Nonlinear Parameter Optimization Using R Tools

Chapter 15Global optimization and stochastic methods

This chapter looks at some tools designed for those awkward problems with potentially many local extrema—we will again present the ideas by talking of minima. Generally, but not exclusively, R approaches these types of problems stochastically. That is, we try many starting points and find many local minima, then choose the “best.”

15.1 Panorama of methods

For the person simply wishing to find a solution to a problem, the fields of global and stochastic optimization are, sadly, overpopulated with methods. Worse, although I have neither had the time nor the inclination to thoroughly research the subject, it appears that there is much rehashing of ideas, so that many of the “new method” papers and programs are really not new. Indeed, one could suggest that the authors of many papers have more in common with the marketers of laundry detergent than mathematicians.

The names associated with these stochastic methods sometimes reflect the philosophical motivation: Simulated Annealing, Genetic Algorithms, Tabu Search, differential evolution, particle swarm optimization, Self-Organizing Migrating Algorithm. The fact that there are so many approaches and methods speaks loudly of the difficulty of such problems. Moreover, it is exceedingly difficult to compare such methods without conducting large-scale tests from different starting points. Guidance to users is therefore limited to the general comment that stochastic methods can have ...