Compressed UAV sensing for flood monitoring by solving the continuous travelling salesman problem over hyperspectral maps

This is the final version. Available from SPIE via the DOI in this record.Remote Sensing of the Ocean, Sea Ice, Coastal Waters, and Large Water Regions 2018, 10 - 13 September 2018, Berlin, GermanyUnmanned Aerial Vehicles (UAVs) have shown great capability for disaster management due to their fast speed, automated deployment and low maintenance requirements. In recent years, disasters such as flooding are having increasingly damaging societal and environmental effects. To reduce their impact, real-time and reliable flood monitoring and prevention strategies are required. The limited battery life of small lightweight UAVs imposes efficient strategies to subsample the sensing field. This paper proposes a novel solution to maximise the number of inspected flooded cells while keeping the travelled distance bounded. Our proposal solves the so-called continuous Travelling Salesman Problem (TSP), where the costs of travelling from one cell to another depend not only on the distance, but also on the presence of water. To determine the optimal path between checkpoints, we employ the fast sweeping algorithm using a cost function defined from hyperspectral satellite maps identifying flooded regions. Preliminary results using MODIS flood maps show that our UAV planning strategy achieves a covered flooded surface approximately 4 times greater for the same travelled distance when compared to the conventional TSP solution. These results show new insights on the use of hyperspectral imagery acquired from UAVs to monitor water resourcesThis work was funded by the Royal Society of Edinburgh and National Science Foundation of China within the international project “Flood Detection and Monitoring using Hyperspectral Remote Sensing from Unmanned Aerial Vehicles” (project NNS/INT 15-16 Casaseca)

Continuous relaxations for the traveling salesman problem

In this work, we aim to explore connections between dynamical systems techniques and combinatorial optimization problems. In particular, we construct heuristic approaches for the traveling salesman problem (TSP) based on embedding the relaxed discrete optimization problem into appropriate manifolds. We explore multiple embedding techniques -- namely, the construction of new dynamical systems on the manifold of orthogonal matrices and associated Procrustes approximations of the TSP cost function. Using these dynamical systems, we analyze the local neighborhood around the optimal TSP solutions (which are equilibria) using computations to approximate the associated \emph{stable manifolds}. We find that these flows frequently converge to undesirable equilibria. However, the solutions of the dynamical systems and the associated Procrustes approximation provide an interesting biasing approach for the popular Lin--Kernighan heuristic which yields fast convergence. The Lin--Kernighan heuristic is typically based on the computation of edges that have a `high probability' of being in the shortest tour, thereby effectively pruning the search space. Our new approach, instead, relies on a natural relaxation of the combinatorial optimization problem to the manifold of orthogonal matrices and the subsequent use of this solution to bias the Lin--Kernighan heuristic. Although the initial cost of computing these edges using the Procrustes solution is higher than existing methods, we find that the Procrustes solution, when coupled with a homotopy computation, contains valuable information regarding the optimal edges. We explore the Procrustes based approach on several TSP instances and find that our approach often requires fewer $k$-opt moves than existing approaches. Broadly, we hope that this work initiates more work in the intersection of dynamical systems theory and combinatorial optimization