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Semidefinite Relaxations for the Scheduling Nuclear Outages Problem

We investigate semidefinite relaxations for solving a MIQP (Mixed-Integer Quadratic Program) formulation of the scheduling of nuclear power plants outages, which is extremely hard to solve with CPLEX. Based on our numerical experiments, results obtained with semidefinite relaxations improve those obtained with continuous relaxation: the gap between the optimal solution and the continuous relaxation is on average equal to 1 .80% whereas the semidefinite relaxation yields an average gap of 1 .56%. These bounds are then used to obtain a feasible solution with a randomized rounding procedure.