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1.
The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study 总被引:1,自引:0,他引:1
Bram Verweij Shabbir Ahmed Anton J. Kleywegt George Nemhauser Alexander Shapiro 《Computational Optimization and Applications》2003,24(2-3):289-333
The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps.We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 21694 scenarios to within an estimated 1.0% of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time. 相似文献
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The effects of different ventilation methods on cardiac output measured by the indicator-dilution method, liver blood flow measured by a deuterium washout technique using 2H nuclear magnetic resonance (NMR) and liver concentrations of ATP and intracellular pH determined with 31P NMR were compared in anesthetized rats. No differences in mean arterial blood pressure were demonstrable with the different modes of ventilation. However, significant drops in cardiac output were observed between freely breathing and animals ventilated with positive pressure but not the high frequency oscillatory method (407 +/- 46 and 520 +/- 88 vs. 633 +/- 86 ml/min/kg, p less than 0.05 and p = NS, respectively). Moreover, liver blood flow was significantly reduced during positive pressure but not high frequency oscillatory ventilation compared with free breathing rats (32 +/- 4 and 43 +/- 10 vs. 46 +/- 8 ml/100 g, p less than 0.05 and p = NS, respectively). 31P NMR spectroscopy revealed no effects of either ventilation method on tissue ATP or intracellular pH as estimated by the chemical shift of inorganic phosphate. These data suggest that controlled ventilation in normal rats accomplished with standard positive pressure methods is associated with major decreases in cardiac output and liver blood flow despite maintenance of normal blood pressure. High frequency oscillatory ventilation appears to effect less compromise of cardiac output and hepatic perfusion than positive pressure ventilation and may, therefore, be preferable for some biological studies. 相似文献
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N. G. Zharova É. D. German A. M. Kuznetsov I. O. Shapiro 《Russian Chemical Bulletin》1989,38(2):270-276
1. | The influence of the components of the effect of the structural reorganization of the anionic fragments of monalkylbenzenes and nitroalkanes on the kinetics of their ionization was determined. |
2. | A model of the mechanism of the elementary act in the ionization of monoalkylbenzenes and nitroalkanes in a polar medium, which takes into account the effects of the reorganization of the solvent, the geometric structure of the reactants, and the redistribution of the electron density in them, has been proposed. |
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