Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems
TLDR
The necessity and efficacy of the techniques is empirically assessed on a two-stage stochastic network flow problem with integer variables in both stages and algorithmic innovations in the context of a broad class of scenario-based resource allocation problem.Abstract:
Numerous planning problems can be formulated as multi-stage stochastic programs and many possess key discrete (integer) decision variables in one or more of the stages. Progressive hedging (PH) is a scenario-based decomposition technique that can be leveraged to solve such problems. Originally devised for problems possessing only continuous variables, PH has been successfully applied as a heuristic to solve multi-stage stochastic programs with integer variables. However, a variety of critical issues arise in practice when implementing PH for the discrete case, especially in the context of very difficult or large-scale mixed-integer problems. Failure to address these issues properly results in either non-convergence of the heuristic or unacceptably long run-times. We investigate these issues and describe algorithmic innovations in the context of a broad class of scenario-based resource allocation problem in which decision variables represent resources available at a cost and constraints enforce the need for sufficient combinations of resources. The necessity and efficacy of our techniques is empirically assessed on a two-stage stochastic network flow problem with integer variables in both stages.read more
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References
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BookDOI
Introduction to Stochastic Programming
John R. Birge,Franois Louveaux +1 more
TL;DR: This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability to help students develop an intuition on how to model uncertainty into mathematical problems.
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AMPL: A Modeling Language for Mathematical Programming
Robert Fourer,Brian W. Kernighan +1 more
TL;DR: An efficient translator is implemented that takes as input a linear AMPL model and associated data, and produces output suitable for standard linear programming optimizers.
Journal ArticleDOI
Scenarios and policy aggregation in optimization under uncertainty
TL;DR: This paper develops for the first time a rigorous algorithmic procedure for determining a robust decision policy in response to any weighting of the scenarios.
Book
AMPL : a modeling language for mathematical programming
Robert Fourer,Brian W. Kernighan +1 more
TL;DR: AMPL as mentioned in this paper is a language designed to make the optimization of large-scale mathematical programs easier and less error-prone than traditional linear programming optimizers, and it can be extended to more general mathematical programs that incorporate nonlinear expressions or discrete variables.