Parallelization and Aggregation of Nested Benders Decomposition

23 Pages Posted: 19 Nov 1997

See all articles by M. A. H. Dempster

M. A. H. Dempster

University of Cambridge - Centre for Financial Research; Cambridge Systems Associates Limited; University of Cambridge - Judge Business School

R. T. Thompson

University of Cambridge; University of Essex - Department of Mathematics

Abstract

Dynamic multistage stochastic linear programming has many practical applications for problems whose current decisions have to be made under future uncertainty. There are a variety of methods for solving these problems, including nested Benders decomposition. In this method, recently shown to be superior to the alternatives for large problems, the problem is decomposed into a set of smaller linear programming problems. These problems can be visualised as being attached to the nodes of a tree which is formed from the realizations of the random data vectors determining the uncertainty in the problem. The tree is traversed forwards and backwards, with information from the solutions to each nodal linear programming problem being passed to its immediate descendants by the formation of their right hand sides and to its immediate ancestor in the form of cuts. Problems in the same time period can be solved independently and it is this inherent parallelism that is exploited in our parallel nested Benders algorithm. A parallel version of the MSLiP nested Benders code has been developed and tested on various types of MIMD machines. The differing structures of the test problems cause differing levels of speed-up. Results show that problems with few variables and constraints per node do not gain from this parallelization. Stage aggregation has been successfully explored for such problems to improve their parallel solution efficiency by increasing the size of the nodes and therefore the time spent calculating relative to the time spent communicating between processors.

JEL Classification: C61

Suggested Citation

Dempster, M. A. H. and Thompson, R. T., Parallelization and Aggregation of Nested Benders Decomposition. Available at SSRN: https://ssrn.com/abstract=37765 or http://dx.doi.org/10.2139/ssrn.37765

M. A. H. Dempster (Contact Author)

University of Cambridge - Centre for Financial Research ( email )

Centre for Mathematical Sciences
Wilberforce Road
Cambridge, CB3 0WA
United Kingdom

Cambridge Systems Associates Limited ( email )

5-7 Portugal Place
Cambridge, CB5 8AF
United Kingdom

University of Cambridge - Judge Business School ( email )

Trumpington Street
Cambridge, CB2 1AG
United Kingdom

R. T. Thompson

University of Cambridge ( email )

Trinity Ln
Cambridge, CB2 1TN
United Kingdom

University of Essex - Department of Mathematics ( email )

Wivenhoe Park
Colchester, Essex CO4 3SQ
United Kingdom
01206 - 873040 (Phone)
01206 - 873043 (Fax)

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