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.
(2013) considered an exact formulation of CT6 constraints, in a CG approach dualizing coupling constraints among units @cite_6 , i.e. CT1 demands and CT14 to CT21 scheduling constraints. The MIP considered a unique scenario, the average one, with production time steps aggregated weekly. The CG approach is deployed to compute a LP relaxation relaxing scheduling constraints CT14-CT21, with subproblems solved by dynamic programming. The further CG heuristic incorporate these scheduling constraints in the integer resolution with the columns generated. The solution of this MIP gives the outage dates and week where the CT6 constraints are activated, the final cost and feasibility issues for the whole problem are given computing the production by Linear Programming (LP). This approach was one of the most effective for the challenge, up to $2
@cite_6
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This paper presents a heuristic method based on column generation for the EDF (Electricite De France) long-term electricity production planning problem proposed as subject of the ROADEF EURO 2010 Challenge. This is to our knowledge the first-ranked method among those methods based on mathematical programming, and was ranked fourth overall. The problem consists in determining a production plan over the whole time horizon for each thermal power plant of the French electricity company, and for nuclear plants, a schedule of plant outages which are necessary for refueling and maintenance operations. The average cost of the overall outage and production planning, computed over a set of demand scenarios, is to be minimized. The method proceeds in two stages. In the first stage, dates for outages are fixed once for all for each nuclear plant. Data are aggregated with a single average scenario and reduced time steps, and a set-partitioning reformulation of this aggregated problem is solved for fixing outage dates with a heuristic based on column generation. The pricing problem associated with each nuclear plant is a shortest path problem in an appropriately constructed graph. In the second stage, the reload level is determined at each date of an outage, considering now all scenarios. Finally, the production quantities between two outages are optimized for each plant and each scenario by solving independent linear programming problems.