Management Science: The Art of Modeling with Spreadsheets, Third Edition

Chapter 14. Optimization of Non-Smooth Models

INTRODUCTION

The previous four chapters cover various types of optimization problems and the Solver algorithms that apply to them. A central theme of those chapters is that success in finding an optimal solution for a particular type of problem often requires 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 10 we learned that in solving smooth optimization problems we must avoid the use of IF functions in our models and the solution provided by the nonlinear solver may be only a local optimum. In Chapter 11 we learned that in solving linear optimization problems we must also avoid the use of IF 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, a Solver algorithm that can be effective on models that cannot be optimized in any other way.

The evolutionary solver is a solution method that is quite different from the other solvers in both its design and its application. It can be applied to some of the most difficult optimization problems. But there is a price to pay for this power: the evolutionary solver does not produce guaranteed optimal solutions. It sometimes falls short of producing an optimal solution and we can seldom tell whether it has done ...