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

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.

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Zverovich, V., Fábián, C.I., Ellison, E.F.D. et al. A computational study of a solver system for processing two-stage stochastic LPs with enhanced Benders decomposition. Math. Prog. Comp. 4, 211–238 (2012). https://doi.org/10.1007/s12532-012-0038-z

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Mathematics Subject Classification

  • 49M27
  • 65K05
  • 90C05
  • 90C06
  • 90C15
  • 90C51