Comparison of deterministic and stochastic approaches to global optimization

In this paper, we compare two different approaches to nonconvex global optimization. The first one is a deterministic spatial Branch-and-Bound algorithm, whereas the second approach is a Quasi Monte Carlo (QMC) variant of a stochastic multi level single linkage (MLSL) algorithm. Both algorithms apply to problems in a very general form and are not dependent on problem structure. The test suite we chose is fairly extensive in scope, in that it includes constrained and unconstrained problems, continuous and mixed-integer problems. The conclusion of the tests is that in general the QMC variant of the MLSL algorithm is generally faster, although in some instances the Branch-and-Bound algorithm outperforms it.