Surrogate-based optimization and nature-inspired metaheuristics have become the state of the art in solving real-world optimization problems. Still, it is difficult for beginners and even experts to get an overview that explains their advantages in comparison to the large number of available methods in the scope of continuous optimization. Available taxonomies lack the integration of surrogate-based approaches and thus their embedding in the larger context of this broad field.
This article presents a taxonomy of the field, which further matches the idea of nature-inspired algorithms, as it is based on the human behavior in path finding. Intuitive analogies make it easy to conceive the most basic principles of the search algorithms, even for beginners and non-experts in this area of research. However, this scheme does not oversimplify the high complexity of the different algorithms, as the class identifier only defines a descriptive meta-level of the algorithm search strategies. The taxonomy was established by exploring and matching algorithm schemes, extracting similarities and differences, and creating a set of classification indicators to distinguish between five distinct classes. In practice, this taxonomy allows recommendations for the applicability of the corresponding algorithms and helps developers trying to create or improve their own algorithms.
Sequential Parameter Optimization is a model-based optimization methodology, which includes several techniques for handling uncertainty. Simple approaches such as sharp- ening and more sophisticated approaches such as optimal computing budget allocation are available. For many real world engineering problems, the objective function can be evaluated at different levels of fidelity. For instance, a CFD simulation might provide a very time consuming but accurate way to estimate the quality of a solution.The same solution could be evaluated based on simplified mathematical equations, leading to a cheaper but less accurate estimate. Combining these different levels of fidelity in a model-based optimization process is referred to as multi-fidelity optimization. This chapter describes uncertainty-handling techniques for meta-model based search heuristics in combination with multi-fidelity optimization. Co-Kriging is one power- ful method to correlate multiple sets of data from different levels of fidelity. For the first time, Sequential Parameter Optimization with co-Kriging is applied to noisy test functions. This study will introduce these techniques and discuss how they can be applied to real-world examples.