Scheduling the maintenances of nuclear power plants is a complex optimization problem, formulated in 2-stage stochastic programming for the EURO ROADEF 2010 challenge. The first level optimizes the maintenance dates and refueling decisions. The second level optimizes the production to fulfill the power demands and to ensure feasibility and costs of the first stage decisions. This paper solves a deterministic version of the problem, studying Mixed Integer Programming (MIP) formulations and matheuristics. Relaxing only two sets of constraints of the ROADEF challenge, a MIP formulation can be written using only binary variables for the maintenance dates. The MIP formulations are used to design constructive matheuristics and a Variable Neighborhood Descent (VND) local search. These matheuristics produce very high quality solutions. Some intermediate results explains results of the Challenge: the relaxation of constraints CT6 are justified and neighborhood analyses with MIP-VND justifies the choice of neighborhoods to implement for the problem. Lastly, an extension with stability costs for monthly reoptimization is considered, with efficient bi-objective matheuristics.
This paper describes a Benders decomposition-based framework for solving the large scale energy management problem that was posed for the ROADEF 2010 challenge. The problem was taken from the power industry and entailed scheduling the outage dates for a set of nuclear power plants, which need to be regularly taken down for refueling and maintenance, in such a way that the expected cost of meeting the power demand in a number of potential scenarios is minimized. We show that the problem structure naturally lends itself to Benders decomposition; however, not all constraints can be included in the mixed integer programming model. We present a two phase approach that first uses Benders decomposition to solve the linear programming relaxation of a relaxed version of the problem. In the second phase, integer solutions are enumerated and a procedure is applied to make them satisfy constraints not included in the relaxed problem. To cope with the size of the formulations arising in our approach we describe efficient preprocessing techniques to reduce the problem size and show how aggregation can be applied to each of the subproblems. Computational results on the test instances show that the procedure competes well on small instances of the problem, but runs into difficulty on larger ones. Unlike heuristic approaches, however, this methodology can be used to provide lower bounds on solution quality.