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The estimation of optimal solution values for large-scale optimization problems is studied. Optimal solution value estimators provide information about the deviation between the optimal solution and the heuristic solution. Some estimation techniques combine heuristic solutions with randomly generated solutions. In particular, we examine a class of jacknife-based estimators which incorporate any heuristic solution value with the two best randomly generated solution values. The primary contribution of this article is that we provide a framework to analytically evaluate a class of optimal solution value estimators. We present closed-form results on the relationship of heuristic performance, sample size, and the estimation errors for the case where the feasible solutions are uniformly distributed. In addition, we show how to compute the estimation errors for distributions other than uniform given a specific sample size. We use a triangular and an exponential distribution as examples of other distributions. A second major contribution of this article is that, to a large extent, our analytical results confirm previous computational results. In particular, the best estimator depends on how good the heuristic is, but seems to be independent of the underlying distribution of solution values. Furthermore, there is essentially an inverse relationship between the heuristic performance and the performance of any estimator. © 1994 John Wiley & Sons, Inc. 相似文献
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Lionel Weiss 《海军后勤学研究》1985,32(2):337-346
For the problem of testing the independence of a set of continuous random variables, where the test is to be based on n independent and identically distributed observations, tests are constructed that guard against all alternatives but are particularly effective against special alternatives of interest. The tests are based on the numbers of observations falling in the cells of a grid constructed using order statistics. 相似文献
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Lionel Weiss 《海军后勤学研究》1976,23(1):139-149
For a fixed number of classes and the number of trials increasing, the approach of the multinomial cumulative distribution function to a normal cumulative distribution function is familiar. In this paper we allow the number of classes to increase as the number of trials increases, and show that under certain circumstances the probabilities assigned to arbitrary regions by the multinomial distribution are all close to the probabilities assigned by the distribution of “rounded off” normal random variables. As the number of trials increases, the amount rounded off approaches zero. The result can be used to study the asymptotic distribution of functions of multinomial random variables. 相似文献
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Lionel Weiss 《海军后勤学研究》1975,22(1):55-63
For each n, X1(n),…, Xn(n) are independent and identically distributed random variables, each with cumulative distribution function F(x) which is known to be absolutely continuous but is otherwise unknown. The problem is to test the hypothesis that \documentclass{article}\pagestyle{empty}\begin{document}$ F(x) = G\left( {{\textstyle{{x - \theta _1 } \over {\theta _2 }}}} \right) $\end{document}, where the cumulative distribution function Gx is completely specified and satisfies certain regularity conditions, and the parameters θ1, θ2 are unknown and unspecified, except that the scale parameter θ2, is positive. Y1 (n) ≦ Y2 (n) ≦ … ≦ Yn (n)are the ordered values of X1(n),…, Xn(n). A test based on a certain subset of {Yi(n)} is proposed, is shown to have asymptotically a normal distribution when the hypothesis is true, and is shown to be consistent against all alternatives satisfying a mild regularity condition. 相似文献
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Gideon Weiss 《海军后勤学研究》1984,31(3):431-446
A set of n spare components whose life lengths are exponentially distributed with rates μ1, …,μn are available to keep a two-component parallel system in operation. We derive the optimal order of replacement of failed components in order to maximize the system life length. 相似文献
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Lionel Weiss 《海军后勤学研究》1971,18(1):111-114
For each n, X1(n),…Xn(n) are independent and identically distributed random variables, with common probability density function Where c, θ, α, and r(y) are all unknown. It is shown that we can make asymptotic inferences about c, θ, and α, when r(y) satisfies mild conditions. 相似文献
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This article describes an algorithm for solving the static electric utility capacity expansion problem. The advantages of this algorithm are twofold. First, it is simpler and yet more efficient than previous algorithms for the same problem. Second, by making simplifying but realistic assumptions on plant sizes it is possible to use this algorithm for the case where one does not allow fractional plant additions. While the model has n variables, it has a clear two-dimensional geometric representation for understanding its properties, developing an algorithm, and interpreting the optimal solution. This algorithm has been implemented in the Intermediate Future Forecasting (IFFS) capacity expansion model at the Department of Energy. 相似文献