# Integrated Simulation-Based Optimization of Operational Decisions at Container Terminals
## 1 Introduction
### Relationship between Hyper-Parameter Optimization and Simulation-Based Optimization  
Identifying high-performing solutions for a given model is a typical research question in many fields of science. The speed of the necessary search process has increased since the advent of computers and the new possibility of automating tedious and complex computations. Complex computations often become quite resource-intensive and tend to contain a large number of parameters that can be varied. Each parameter configuration describes an alternative shape of the executed computation. For categorical parameters (i.e., an element of a finite set), the size of the parameter configuration space grows exponentially with every additional parameter. For continuous parameters (e.g., a range of real numbers), even for a single parameter, the search space is infinite. Therefore, for many applications, the parameter configuration reaches a size that is impossible or impractical to cover. Hence, scientists are forced to evaluate only a subset of all feasible parameter configurations. This search process is further complicated if the model contains stochastic components. Therefore, a single parameter configuration often needs to be tested several times before the resulting statistics reliably inform the scientist of the quality of a parameter configuration. One field of science that faces similar difficulties is machine learning. Here, often learning algorithms that consist of many exchangeable components are optimized according to some metric. For neural networks, e.g., for the activation function, different mathematical functions can be inserted, the weights inside a neural network can be adjusted by different algorithms, the number of neurons for each layer can vary, etc. [38]. These decisions are referred to as hyper-parameters. They are usually considered to be constant during one experiment. It is a non-trivial problem to identify the best hyper-parameters for a given machine learning problem. Since machine learning pipelines often contain stochastic components, a repeated evaluation is often necessary. The task of constructing and adjusting machine learning is so complex that, in some cases, randomly picking parameter configurations outperforms manual model calibration by scientists [39]. The authors explain these results by the higher resolution of the search grid and less wasting of the computational budget on the variation of parameters that have little or no impact on the final result. To support the expert in automating the search through a parameter configuration space, [PERSON] et al. [40] were the first to present an optimization procedure that can deal with numerical and categorical parameters in a problem-independent manner. [PERSON] et al. [41] quickly followed with an alternative approach that they called TFE. A comparison between several data sets showed that the performance of such a hyper-parameter optimization technique varies with each setup [42; 43; 44]. This research topic is often referred to as hyper-parameter optimization and is the subject of active research and development [45; 44; 46]. In the past several years, many newly developed hyper-parameter optimization approaches have advanced the field. Studies such as [42; 43; 44] have empirically compared different meta-heuristics. This approach is the key to identifying characteristics of each meta-heuristic, which, in turn, can result in the recommendation of one meta-heuristic. Such an empirical approach is necessary because of the No Free Lunch Theorem (NFLT) in the optimization of black-box functions: One cannot determine the most successful optimization algorithm for an unseen problem [47]. This means that, for simulation-based optimization, a meta-heuristic that has worked well in one study might fail to lead to good approximations of the optimum for a different \"problem\", i.e., the black-box function that consists of a simulation model and an objective function.