A Comparative Study of Decomposition Algorithms for Stochastic Combinatorial Optimization

Lewis Ntaimo; Suvrajeet Sen

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SPEPS Preprint

Author(s):	Lewis Ntaimo, Texas A&M University Suvrajeet Sen, The University of Arizona
Title:	A Comparative Study of Decomposition Algorithms for Stochastic Combinatorial Optimization
Date of Acceptance:	29.12.2005
Submission Date:	11.08.2005
Series Title:	Stochastic Programming E-Print Series (SPEPS)
Editors:	Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint:	pdf (urn:nbn:de:kobv:11-10059954)
Keywords (eng):	Stochastic mixed-integer programming, disjunctive decomposition, stochastic server location, strategic supply chain planning, stochastic matching
Appeared in:	Computational Optimization and Applications
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Abstract (eng):

This paper presents comparative computational results using three decomposition algorithms on a battery of instances drawn from three different applications. In order to preserve the commonalities among the algorithms in our experiments, we have designed a testbed which is used to study instances arising in server location under uncertainty, strategic supply chain planning under uncertainty, and stochastic bipartitite matching. Insights related to alternative implementation issues leading to more efficient implementations, benchmarks for serial processing, and scalability of the methods are also presented. The computational experience demonstrates the promising potential of the disjunctive decomposition $(D^2)$ approach towards solving several large-scale problem instances from the three application areas. Furthermore, the study shows that convergence of the $D^2$ methods for stochastic combinatorial optimization (SCO) is in fact attainable since the methods scale well with the number of scenarios.

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