- The paper proposes an approximation algorithm and construction/improvement heuristics to solve the NP-Hard Fuel Constrained UAV Routing Problem (FCURP).
- Computational results show the proposed algorithms efficiently find solutions with only a 1.4% average deviation from optimal, outperforming MILP in speed.
- This research provides practical techniques for routing fuel-limited UAVs, enabling high-quality mission planning in complex environments with depots.
UAV Routing with Fuel Constraints: An Approximation Algorithm and Heuristic Approach
The paper "Algorithms for Routing an Unmanned Aerial Vehicle in the presence of Refueling Depots" by Kaarthik Sundar and Sivakumar Rathinam addresses a challenging optimization problem in the domain of unmanned aerial vehicle (UAV) path planning. The research focuses on devising efficient algorithms for routing a UAV with fuel constraints among multiple targets and depots. This specific problem, known as the Fuel Constrained UAV Routing Problem (FCURP), poses significant computational challenges due to its resemblance to the asymmetric traveling salesman problem (ATSP), which is NP-Hard.
In exploring FCURP, the authors propose an approximation algorithm, alongside construction and improvement heuristics, to tackle the task of finding a minimum-cost path that respects fuel constraints and ensures all targets are visited. The primary algorithmic focus is on developing a feasible tour that minimizes the total fuel consumed, considering UAVs with limited operational range. To achieve this, the research introduces a novel approximation algorithm with performance guarantees.
The authors detail a multi-step approach for their approximation algorithm. Initially, they determine feasible paths between targets that respect fuel constraints through both direct and indirect routing strategies. These paths form a basis for constructing a tour using a cycle cover approach that ensures all targets are visited at least once. The resulting tour is refined further to meet all fuel constraints using a greedy strategy that introduces necessary depot visits.
For additional refinement, the paper presents a construction heuristic that leverages the Lin-Kernighan-Helgaun (LKH) heuristic in place of the covering algorithm used in the approximation. Furthermore, an improvement heuristic is proposed that employs a combination of k-opt heuristics and depot-exchange strategies to iteratively enhance the tour's quality, emphasizing the local search around refueling depots for optimization.
The theoretical findings are supported by computational results wherein the algorithms are tested on randomly generated problem instances with up to 25 targets and multiple refueling depots. The proposed algorithms efficiently yield solutions that, on average, deviate only by 1.4% from the optimal. The approximation algorithm exhibits efficient computation times compared to the mixed-integer linear programming (MILP) approach, solved by CPLEX, which demonstrates the feasibility and practicality of the heuristics for real-time applications.
In conclusion, this research makes significant contributions towards solving UAV routing problems with fuel constraints by combining approximation algorithms and heuristic methods. The results suggest that the proposed techniques can efficiently handle the computational complexity of FCURP while producing high-quality solutions. Future work is indicated towards adapting these strategies to broader applications, such as incorporating heterogeneous fleets of UAVs or extending the methodology to multi-vehicle scenarios, potentially incorporating coordination schemes and dynamic environments.