LOOM, an algorithm for finding local optima of expensive functions

Abstract—Engineering optimization often involves one or many computationally intensive softwares that must be called to calculate the performance of candidate solutions. Despite the calculation cost, it is useful to characterize the global and the local optima. A new algorithm is described here that searches for all the local optima in a reduced number of calls to the true performance function. The algorithm is based on repeated local searches on a metamodel of the true performance function and is called LOOM for LOcal Optima through Metamodels. The local optima are identified as an output of the search. The search distributes computational resources equally among the basins of attraction. Priority is put on local search (intensification) and exploration occurs within a limited budget of calls to the objective function. This article presents the algorithm and describes a first series of tests in two dimensions where a kriging metamodel is used. I