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Applying oracles of on-demand accuracy in two-stage stochastic programming - a computational study

Christian Wolf(christian.wolf***at***dsor.de)
Csaba Fábián(fabian.csaba***at***gamf.kefo.hu)
Achim Koberstein(koberstein***at***wiwi.uni-frankfurt.de)
Leena Suhl(suhl***at***dsor.de)

Abstract: Traditionally, two variants of the L-shaped method based on Benders' decomposition principle are used to solve two-stage stochastic programming problems: the single-cut and the multi-cut version. The concept of an oracle with on-demand accuracy was originally proposed in the context of bundle methods for unconstrained convex optimzation to provide approximate function data and subgradients. In this paper, we show how a special form of this concept can be used to devise a variant of the L-shaped method that integrates the advantages of the traditional variants while avoiding their disadvantages. On a set of 104 test problems, we compare and analyze parallel implementations of regularized and unregularized versions of the algorithms. The results indicate that significant speed-ups in computation time can be achieved by applying the concept of on-demand accuracy.

Keywords: Stochastic programming, two-stage problems, decomposition, bundle methods

Category 1: Stochastic Programming

Category 2: Optimization Software and Modeling Systems (Optimization Software Benchmark )

Citation:

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Entry Submitted: 02/17/2014
Entry Accepted: 02/17/2014
Entry Last Modified: 02/17/2014

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