This paper deals with the long-term Military Flight and Maintenance Planning problem. In order to solve this problem efficiently, we propose a new solution approach based on a new Mixed Integer Program and the use of both valid cuts generated on the basis of initial conditions and learned cuts based on the prediction of certain characteristics of optimal or near-optimal solutions. These learned cuts are generated by training a Machine Learning model on the input data and results of 5000 instances. This approach helps to reduce the solution time with little losses in optimality and feasibility in comparison with alternative matheuristic methods. The obtained experimental results show the benefit of a new way of adding learned cuts to problems based on predicting specific characteristics of solutions.

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We present the Flight and Maintenance Planning (FMP) problem in its military variant and applied to long term planning. The problem has been previously studied for short-and medium-term horizons only. We compare its similarities and differences with previous work and prove its complexity. We generate scenarios inspired by the French Air Force fleet. We formulate an exact Mixed Integer Programming (MIP) model to solve the problem in these scenarios and we analyse the performance of the solving method under these circumstances. A heuristic was built to generate fast feasible solutions, that in some cases were shown to help warm-start the model.