Academic literature on the topic 'Programmation stochastique multi-étapes prudente'
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Dissertations / Theses on the topic "Programmation stochastique multi-étapes prudente"
Quezada, Valenzuela Franco. "Cutting planes generation and decomposition-based approaches for solving multi-stage stochastic lot-sizing problems." Electronic Thesis or Diss., Sorbonne université, 2021. http://www.theses.fr/2021SORUS574.
Full textThe main purpose of the work presented here is to develop mathematical models and algorithms that may enable industrial managers to efficiently plan production activities for complex remanufacturing production systems under uncertainty. In order to achieve this, we consider a remanufacturing system involving three processing echelons: disassembly, refurbishing and reasembly. We investigate the problem of planning remanufacturing activities in this system over a finite and discrete-time planning horizon when there are uncertainties on the quantity and quality of returned products, on the customers' demand, and on the various production costs. We propose to model this stochastic combinatorial optimization problem as a multi-stage stochastic integer program and to use a scenario tree to represent the evolution of the stochastic input process over time. We first focus on enhancing the performance of the generic branch-and-cut algorithms embedded in mathematical programming solvers through the use of cutting plane generation approaches. Second, in order to solve larger instances of our problem, we investigate a second kind of solution approach based on a decomposition of the original problem into a series of small sub-problems linked together by dynamic programming equations. Finally, we present an on-going exploratory work on risk-averse multi-stage stochastic lot-sizing. We thus study several ways of incorporating risk aversion in the multi-stage stochastic uncapacitated lot-sizing (SULS) problem and show how the risk-averse SULS can be reformulated as a mixed-integer linear program in each case
Tran, Duy-Nghi. "Programmation dynamique tropicale en optimisation stochastique multi-étapes." Thesis, Paris Est, 2020. http://www.theses.fr/2020PESC1040.
Full textIn this thesis, we are interested in the resolution by dynamic programming of Multistage Stochastic optimization Problems (MSP).In the first part, we are interested in the approximation of the value functions of a MSP as min-plus or max-plus linear combinations of basic functions. This approach can be interpreted as the tropical algebra analogue of Approximate Dynamic Programming parametric models, notably studied by Bertsekas and Powell.In the simplified framework of multistage deterministic optimisation problems, we introduce an algorithm, called Tropical Dynamic Programming (TDP), which iteratively constructs approximations of value functions as min-plus or max-plus linear combinations. At each iteration, a trajectory of states is randomly drawn and the states forming this trajectory are called trial points. Based on the current approximations of the value functions, TDP then recursively calculates, by going back in time, a new basic function to be added to the current linear min-plus or max-plus combination. The basic function added to the approximation at time t must verify two compatibility conditions: it must be tight at the t-th trial point and valid. In this way TDP avoids discretising the entire state space and tries to emancipate itself from the curse of dimensionality.Our first contribution, within the framework of deterministic multistage optimization problems, is sufficient conditions on the richness of the trial points in order to ensure almost surely the asymptotic convergence of the generated approximations to the value functions, at points of interest.In the second part, the framework of the TDP algorithm was extended to Lipschitz MSPs where the noises are finite and independent. In this framework, max-plus linear and min-plus linear approximations of the value functions are generated simultaneously. At each iteration, in a forward phase, a particular deterministic trajectory of states called the problem-child trajectory is generated. Then, in the backward phase in time, the common approximations are refined by adding basic functions that are tight and valid.Our second contribution is the proof that the difference between the max-plus and min-plus linear combinations thus generated tends towards 0 along the problem-child trajectories. This result generalises a result from Baucke, Downward and Zackeri in 2018 who proved the convergence of a similar scheme, introduced by Philpott, de Matos and Zackeri in 2013, for convex MSPs. However, the algorithmic complexity of the TDP extension presented is highly dependent on the size of the noise support of a given MSP.In the third part, we are interested in quantifying the difference between the values of two MSPs differing only in their scenario tree. Under assumptions of regularities, Pflug and Pichler showed in 2012 that the value of such MSPs is Lipschitz-continuous with respect to the Nested Distance they introduced. However, the computation of the Nested Distance requires an exponential number (w.r.t. the horizon T) of computation of optimal transport problems.Motivated by the success of Sinkhorn's algorithm for computing entropic relaxation of the optimal transport problem, as a third contribution we propose an entropic relaxation of the Nested Distance which we illustrate numerically.Finally, in order to justify the resolution by dynamic programming in more general cases of MSPs, interchange between integration and minimisation must be justified. In the fourth contribution, we establish a general interchange result between integration and minimization which includes some usual results
Kolomvos, Georgios. "Résolution de grands problèmes stochastiques multi-étapes : application à un problème de dimensionnement de capacités et de gestion de flux et de stocks." Châtenay-Malabry, Ecole centrale de Paris, 2007. http://www.theses.fr/2007ECAP1044.
