Efficient Solution of Maximum-Entropy Sampling Problems

Abstract

Maximum-entropy sampling is a difficult nonlinear discrete optimization problem that arises in spatial statistics, for example, in the design of weather-monitoring networks. An exact algorithm for maximum-entropy sampling was first described in 1995, and subsequent papers have devised a variety of methods that obtain bounds and, in some cases, exact solutions. In “An Efficient Algorithm for Maximum-Entropy Sampling,” Anstreicher describes a new bound for the maximum-entropy sampling problem that is superior to all previously known bounds and is also efficiently computable. A branch-and-bound algorithm that incorporates the new bound solves challenging benchmark instances to optimality for the first time.