Characterizing distributions of discrete bivariate random variables for simulation and evaluation of solution methods

Abstract

Results are presented from empirical evaluations of the performance of solution procedures on random binary knapsack and weighted set covering problems in which correlation is induced between the objective function and constraint coefficients. It is concluded that the performance of the solution procedures degrades as the correlation induced among the test problem parameters is increased and that test problems with structured dependence should be used for many empirical evaluations of solution methods.Since structured dependence in discrete optimization test problems is desirable, ways t o characterize the joint distribution of a discrete bivariate random variable for any feasible correlation are needed. The problem of finding a characterization with the maximum value of the smallest probability for any possible point is formulated as a linear program. An efficient algorithm based on the Northwest Corner Rule and a simple probability reallocation scheme is presented and demonstrated on a small example.

Synthetic Optimization Problem Generation: Show Us the Correlations!

“…For example, Moore et al (1990) and Reilly (1991Reilly ( , 1993Reilly ( , 1999 show how to induce a target correlation level between two types of coefficients using composite joint distributions of coefficient values. We refer to approaches where marginal distributions of coefficient values and a correlation structure are specified as ECI methods.…”

“…We consider an ICI method that induces positive correlation between the objective function coefficients and the corresponding sums of constraint coefficients. Moore et al (1990) and Rushmeier and Nemhauser (1993) report an adverse effect of such correlation on algorithm performance.…”