Use Automatic Scaling Option

The Use Automatic Scaling check box in the Solver Options dialog can be used to help compensate for the ill effects of a poorly scaled Solver model on the solution process. Poorly scaled models are one of the most common causes of problems in which the Solver appears to stop prematurely without reaching the true optimal solution; it is a good idea to keep this box checked for all of your Solver models.

Effects of Poor Scaling

A poorly scaled model is one in which the typical values of the objective and constraint functions differ by several orders of magnitude. A classic example is a financial model with some dollar amounts in millions, and other rate of return figures in percent. Poorly scaled models often cause difficulty for both linear and nonlinear Solver algorithms; the effect is often more severe for the nonlinear GRG solver.

The Solver must perform many calculations where quantities derived from the values of the objective and constraints must be divided into and subtracted from one another. Because of the finite precision of computer arithmetic, when these calculations are performed with values of very different magnitudes, roundoff error builds up to the point where the Solver can no longer reliably find the optimal solution.

When this box is checked, the Solver will attempt to scale the values of the objective and constraint functions internally in order to minimize the effects of a poorly scaled model. In the built-in Microsoft Excel Solver, this option is effective only for nonlinear problems solved with the standard GRG solver. In the enhanced solvers, this option works for all types of models.

Starting Values for Nonlinear Problems

For problems where you are not using the Assume Linear Model option where you check the Use Automatic Scaling box, make sure that the starting values for the decision variables are "reasonable," i.e. of roughly the same magnitudes that you expect for those variables at the optimal solution. For problems solved by the nonlinear GRG solver, the effectiveness of the Use Automatic Scaling option depends on how well these starting values reflect the values encountered during the solution process.

Copyright © 1996 Frontline Systems Inc.
Last modified: December 01, 1996