A key application of Operation Research to the energy industry is the design of production plans for electricity producers. The production plan of a unit is the sequence of production levels at which it operates. Due to technical constraints, a unit can produce only at given power levels, and there are constraints on the changes of level that can be operated : for instance, a nuclear unit cannot be launched or stopped instantaneously. A typical production plan is illustrated on Figure 1. The revenue and the costs generated by a unit both depend on its production plan. Given electricity prices, the single unit commitment problem builds a profit maximizing production plan for one unit. Electricity producers are primarily interested in solving the unit commitment problem, which aims at building the production plans of all their units in order to meet a given demand at minimum cost. Tanahan et al. mention in their recent survey on unit commitment [5] that one of the state of the art solution method for this problem is Lagrangian relaxation. This if for instance the method used at EDF [2], the main French electricity producer. The idea of the method is to relax the linking constraints between the different units in order to obtain one single unit commitment subproblem for each unit. For large producers like EDF, hundreds of single unit commitment subproblems must be solved at each iteration of the Lagrangian relaxation, and the total time needed by the method must not exceed one hour. It is therefore practically crucial to be able to solve single unit commitment problems in fractions of a second. The structure of the single unit commitment problem depends on the technology of the unit, and there is a literature specialized on hydro, nuclear, or thermal unit commitment [5]. The present contribution is the result of a partnership with EDF, whose objective was to design more efficient algorithms for EDF thermal single unit commitment problem. The standard method to solve the single unit commitment problem is dynamic programming [5]. It is the one currently in use at EDF. However, due to the curse of dimensionality, the complexity of the dynamic programming algorithm is exponential in the number of constraints
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