As discussed in the local optimization demo, it is sometimes desirable to find the best of all possible minimum values of a function. As might be expected, this problem can be very much harder than the local optimization problem, but the NAG library supplies several routines which tackle it. Once again, we use the number of function evaluations as a measure of efficiency of an algorithm. For advice on which routine to choose, as well as more details on the methods used, see the E05 Chapter Introduction.

In this demo we apply various methods to a set of problems so that you can compare the efficiency of the methods. Do bear in mind that all the methods we describe have optional parameters or inital settings which allow the user some control over how the algorithms proceed and how they decide to terminate. Best performance can often only be achieved by experimentation with these options. For the NAG routines, see the individual routine documents for details. For the simulated annealing method, you can choose the starting temperature and the cooling factor. The higher the values chosen for these two parameters, the more function evaluations will be required.