We compare empirically accuracy and speed of low-discrepancy sequence generators of Sobol' and Faure. These generators are useful for multidimensional integration and global optimization. We discuss our implementation of the Sobol' generator.
Low-discrepancy sequences are used for numerical integration, in simulation, and in related applications.Techniques for producing such sequences have been proposed by, among others, Halton, Sobol', Faure, and Niederreiter. Niederreiter's sequences have the best theoretical asymptotic properties. The paper describes two ways to implement the latter sequences on a computer and discusses the results obtained in various practical tests onparticu[ar integrals.
ABSTRAtXRecent efforts to improve lower bounds in implicit enumeration algorithms for the general (nlmlGIF,) crequencing problem have been directed to the solution of M auxiliary single machine problem that results from the relaxation of some of the interference constraints. We develop M algorithm that obtains optimal and near optimal solutions for this relaxed problem with relatively little computational effort. We report on computational results achieved when this method is used to obtain lower bounds for the general problem. Finally, we show the equivalence of this problem to a single machine sequencing problem with earliest start and due date constraints where the objective is to minimize the maximum lateness.
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