Reliable Computing 9: 143–159, 2003.
2003 Kluwer Academic Publishers. Printed in the Netherlands.
Interval Methods for Accelerated Global Search
in the Microsoft Excel Solver
IVO P. NENOV
5 Commodore Dr. #213, Emeryville, CA 94608, USA, e-mail: ivo firstname.lastname@example.org
DANIEL H. FYLSTRA
P.O. Box 4288, Incline Village, NV 89450, USA, e-mail: email@example.com
(Received: 19 March 2002; accepted: 28 September 2002)
Abstract. This paper describes advanced interval methods for ﬁnding a 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 real and interval numbers, 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.
The Solver bundled with Microsoft Excel, developed by Frontline Systems for
Microsoft, is among the most widely used tools for optimization and equation solv-
ing. It is capable of solving small-scale linear programming (LP), smooth nonlinear
programming (NLP), and mixed integer programming (MIP) problems. Included
in nearly 100 million copies of Microsoft Excel, it offers Excel spreadsheet users
an easy introduction to classical methods of optimization. An upgraded Premium
Solver for Education, now bundled with more than a dozen textbooks, is used in a
wide range of MBA and engineering courses.
The Premium Solver Platform is a compatible upgrade that extends the func-
tionality, capacity and speed of the Microsoft Excel Solver to handle industrial-
scale problems, including LP problems of over 100,000 variables and constraints;
NLP problems with tens of thousands of variables and constraints; challenging
mixed-integer problems; global optimization problems using multi-start or clus-
tering methods; and non-smooth problems using methods based on genetic and
evolutionary algorithms and tabu search.
In the past two years, we have sought to greatly extend the capabilities of the
Premium Solver Platform for deterministic global optimization and solution of