ABSTRACT
The first method to be examined for minimising a function of n parameters is a search procedure based on heuristic ideas. Its strengths are that it requires no derivatives to be computed, so it can cope with functions which are not easily written as analytic expressions (for instance, the result of simulations), and that it always increases the information available concerning the function by reporting its value at a number of points. Its weakness is primarily that it does not use this information very effectively, so may take an unnecessarily large number of function evaluations to locate a solution. Furthermore, the method requires (n + 1) by (n + 2) storage locations to hold intermediate results in the algorithm, so is not well adapted to problems in a large number of parameters. However, for more than about five parameters the procedure appears to become inefficient. Justification of the choice of this algorithm is postponed until §14.4.
