Global optimizers are useful when the search space is likely to have many minima, making it hard to locate the true global minimum. In low dimensional or constrained problems it may be enough to apply a local optimizer starting at a set of possible start points, generated either randomly or systematically (for instance at grid locations), and choose the best result. However this approach is less likely to locate the true optimum as the ratio of volume of the search region to number of starting points increases. Correctly applied, the Simulated Annealing and Genetic Algorithm approaches described below can explore the search space better than a grid search for a given number of function evaluations, and are more likely to find the true global minimum. Note that both these approaches involve a stochastic element and so may fail to find the true minimum. In addition, since they are better at global searching than local optimization, it is usually worthwhile to `polish' any final solution using one of the local optimizers above.