2 ALGORITHMS FOR GLOBAL OPTIMIZATION

In this paper, we develop and compare two methods for solving the prob lem of determining the global maximum of a function over a feasible se t. The two methods begin with a random sample of points over the feasi ble set. Both methods then seek to combine these points into ''regions of attraction'' which represent subsets of the points which will yiel d the same local maximums when an optimization procedure is applied to points in the subset. The first method for constructing regions of at traction is based on approximating the function by a mixture of normal distributions over the feasible region and the second involves attemp ts to apply cluster analysis to form regions of attraction. The two me thods are then compared on a set of well-known test problems.