Abstract Constructing ambiguity sets in distributionally robust optimization is difficult and currently receives increased attention. In this paper, we focus on mixture models with finitely many reference distributions. We present two different solution concepts for robust joint chance-constrained optimization problems with these ambiguity sets and non-convex constraint functions. Both concepts rely on solving an approximation problem that is based on well-known smoothing and penalization techniques. On the one side, we consider a classical bundle method together with an approach for finding good starting points. On the other side, we integrate the Continuous Stochastic Gradient method, a variant of the stochastic gradient descent that is able to exploit regularity in the data. On the example of gas networks, we compare the two algorithmic concepts for different topologies and two types of mixture ambiguity sets with Gaussian reference distributions and polyhedral and $$\phi $$ ϕ -divergence based feasible sets for the mixing coefficients. The results show that both solution approaches are well-suited to solve this difficult problem class. Based on the numerical results, we provide some general advice for choosing the more efficient algorithm depending on the main challenges of the considered optimization problem. We give an outlook for the applicability of the method in a wider context.

Abstract Surrogate-based Bayesian optimization has been widely applied in design optimization to increase sampling efficiency. However, the cost for each evaluation of the objective function can still be very high when physical experiments or large-scale simulations are involved. Multi-fidelity Bayesian optimization is the new approach to further improve the sampling efficiency by reducing the number of expensive samples at the highest fidelity level and supplementing them with less expensive ones at low-fidelity levels. In this paper, a new consequential improvement (CI) acquisition function is proposed to allow for the simultaneous selection of the solution and the fidelity level in problems with a known hierarchy of fidelity levels. The new CI acquisition function incorporates the consequential effectiveness of objective improvement with the considerations of cost, accuracy, and validity differences between high- and low-fidelity samples in engineering practice. The new method of multi-fidelity Bayesian optimization based on the CI is demonstrated with several analytical and simulation-based design examples. In the simulation-based design optimization example, the results show that the CI acquisition function has a decisive advantage in the sampling efficiency over the other methods of multi-fidelity Bayesian optimization with simultaneous selection. The results indicate that the proposed method is particularly advantageous in solving high-dimensional problems and when large cost ratios between high- and low-fidelity evaluations exist and high-fidelity validation is mandatory. Furthermore, the method robustly avoids the prevalent issue of over sampling at low-fidelity levels.

Abstract Data-driven optimization utilizing machine learning has gained significant popularity in recent times. Nevertheless, machine learning methodologies often presuppose that the target variable of the dataset is uniformly distributed, leading to the imbalance problem. Classical approaches developed to address data imbalance are not suitable for application in the newsvendor problem due to the varying costs associated with over/under predictions. Additionally, there is a lack of appropriate metrics for selecting the correct model that accounts for imbalance in data-driven newsvendor problems. In this study, we propose a relevance-weighted (RW) learning framework adapted to deal with the imbalanced dataset and the newsvendor’s asymmetric costs, specifically by incorporating both demand rareness and over/under-prediction costs into a unified loss function. We also introduce the Newsvendor Error Cost Relevance Area (NECRA) metric, an adaptation of cumulative relevance-weighted metrics, specifically tailored for model selection under demand imbalance. Relevance-weighted learning allows researchers to construct a neural network model that assigns sample weights based on the rareness of demand values, thereby enabling the final model to predict rare demands more effectively than classical network models. We simulate an extensive amount of datasets with varying properties and compare our method to the classical data-driven newsvendor objective function. We analyze the findings using statistical tests and results confirm that relevance-weighted learning performs better for the imbalanced datasets.

Abstract Prescription drug collection boxes have been deployed in many communities to collect unused prescription opioids and other medications to prevent misuse. However, their current ad hoc placement leaves some communities without nearby disposal options. This paper addresses this issue by exploring how to evaluate the performance of a network of prescription collection boxes and how to locate new collection boxes. To do so, we introduce performance measures based on the set cover problem to identify areas lacking access to prescription collection boxes, termed “deserts.” We then formulate the Collection Box Location Problem, an integer programming model based on the maximal covering with mandatory closeness problem, to strategically identify sites for new prescription collection boxes. We present practical model variants that incorporate restrictions on placing boxes only at non-law enforcement facilities, relocation of existing boxes under a budget constraint, and penalties for leaving regions without nearby access. A case study using data from Wisconsin illustrates the applicability of our methodology.

Abstract Accurate parameter dependent electro-chemical numerical models for lithium-ion batteries are essential in industrial application. However, some parameters of each battery cell are unknown, so that a parameter estimation is necessary to infer them. The field of optimal input/experimental design deals with creating an optimal experimental settings facilitating the estimation problem. Here we apply two different input design algorithms that aim at maximizing the observability of the true, unknown parameters. As the design algorithms are built independent of the model, the same results and motivation are applicable to more complex battery cell models and, moreover, to other applications.