A Hybrid Algorithm for Identifying Global and Local Minima When Optimizing Functions with Many Minima

The problem of determining most global minima including some of the local ones for unconstrained non-convex functions is investigated. This is tackled using a hybrid approach that combines simulated annealing, tabu search and a descent method. This approach has the advantage of not requiring differentiability of the function. The special feature of this approach is that it produces not only all the global minima with a high frequency but also those good local minima which may be of relevance to the user. This is the first time such a view is put forward, especially in the context of functions of continuous variables. This method is tested on standard test functions used in the literature, and encouraging results are obtained.