Algorithms for Simulation-Based Optimization Problems

Many industries use simulation tools for virtual product design, and there is a growing trend towards using simulation in combination with optimization algorithms for tuning simulation input parameters. The requirements for optimization under such circumstances are often very strong, involving many design variables and constraints and a strict limitation of the number of function evaluations to a surprisingly small number (often around one thousand or less). Tuning optimization algorithms for such challenges has led to very good results obtained by variants of evolution strategies and of Bayesian optimization algorithms. Evolutionary algorithms are nowadays standard solvers for such applications. In the presentation, sample cases from industry are presented, and their challenges are discussed in more detail. Results of an experimental comparison of contemporary evolution strategies [1] on the black box optimization benchmark (BBOB) test function set for a small number of function evaluations are discussed, and further enhancements of contemporary evolution strategies are outlined. In addition, we will also briefly discuss the concept of Bayesian global optimization [2] and its connection with research in evolutionary strategies, motivated by a generalized infill criterion [3]. The corresponding algorithms typically combine so-called metamodels (i.e., datadriven nonlinear regression models using Gaussian process or random forests for regression) with state-of-the-art optimization algorithms for the identification of new sampling points, based on the above mentioned infill criterion. Essentially, the latter is also again a multimodal objective function defined over the metamodel, which in turn requires an optimizer to solve the optimization problem defined by the infill criterion. Our practical examples are motivated by industrial applications. A typical challenge is to find innovative solutions to a design optimization task. Based on a suitable optimization algorithm, which often also needs to deal with multiple, conflicting objectives, an application of this concept to an industrial design optimization task is discussed in the presentation. Discussing these applications and the variants of evolution strategies applied, the capabilities of these algorithms for optimization cases with a small number of function evaluations are illustrated.