Step decision rules for multistage stochastic programming: A heuristic approach

Thénie, Julien; Vial, Jean–Philippe

doi:10.1016/j.automatica.2008.02.001

Cited by 16 publications

(10 citation statements)

References 26 publications

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“…Research methods of dynamic decision-making problems can be divided into normative and descriptive research. In normative research, references [44] and [11] aimed at seeking the optimal decision by theoretical methods, and its achievements presented the optimal stop time of dynamic decision-making and income of optimal decision. References [6], [5], [46] et.al , applied dynamic programming to study solution and application of multi-stage dynamic decision-making from uncertain angle.…”

Section: Chun-xiang Guo Guo Qiang Jin Mao-zhu and Zhihan LVmentioning

confidence: 99%

Dynamic systems based on preference graph and distance

Guo¹,

Guo²,

Jin³

et al. 2015

Discrete &Amp; Continuous Dynamical Systems - S

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A group decision-making approach fusing preference conflicts and compatibility measure is proposed , focused on dynamic group decision making with preference information of policymakers at each time describing with dynamic preference Hasse diagram with the identification framework of relation between alternative pairs is H={ , , , , ≈, ≺, φ}, and the preference graph may contain incomplete decision making alternatives. First, the relationship between preference sequences is be defined on the basis of concepts about preference, preference sequence and preference graph; and defining the decision function that can reflect dynamic preference, such as conflict ,comply support and preference distance measure. Finally, through the perspective of conflict and compatible aggregating the comprehensive preference of each decision makers in each period, and by establishing the optimization model based on lattice preference distance measure to assemble group preference, gives the specific steps of the decision making. The feasibility and effectiveness of the approach proposed in this paper are illustrated with a numerical example.

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Section: Chun-xiang Guo Guo Qiang Jin Mao-zhu and Zhihan LVmentioning

confidence: 99%

Dynamic systems based on preference graph and distance

Guo¹,

Guo²,

Jin³

et al. 2015

Discrete &Amp; Continuous Dynamical Systems - S

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“…The need for generalizing decisions on a subset of scenarios to an admissible policy is well recognized in the stochastic programming literature [11]. Some authors addressing this question propose to assign to a new scenario the decisions associated to the nearest scenario of the approximate solution [20,21], thus essentially reducing the generalization problem to the one of defining a priori a measurable similarity metric in the scenario space (we note that [21] also proposes several variants for a projection step restoring the feasibility of the decisions). Put in perspective of the present framework, this amounts to adopt, without model selection, the nearest neighbor approach to regression [22] -arguably one of the most unstable prediction algorithm [17].…”

Section: Related Workmentioning

confidence: 99%

Bounds for Multistage Stochastic Programs Using Supervised Learning Strategies

Defourny

Ernst

Wehenkel

2009

Stochastic Algorithms: Foundations and Applications

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We propose a generic method for obtaining quickly good upper bounds on the minimal value of a multistage stochastic program. The method is based on the simulation of a feasible decision policy, synthesized by a strategy relying on any scenario tree approximation from stochastic programming and on supervised learning techniques from machine learning. 1 Context Let Ω denote a measurable space equipped with a sigma algebra B of subsets of Ω, defined as follows. For t = 0, 1,. .. , T − 1, we let ξ t be a random variable valued in a subset of an Euclidian space Ξ t , and let B t denote the sigma algebra generated by the collection of random variables ξ [0: t−1] def = {ξ 0 ,. .. , ξ t−1 }, with B 0 = {∅, Ω} corresponding to the trivial sigma algebra. Then we set B T −1 = B. Note that B 0 ⊂ B 1 ⊂ • • • ⊂ B T −1 form a filtration; without loss of generality, we can assume that the inclusions are proper-that is, ξ t cannot be reduced to a function of ξ [0: t−1]. Let π t : Ξ → U t denote a B t-measurable mapping from the product space Ξ = Ξ 0 × • • • × Ξ T −1 to an Euclidian space U t , and let Π t denote the class of such mappings. Of course Π 0 is a class of real-valued constant functions. We equip the measurable space (Ω, B) with the probability measure P and consider the following optimization program, which is a multistage stochastic program put in abstract form: S : min π∈Π E {f (ξ, π(ξ))} subject to π t (ξ) ∈ U t (ξ) almost surely. (1) Here ξ denotes the random vector [ξ 0. .. ξ T −1 ] valued in Ξ, and π is the mapping from Ξ to the product space U = U 0 × • • • × U T −1 defined by π(ξ) = [π 0 (ξ). .. π T −1 (ξ)] with π t ∈ Π t. We call such π an implementable policy and let Π denote the class of implementable policies. The function f : Ξ × U → R ∪ {±∞} is B-measurable and such that f (•, ξ) is convex for each ξ. It can be interpreted as a multi-period cost function. The sets U t (ξ) are defined as B t-measurable closed convex subsets of U t. A set U t (ξ) may implicitly depend on π 0 (ξ),. .. , π t−1 (ξ) viewed as B t-measurable

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“…Although climate change might be one of the biggest challenges of forest management, it has received little attention in forest harvest planning in part because stochastic programs, especially multistage stochastic programs, are considered one of the most challenging classes of optimization problems to solve [5,23,40,45]. For instance, the number of scenarios in [2] was limited to 32 although climate scientists forecast at least four climate pathways [31] which may translate into hundreds of possible forest growths.…”

Section: Introductionmentioning

confidence: 99%

A Parallelized Variable Fixing Process for Solving Multistage Stochastic Programs with Progressive Hedging

Bagaram

Tóth

Jaross³

et al. 2020

Advances in Operations Research

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Long time horizons, typical of forest management, make planning more difficult due to added exposure to climate uncertainty. Current methods for stochastic programming limit the incorporation of climate uncertainty in forest management planning. To account for climate uncertainty in forest harvest scheduling, we discretize the potential distribution of forest growth under different climate scenarios and solve the resulting stochastic mixed integer program. Increasing the number of scenarios allows for a better approximation of the entire probability space of future forest growth but at a computational expense. To address this shortcoming, we propose a new heuristic algorithm designed to work well with multistage stochastic harvest-scheduling problems. Starting from the root-node of the scenario tree that represents the discretized probability space, our progressive hedging algorithm sequentially fixes the values of decision variables associated with scenarios that share the same path up to a given node. Once all variables from a node are fixed, the problem can be decomposed into subproblems that can be solved independently. We tested the algorithm performance on six forests considering different numbers of scenarios. The results showed that our algorithm performed well when the number of scenarios was large.

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Step decision rules for multistage stochastic programming: A heuristic approach

Cited by 16 publications

References 26 publications

Dynamic systems based on preference graph and distance

Dynamic systems based on preference graph and distance

Bounds for Multistage Stochastic Programs Using Supervised Learning Strategies

A Parallelized Variable Fixing Process for Solving Multistage Stochastic Programs with Progressive Hedging

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