Benchmarking Classical Coverage Path Planning Heuristics on Irregular Hexagonal Grids for Maritime Coverage Scenarios

2026-04-16

AI Summary

This study addresses the lack of systematic and reproducible evaluation of heuristic algorithms for single-vessel coverage path planning on irregular hexagonal grids. The authors construct a benchmark dataset comprising 10,000 Hamiltonian-feasible instances representing synthetic maritime regions with compact, elongated, and irregular shapes, and uniformly evaluate the performance of 17 graph-theoretic deterministic heuristics—including multiple Warnsdorff variants—in terms of path length, number of turns, and complete coverage. For the first time on large-scale irregular hexagonal graphs, the work reveals the critical impact of implementation details such as degree-of-residue definition and endpoint reservation on algorithmic performance in sparse geometric graphs. Experiments show that the best classical approach (an improved Warnsdorff heuristic) achieves a Hamiltonian success rate of 79.0%; while incorporating shortest-path reconnection reliably enables relaxed coverage, it remains challenging to achieve zero repeated visits.

Technology Category

• Search and Optimization: Heuristic Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Coverage path planning on irregular hexagonal grids is relevant to maritime surveillance, search and rescue and environmental monitoring, yet classical methods are often compared on small ad hoc examples or on rectangular grids. This paper presents a reproducible benchmark of deterministic single-vehicle coverage path planning heuristics on irregular hexagonal graphs derived from synthetic but maritime-motivated areas of interest. The benchmark contains 10,000 Hamiltonian-feasible instances spanning compact, elongated, and irregular morphologies, 17 heuristics from seven families, and a common evaluation protocol covering Hamiltonian success, complete-coverage success, revisits, path length, heading changes, and CPU latency. Across the released dataset, heuristics with explicit shortest-path reconnection solve the relaxed coverage task reliably but almost never produce zero-revisit tours. Exact Depth-First Search confirms that every released instance is Hamiltonian-feasible. The strongest classical Hamiltonian baseline is a Warnsdorff variant that uses an index-based tie-break together with a terminal-inclusive residual-degree policy, reaching 79.0% Hamiltonian success. The dominant design choice is not tie-breaking alone, but how the residual degree is defined when the endpoint is reserved until the final move. This shows that underreported implementation details can materially affect performance on sparse geometric graphs with bottlenecks. The benchmark is intended as a controlled testbed for heuristic analysis rather than as a claim of operational optimality at fleet scale.

Problem

• coverage path planning
• irregular hexagonal grids
• benchmarking
• Hamiltonian paths
• maritime coverage

Innovation

• hexagonal grids
• coverage path planning
• Hamiltonian feasibility
• heuristic benchmarking
• residual degree