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Stochastic optimization of maintenance scheduling : blackbox methods, decomposition approaches - Theoretical and numerical aspects

Abstract : The aim of the thesis is to develop algorithms for optimal maintenance scheduling. We focus on the specific case of large systems that consist of several components linked by a common stock of spare parts. The numerical experiments are carried out on systems of components from a single hydroelectric power plant.The first part is devoted to blackbox methods which are commonly used in maintenance scheduling. We focus on a kriging-based algorithm, Efficient Global Optimization (EGO), and on a direct search method, Mesh Adaptive Direct Search (MADS). We present a theoretical and practical review of the algorithms as well as some improvements for the implementation of EGO. MADS and EGO are compared on an academic benchmark and on small industrial maintenance problems, showing the superiority of MADS but also the limitation of the blackbox approach when tackling large-scale problems.In a second part, we want to take into account the fact that the system is composed of several components linked by a common stock in order to address large-scale maintenance optimization problems. For that purpose, we develop a model of the dynamics of the studied system and formulate an explicit stochastic optimal control problem. We set up a scheme of decomposition by prediction, based on the Auxiliary Problem Principle (APP), that turns the resolution of the large-scale problem into the iterative resolution of a sequence of subproblems of smaller size. The decomposition is first applied on synthetic test cases where it proves to be very efficient. For the industrial case, a "relaxation" of the system is needed and developed to apply the decomposition methodology. In the numerical experiments, we solve a Sample Average Approximation (SAA) of the problem and show that the decomposition leads to substantial gains over the reference algorithm.As we use a SAA method, we have considered the APP in a deterministic setting. In the third part, we study the APP in the stochastic approximation framework in a Banach space. We prove the measurability of the iterates of the algorithm, extend convergence results from Hilbert spaces to Banach spaces and give efficiency estimates
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Submitted on : Tuesday, May 11, 2021 - 5:02:54 PM
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Thomas Bittar. Stochastic optimization of maintenance scheduling : blackbox methods, decomposition approaches - Theoretical and numerical aspects. Optimization and Control [math.OC]. École des Ponts ParisTech, 2021. English. ⟨NNT : 2021ENPC2004⟩. ⟨tel-03224451⟩

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