Glider Routing and Trajectory Optimisation in disaster assessment

In this paper, we introduce the Glider Routing and Trajectory Optimisation Problem (GRTOP), the problem of simultaneously finding optimal routes and trajectories for a fleet of gliders with the aim of surveying a set of locations. We propose a novel Mixed-Integer Nonlinear Programming (MINLP) formulation for the GRTOP, which optimises the routes as well as the trajectories along these routes, while flight dynamics is modelled as constraints. We avoid solving a non-convex problem by linearising the gliders’ flight dynamics, converting the proposed MINLP into a Mixed-Integer Second-order Cone Programming (MISOCP) problem. To allow for a more tractable formulation, the dynamical constraints are relaxed and a penalisation is added to the objective function. Several different discretisation techniques are compared. The formulation is tested on instances inspired by risk maps of flooding-prone cities across the UK and on 180 randomly generated instances.