Mathematical Programming Computation

, Volume 4, Issue 3, pp 211–238

A computational study of a solver system for processing two-stage stochastic LPs with enhanced Benders decomposition

  • Victor Zverovich
  • Csaba I. Fábián
  • Eldon F. D. Ellison
  • Gautam Mitra
Full Length Paper

DOI: 10.1007/s12532-012-0038-z

Cite this article as:
Zverovich, V., Fábián, C.I., Ellison, E.F.D. et al. Math. Prog. Comp. (2012) 4: 211. doi:10.1007/s12532-012-0038-z
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Abstract

We report a computational study of two-stage SP models on a large set of benchmark problems and consider the following methods: (i) Solution of the deterministic equivalent problem by the simplex method and an interior point method, (ii) Benders decomposition (L-shaped method with aggregated cuts), (iii) Regularised decomposition of Ruszczyński (Math Program 35:309–333, 1986), (iv) Benders decomposition with regularization of the expected recourse by the level method (Lemaréchal et al. in Math Program 69:111–147, 1995), (v) Trust region (regularisation) method of Linderoth and Wright (Comput Optim Appl 24:207–250, 2003). In this study the three regularisation methods have been introduced within the computational structure of Benders decomposition. Thus second-stage infeasibility is controlled in the traditional manner, by imposing feasibility cuts. This approach allows extensions of the regularisation to feasibility issues, as in Fábián and Szőke (Comput Manag Sci 4:313–353, 2007). We report computational results for a wide range of benchmark problems from the POSTS and SLPTESTSET collections and a collection of difficult test problems compiled by us. Finally the scale-up properties and the performance profiles of the methods are presented.

Mathematics Subject Classification

49M2765K0590C0590C0690C1590C51

Copyright information

© Springer and Mathematical Optimization Society 2012

Authors and Affiliations

  • Victor Zverovich
    • 1
  • Csaba I. Fábián
    • 3
    • 4
  • Eldon F. D. Ellison
    • 1
    • 2
  • Gautam Mitra
    • 1
    • 2
  1. 1.OptiRisk Systems, OptiRisk R&D HouseUxbridge, MiddlesexUK
  2. 2.The Centre for the Analysis of Risk and Optimisation Modelling Applications (CARISMA), School of Information Systems, Computing and MathematicsBrunel UniversityLondonUK
  3. 3.Institute of Informatics, Kecskemét CollegeKecskemétHungary
  4. 4.Department of ORLoránd Eötvös UniversityBudapestHungary