Multivariate Sampling with Explicit Correlation Induction for Simulation andOptimization Studies

摘要

Composite distributions based on specified marginal distributions and a specifiedPearson product-moment correlation structure are formed by mixing extreme-correlation distributions of a multivariate random variable and the joint distribution under independence. Closed-form expressions are provided for the composition probabilities for composite distributions for trivariate random variables, and a simple algorithm for finding composition probabilities in the case of quadravariate random variables is presented. A linear program provides a general approach for finding composition probabilities. For all but the extreme correlation structures a range of composite distributions is provided. Composite distributions are used to generate coefficients for 1120 two-dimensional knapsack problems based on a variety of Pearson correlation structures. An equal number of problems is generated based on Spearman rank correlation structures. The computational results with a branch-and-bound procedure and a well-known heuristic indicate that the type of correlation structure induced (Pearson or Spearman) can affect the performance of solution procedures. The correlation structure specified matters, as do the values specified for each correlation term. There is a noticeable interaction between the correlation structure induced and the constraint slackness settings. Finally, the interconstraint correlation is found to affect solution procedure performance more than either of the objective-constraint correlations.