Interval Methods for Accelerated Global Search in the Microsoft Excel Solver

This paper describes advanced interval methods for finding a verified global optimum and finding all solutions of a system of nonlinear equations, as implemented in the Premium Solver Platform, an extension of the Solver bundled with Microsoft Excel. It also describes the underlying tools that allow Excel spreadsheets to be evaluated over reals and intervals, with fast computation of real gradients and interval gradients. The advanced interval methods described include mean value (MV) and generalized interval (GI) representations for functions, constraint propagation for both the MV and GI forms, and a linear programming test for the GI form, in the context of an overall interval branch and bound algorithm. Numerical results for a set of sample problems demonstrate a significant speed advantage for the GI techniques, compared to alternative methods.