Coupled Local Minimizers: a new global optimization method

A new efficient global optimization technique, named Coupled Local Minimizers (CLM), is presented in the paper. The CLM method uses a set of search points, initially spread over the search space. In each search point the function and derivative values are calculated and used to direct the search 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 in order to create interaction between them, which results in a cooperative search mechanism. The combination of a fast convergence—due to the derivative information that is used—with the capability of finding the global minimum — resulting from the parallel strategy — guarantees an efficient global optimization algorithm. The paper proposes an implementation based on the second-order Newton method in order to increase the convergence speed. The CLM method and its implementation are described extensively in the paper and are illustrated with a test function containing several local minima. The paper focusses on low-dimensional optimization problems only.