 2D continuous environments remains largely underexplored due to the intractability of objective evaluation, stemming from the continuous nature of the environment and the interplay of motion and visibility constraints. Prior work has addressed this through partial discretization, leading to discrete-sensing formulations tackled via utility-greedy heuristics. Others have taken an indirect approach by heuristically approximating the objective using minimum latency problems on fixed graphs, enabling global route optimization via efficient metaheuristics. This paper builds on and significantly extends the latter by introducing Milaps (Minimum latency problems), a model-based solution framework for ETS. Milaps integrates novel auxiliary objectives and adapts a recent anytime metaheuristic for the traveling deliveryman problem, chosen for its strong performance under tight runtime constraints. Evaluations on a novel large-scale dataset demonstrate superior trade-offs between solution quality and runtime compared to state-of-the-art baselines. The best-performing strategy rapidly generates a preliminary solution, assigns static weights to sensing configurations, and optimizes global costs metaheuristically. Additionally, a qualitative study highlights the framework's flexibility across diverse scenarios.

Figures (11)

• Figure 1: Motivating example of a search scenario.
• Figure 2: Illustrations of the tractable ETS objective.
• Figure 3: Illustration of the complete GSPT graph $\mathbb{G}$ (\ref{['fig:graph']}) and the five types of node weights (\ref{['fig:w1']}--\ref{['fig:w5']}). All weights, except Const (\ref{['fig:w1']}), are computed using the visibility model and have associated weight-defining regions, depicted in (\ref{['fig:w2']}--\ref{['fig:w5']}). The weights DisGreedy are determined based on the utility-greedy solution to D-ETS, as additionally illustrated in (\ref{['fig:w5']}).
• Figure 4: Dataset metrics overview (\ref{['fig:dataset-overview']}) and example instances (\ref{['fig:inst00-11']}--\ref{['fig:inst15-13']}) showing the map, all guards, and 10% of visibility regions. Captions use the format SubsetID-InstanceID: $n_G$, $o_G$.
• Figure 5: D-ETS results for subsets 6, 3, and 15.