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Management Science: The Art of Modeling with Spreadsheets, 4th Edition by Kenneth R. Baker, Stephen G. Powell

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12 Optimization of Nonsmooth Models

12.1 INTRODUCTION

The previous four chapters cover various types of optimization problems and the Solver algorithms that apply. A central theme of those chapters is that success in finding an optimal solution for a particular type of problem often requires both careful model building and choice of a solution algorithm. Furthermore, the choice of an algorithm has important implications for the degree of confidence we can have that the solution is a global optimum.

For example, in Chapter 8, we learned that in solving smooth optimization problems we must avoid the use of nonsmooth functions in our models and the solution provided by the nonlinear solver may be only a local optimum. In Chapter 9, we learned that in solving linear optimization problems we must also avoid the use of nonsmooth functions in our models, but the solution provided by the linear solver is guaranteed to be a global optimum. In this chapter, we introduce the evolutionary solver, which can be effective on models that cannot be optimized in any other way.

The evolutionary solver, as implemented in Analytic Solver Platform, actually consists of two alternative algorithms, each of which has several variations. For simplicity we refer to it as if it were a single procedure. The evolutionary solver is quite different from the other Analytic Solver Platform solvers in both its design and its application. It can be applied to some of the most difficult optimization problems, but ...

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