Dominik Kirchhoff

Gaussian process (GP) models of time‐consuming computer simulations are nowadays widely used within metamodel‐based optimization. In recent years, GP models with mixed inputs have been proposed to handle both numerical and categorical inputs. Using a case study of a high‐bay warehouse, we demonstrate the use of GP models with low‐rank correlation (LRC) kernels in the context of efficient global optimization (EGO). As is common in many logistics applications, the high‐bay warehouse is modeled with a discrete‐event simulation model. Input variables include, for example, the choice between different task assignment strategies. A shift scheduling problem is considered in which personnel and energy costs as well as the delay of tasks are to be minimized at the same time. Evaluations of an initial experimental design provide a first approximation of the Pareto front, which we manage to extend substantially within only 15 iterations of identifying new points using the expected hypervolume improvement (EHI) and the metric selection (SMS) criteria. We penalize the criteria in the last five iterations using the known total costs of proposed points to guide the search towards a more desired area. The resulting Pareto front approximation provides a selection of shift plans that have different characteristics. This enables decision makers in practice to choose a shift plan with desirable features.