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Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work introduces a new class of constraints in which the same black-box function occurs multiple times evaluated at different domain points. Such constraints are important in applications where, e.g., safety-critical measures are aggregated over multiple time periods. Our approach, which uses robust optimization, reformulates these uncertain constraints into deterministic constraints guaranteed to be satisfied with a specified probability, i.e., deterministic approximations to a chance constraint. This approach extends robust optimization methods from parametric uncertainty to uncertain functions modeled by warped Gaussian processes. We analyze convexity conditions and propose a custom global optimization strategy for non-convex cases. A case study derived from production planning and an industrially relevant example from oil well drilling show that the approach effectively mitigates uncertainty in the learned curves. For the drill scheduling example, we develop a custom strategy for globally optimizing integer decisions.

The pooling problem has applications, e.g., in petrochemical refining, water networks, and supply chains and is widely studied in global optimization. To date, it has largely been treated deterministically, neglecting the influence of parametric uncertainty. This paper applies two robust optimization approaches, reformulation and cutting planes, to the non-linear, non-convex pooling problem. Most applications of robust optimization have been either convex or mixed-integer linear problems. We explore the suitability of robust optimization in the context of global optimization problems which are concave in the uncertain parameters by considering the pooling problem with uncertain inlet concentrations. We compare the computational efficiency of reformulation and cutting plane approaches for three commonly-used uncertainty set geometries on 14 pooling problem instances and demonstrate how accounting for uncertainty changes the optimal solution.

In chemical and manufacturing processes, unit failures due to equipment degradation can lead to process downtime and significant costs. In this context, finding an optimal maintenance strategy to ensure good unit health while avoiding excessive expensive maintenance activities is highly relevant. We propose a practical approach for the integrated optimization of production and maintenance capable of incorporating uncertain sensor data regarding equipment degradation. To this end, we integrate data-driven stochastic degradation models from Condition-based Maintenance into a process level mixed-integer optimization problem using Robust Optimization. We reduce computational expense by utilizing both analytical and data-based approximations and optimize the Robust optimization parameters using Bayesian Optimization. We apply our framework to five instances of the State-Task-Network and demonstrate that it can efficiently compromise between equipment availability and cost of maintenance.