On Locating All Local Minima of Multidimensional Function for Box Constrained

A novel method of locating all local minima of a function is presented here. Among many methods that exist in global optimization literature, Multi-start and Min-finder are effective methods because of their ability to locate not only the global minimum but also all local minima of the objective function. Both of these methods have the disadvantage of high computational cost. To remedy this, we propose a quality measure called G-measure to measure the local minima of a multidimensional continuous and differentiable function distribution inside a bounded domain. The proposed algorithm greatly reduces the frequency of the local optimal search, and it does not make use of a priori knowledge of the number of local minima. We compare the performance of this new method with that of Multi-start and Min-finder on a set of benchmark problems.