Coupled Local Minimizers: a new global optimization method

Abstract

Global optimization technique, Coupled Local Minimizers, CLM methodABSTRACT:Anewefficientglobaloptimization technique, namedCoupledLocalMinimizers(CLM),is presented in the paper. The CLMmethod uses aset of search points, initially spread over the searchspace. In each search point the function and derivative values are calculated and used to direct thesearch process. But instead of performing separate, independent searches from each of these points(i.e. multi-start local optimization), the set of optimizers are coupled during the search process inorder to create interaction between them, which results in a cooperative search mechanism. The com-bination of a fast convergence –due to the derivative information that is used– with the capabilityof finding the global minimum –resulting from the parallel strategy– guarantees an efficient globaloptimization algorithm. The paper proposes an implementation based on the second-order Newtonmethod in order to increase the convergence speed. The CLM method and its implementation aredescribed extensively in the paper and are illustrated with a test function containing several localminima. The paper focusses on low-dimensional optimization problems only.1 INTRODUCTIONThe general purpose of