Matheuristics approaches for the satellite constellation design problem

In this paper, we propose two novel matheuristic algorithms, i.e., heuristics based on mathematical formulations of the problem, in order to find a good feasible solution to the satellite constellation design problem for discontinuous coverage with a constrained revisit time. This problem consists in searching for a constellation able to periodically observe several targets at the Earth surface with the smallest number of satellites achievable. A Feasibility Pump approach is described: we specifically adapt the Feasibility Pump procedure to our design problem and we report results highlighting the benefits of this approach compared to the base Mixed Integer Nonlinear Programming (MINLP) algorithm it is derived from. Then, we propose a second matheuristic based on the discretized Mixed Integer Linear Programming (MILP) formulation of the problem, which outperforms the plain MILP formulation.