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

机译:具有增强的Benders分解的处理两阶段随机LP的求解器系统的计算研究

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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.
机译:我们报告了针对大量基准问题的两阶段SP模型的计算研究,并考虑了以下方法:(i)通过单纯形法和内点法求解确定性等价问题,(ii)Benders分解(L形状的方法,具有聚集的切口),(iii)Ruszczyński的正则分解(数学程序35:309–333,1986年),(iv)通过层次方法对预期资源进行正则化的Benders分解(Lemaréchal等人,在Math Program中69:111–147,1995),(v)Linderoth和Wright的信任区域(正则化)方法(Comput Optim Appl 24:207–250,2003)。在这项研究中,在Benders分解的计算结构中引入了三种正则化方法。因此,通过实施可行性削减,以传统方式控制第二阶段的不可行性。这种方法可以将正则化扩展到可行性问题,如Fábián和Szőke(Comput Manag Sci 4:313–353,2007)。我们从POSTS和SLPTESTSET集合以及我们编译的一系列困难测试问题中报告了各种基准问题的计算结果。最后,介绍了该方法的放大属性和性能概况。

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