Robust optimization (RO) is a well-known methodology used in applications where the worst-case scenario of uncertainty must be prevented. A drawback of this approach is that it does not optimize for non-worst-case scenarios and may result in over-conservative solutions. Pareto robust optimization (PRO) is a recent methodology that can further optimize for non-worst-case scenarios and generate less conservative robust solutions when a non-worst-case scenario occurs. In this paper, we extend the theory of Pareto robust optimization to enhance its applicability to practical settings where expert knowledge on likely uncertain scenarios exists. We define and characterize superior PRO solutions and develop algorithms that can partition the set of RO solutions to determine the Pareto robust frontier of superior PRO solutions. We demonstrate how this Pareto frontier can aid decision-makers in determining superior solutions, based on their expert knowledge of the application. To further reduce the conservatism of the PRO solutions, we also introduce the concept of light PRO solutions that slightly sacrifice the worst-case performance to improve non-worst-case behavior while maintaining the robustness of the solution guaranteed. We quantify the gain in non-worst-case scenarios as a function of worst-case loss, discuss the theoretical properties of this gain
function, and analyze the trade-off between worst-case optimality and non-worst-case performance. We illustrate the application of the proposed approach to the radiation therapy treatment planning for breast cancer using realistic patient data sets. The results of both a basic and a clinical case study confirm that the proposed approach can significantly improve the quality of the solution in non-worst-case scenarios while maintaining robustness and limiting the optimality error of the worst-case outcome within a reasonable threshold.

In our research we look to optimize long-term strategic decisions regarding the production, transportation and storage of hydrogen for an industrial cluster in the Netherlands. As the long-term future is highly uncertain, there is much parametric uncertainty regarding future developments in technology, economics and policymaking. As a first step we apply Robustness Analysis to examine the robustness of the nominal solution, where we extend the methodology to a multistage adaptive optimization setting. As a second step, we apply our novel method “Robust Optimization by Iterative Scenario Sampling and Statistical Testing” to obtain a more robust solution.

In light of rapidly decreasing costs of renewable energy technologies, companies are increasingly looking to integrate renewable energy sources into their energy mix. In the last decade, the costs of solar, wind, and battery energy storage systems have fallen by 90\%, 70\%, and 85\% respectively, making clean energy projects increasingly cost-effective compared to fossil fuel-based energy, especially for large-scale operations with long-term planning horizons. However, the intermittent nature of renewable energy sources, such as solar and wind, poses significant reliability challenges for energy systems, especially when coupled with the need to meet growing energy demands. In this work, we collaborate with OCP, one of the world's largest exporters of phosphate rock and fertilizers, to achieve their ambitious goal of decarbonizing their energy mix by 2027, while expanding their operations to meet a projected energy demand of approximately 12 TWh per annum by 2030, which is four times their current energy consumption and nearly a quarter of Morocco's current electricity production. We develop a holistic, tractable, and robust framework for decarbonization at OCP, which addresses the challenges of integrating solar and wind energy sources over a long-term planning horizon. This framework consists of two main components: (i) a robust strategic capacity expansion planning model that determines the up-front capital expenditures (CAPEX) for renewable energy installations and battery placement decisions, and (ii) an adaptive robust economic dispatch model that provides operational policies on an hourly basis for energy transmission, generation, and procurement, and also serves to validate the robustness of the strategic decisions. Our framework is designed to be utilized by a broad range of stakeholders in the renewable energy sector, with a focus on facilitating bankable feasibility studies, including detailed modeling of the Levelized Cost of Electricity (LCOE), strategic CAPEX planning, and validation of robustness guarantees, akin to P50/P95/P99 exceedance probabilities used by lenders. After simulating the final robust strategic decisions, we achieve a 97\% clean energy utilization starting in 2027.

Earthquakes are one of the deadliest natural disasters that can cause catastrophic damages, leading to loss of life and property and displacing thousands of people. Often, most earthquakes are followed by major and minor aftershocks. The aftershocks could also lead to other secondary disasters like tsunamis, floods, avalanches, building collapses, etc. Thus, it is crucial to take into account the damages caused by aftershocks in the planning process. In this paper, we study an uncapacitated facility location problem for storing relief materials in the event of such a disaster. We adopt a two-stage budgeted-robustness approach. We consider a major earthquake in the first stage, followed by aftershocks in the second stage. We propose several Mixed-Integer Linear Programming formulations for our problem and employ Branch-and-Cut methods to solve two of them. We analyze the performance of our models on synthetically generated instances and provide a case study on Turkey which is highly prone to earthquakes. Finally, we provide managerial insights regarding, in particular, the relevance of modeling the second-stage aftershocks and its impact on optimal locations.