MISO: Mixed-Integer Surrogate Optimization Framework

We introduce MISO, the Mixed-Integer Surrogate Optimization framework. MISO aims at solving computationally expensive black-box optimization problems with mixed-integer variables. Although encountered in many applications, such as optimal reliability design or structural optimization, for example, where time consuming simulation codes have to be run in order to obtain an objective function value, the development of algorithms for this type of optimization problem has rarely been addressed in the literature. A single objective function evaluation may take from several minutes to hours or even days. Thus, only very few objective function evaluations are allowable during the optimization. Because the objective function is black-box, derivatives are not available and numerically approximating the derivatives requires a prohibitively large number of function evaluations. Therefore, we use surrogate models to approximate the expensive objective function and to decide at which points in the variable domain the expensive objective function should be evaluated. We develop a general surrogate model framework and show how sampling strategies of well-known surrogate model algorithms for continuous optimization can be modified for mixed-integer variables. We introduce two new algorithms that combine different sampling strategies and local search to obtain high-accuracy solutions. We compare MISO in numerical experiments to a genetic algorithm, NOMAD, and SO-MI. The results show that MISO is in general very efficient with respect to finding improved solutions within very few function evaluations. The performance of MISO depends on the chosen sampling strategy. The MISO algorithm that combines a dynamic coordinate search with a target value strategy and a local search performs best among all algorithms. J. Müller Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720 E-mail: [email protected]