Scenario cluster Lagrangean decomposition for risk averse in multistage stochastic optimization

•A Multistage scenario Cluster Dualization and Lagrangean Relaxation is presented.•Time Stochastic Dominance (TSD) risk averse measure is considered.•Dualization of the NAC and Relaxation of the cross node constraints are considered.•Three Lagrangean multipliers updating procedures are presented.•A...

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Veröffentlicht in:Computers & operations research Jg. 85; S. 154 - 171
Hauptverfasser: Escudero, Laureano F., Garín, María Araceli, Unzueta, Aitziber
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Elsevier Ltd 01.09.2017
Pergamon Press Inc
Schlagworte:
Cluster Lagrangean problem
Clusters
Computing time
Decomposition
Dominance
Dynamic Constrained Cutting Plane algorithm
Economic models
Lower bounds
Multipliers
Multistage
Multistage stochastic mixed 0–1 optimization
Operations research
Probability theory
Progressive Hedging algorithm
Risk
Splitting
Subgradient method
Thresholds
Time stochastic dominance risk averse measure
Traveling salesman problem
Time stochastic dominance risk averse measure
Dynamic Constrained Cutting Plane algorithm
Multistage stochastic mixed 0–1 optimization
Cluster Lagrangean problem
Subgradient method
Progressive Hedging algorithm
ISSN:0305-0548, 1873-765X, 0305-0548
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Zusammenfassung:•A Multistage scenario Cluster Dualization and Lagrangean Relaxation is presented.•Time Stochastic Dominance (TSD) risk averse measure is considered.•Dualization of the NAC and Relaxation of the cross node constraints are considered.•Three Lagrangean multipliers updating procedures are presented.•A broad computational comparison between our algorithm and CPLEX is reported. In this work we present a decomposition approach as a mixture of dualization and Lagrangean Relaxation for obtaining strong lower bounds on large-sized multistage stochastic mixed 0–1 programs with a time stochastic dominance risk averse measure. The objective function to minimize is a composite function of the expected cost along the time horizon over the scenarios and the penalization of the expected cost excess on reaching the set of thresholds under consideration, subject to a bound on the expected cost excess for each threshold and a bound on the failure probability of reaching it. The main differences with some other risk averse strategies are presented. The problem is represented by a mixture of the splitting representation up to a given stage, so-called break stage, and the compact representation for the other stages along the time horizon. The dualization of the nonanticipativity constraints for the node-based and risk averse variables up to the break stage and the Lagrangean Relaxation of the cross node constraints of the risk averse strategy result in a model that can be decomposed into a set of independent scenario cluster submodels. Three Lagrangean multipliers updating schemes as the Subgradient method, the Lagrangean Progressive Hedging algorithm and the Dynamic Constrained Cutting Plane are computationally compared. We have observed in the randomly generated instances we have experimented with that the smaller the number of clusters, the stronger the lower bound provided for the original problem (even, frequently, it is the solution value) obtained with an affordable computing time.
Bibliographie:ObjectType-Article-1
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content type line 14
ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2017.04.007