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.
A natural idea to solve the problem by decomposition is to follow the 2-stage structure of stochastic programming, distinguishing the high-level maintenance and refueling problem of T2 units from the lower level production problems, as in @cite_18 @cite_19 @cite_2 @cite_23 @cite_25 @cite_3 . The high-level problem fixes the maintenance dates and the refueling levels modifying slightly the current solution and respecting scheduling constraints CT7-CT11 and CT13-CT21. The previous maintenance planning of the last iteration (or the initial planning) is slightly modified in a defined neighborhood, where the feasibility of constraints CT13-CT21 can be ensured using MIP of Constraint Programming models. The low-level subproblems compute independently for all scenario the production plans optimizing the production costs and fulfilling the constraints CT1-CT6 and CT12 having fuel levels and maintenance dates fixed. Such production problems can be solved using greedy strategies following increasing production costs or using LP problems.
@cite_18 @cite_3 @cite_19 @cite_23 @cite_2 @cite_25
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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. This paper addresses a large-scale power plant maintenance scheduling and production planning problem, which has been proposed by the ROADEF EURO Challenge 2010. We develop two lower bounds for the problem: a greedy heuristic and a flow network for which a minimum cost flow problem has to be solved. Furthermore, we present a solution approach that combines a constraint programming formulation of the problem with several heuristics. The problem is decomposed into an outage scheduling and a production planning phase. The first phase is solved by a constraint program, which additionally ensures the feasibility of the remaining problem. In the second phase we utilize a greedy heuristic--developed from our greedy lower bound--to assign production levels and refueling amounts for a given outage schedule. All proposed strategies are shown to be competitive in an experimental evaluation. This paper presents a joint market structure for energy, spinning reserves and VAR support in a multiarea setting. It is based on a cooptimization that can simultaneously optimize all three commodities across the "seams". An auxiliary problem principle based decomposition scheme is applied to the overall optimization for coordinating interchanges of energy and ancillary services between control areas. The proposed decomposition approach preserves independent dispatching for neighboring areas while achieves overall optimum. Nodal prices for energy and opportunity cost payments to forgone energy profit due to providing reserves and VAR support are also addressed. We believe the algorithm is of particular interest in the restructuring electricity industry for resolving seams issues. An illustrative example of a modified IEEE 30-bus system is used to demonstrate the validity of proposed algorithm. In this article, the following stochastic vehicle routing problem is considered. Each customer has a known probability of presence and a random demand. This problem arises in several contexts, e.g., in the design of less-than-truckload collection routes. Because of uncertainty, it may not be possible to follow vehicle routes as planned. Using a stochastic programming framework, the problem is solved in two stages. In a first stage, planned collection routes are designed. In a second stage, when the set of present customers is known, these routes are followed as planned by skipping the absent customers. Whenever the vehicle capacity is attained or exceeded, the vehicle returns to the depot and resumes its collections along the planned route. This generates a penalty. The problem is to design a first stage solution in order to minimize the expected total cost of the second state solution. This is formulated as a stochastic integer program, and solved for the first time to optimality by means of an integer L-shaped method.