Full textIn a deterministic setting, data input are considered to be known. However, in real-world applications one may face problems whose parameters are partially or totally uncertain. The approach where one considers a single scenario, which is supposed to represent a mean case, shows quickly its limits. We consider working on a discretized uncertainty space spreading over several time periods; we therefore consider scenario trees and introduce the multistage models associated. Problems dimensions rise exponentially with the number of stages which renders direct solution methods inappropriate. What has motivated our work is an industrial application arising in a gas market, concerning more precisely capacity reservation in the context of a contractual agreement that has to hold over a certain time horizon. Spot prices and clients' demands are considered to be uncertain and are modeled using a scenario tree. The problem structure presents strong similarities with a wide family of problems, where variables are coupling with each other in a very characteristic manner. After a literature survey focusing on (but not limited to) solution methods for multistage models, the Nested Decomposition (ND)method has been chosen. Over very large cases, even decomposition methods show their limits; this concerns in principle convergence times. This work is mostly devoted to the development of new procedures inside the ND method in order to work with larger scenario trees in less time. Other aspects, concerning time reduction over a single iteration are also studied. Comparisons between the classic and the newly presented approaches revealed the superiority of the latter over the former
Kolomvos, Georges. "Résolution de grands problèmes stochastiques multi-étapes : Application à un problème de dimensionnement de capacités et de gestion de flux et de stocks." Phd thesis, Ecole Centrale Paris, 2007. http://tel.archives-ouvertes.fr/tel-00275775.
Full textZehtabian, Shohre. "Development of new scenario decomposition techniques for linear and nonlinear stochastic programming." Thèse, 2016. http://hdl.handle.net/1866/16182.
Full textIn the literature of optimization problems under uncertainty a common approach of dealing with two- and multi-stage problems is to use scenario analysis. To do so, the uncertainty of some data in the problem is modeled by stage specific random vectors with finite supports. Each realization is called a scenario. By using scenarios, it is possible to study smaller versions (subproblems) of the underlying problem. As a scenario decomposition technique, the progressive hedging algorithm is one of the most popular methods in multi-stage stochastic programming problems. In spite of full decomposition over scenarios, progressive hedging efficiency is greatly sensitive to some practical aspects, such as the choice of the penalty parameter and handling the quadratic term in the augmented Lagrangian objective function. For the choice of the penalty parameter, we review some of the popular methods, and design a novel adaptive strategy that aims to better follow the algorithm process. Numerical experiments on linear multistage stochastic test problems suggest that most of the existing techniques may exhibit premature convergence to a sub-optimal solution or converge to the optimal solution, but at a very slow rate. In contrast, the new strategy appears to be robust and efficient, converging to optimality in all our experiments and being the fastest in most of them. For the question of handling the quadratic term, we review some existing techniques and we suggest to replace the quadratic term with a linear one. Although this method has yet to be tested, we have the intuition that it will reduce some numerical and theoretical difficulties of progressive hedging in linear problems.