Constructing uncertainty sets as unions of multiple subsets has emerged as an effective approach for creating compact and flexible uncertainty representations in data-driven robust optimization (RO). This paper focuses on two separate research questions. The first concerns the computational challenge in applying these uncertainty sets in RO-based predictive control. To address this, a monolithic mixed-integer representation of the uncertainty set is proposed to uniformly describe the union of multiple subsets, enabling the computation of the worst-case uncertainty scenario across all subsets within a single mixed-integer linear programming (MILP) problem. The second research question focuses on mitigating the conservatism of conventional RO formulations by leveraging the structure of the uncertainty set. To achieve this, a novel objective function is proposed to exploit the uncertainty set structure and integrate the existing RO and distributionally robust optimization (DRO) formulations, yielding less conservative solutions than conventional RO formulations, while avoiding the high-dimensional continuous uncertainty distributions and the high computational burden typically associated with existing DRO formulations. Given the proposed formulations, numerically efficient computation methods based on column-and-constraint generation (CCG) are also developed. Extensive simulations across three case studies are performed to demonstrate the effectiveness of the proposed schemes.

Corruption is a familiar and pressing problem in the performance of administrative bureaucracies. Changing the organisational structure is one way ventured to combat corrupt practices within a hierarchical organisation. Previous works have studied organisational change from various lenses, including equation-based modelling. We address the question of what level of hierarchy is optimal in such an organisation by means of agent-based simulation. We argue that agent-based models are uniquely suited for the exploratory modelling of corruption due to their capturing of localised, individualised behaviours. Our preliminary findings are that a less hierarchical organisational structure: 1) tend to lead to less corrupt acts committed, and 2) tends to lead to more societal welfare generated – however, 3) less corruption and more societal welfare do not always go hand in hand. We begin to reconcile these seemingly paradoxical results using theories from developmental economics.

Training neural networks (NNs) using combinatorial optimization solvers has gained attention in recent years. In low-data settings, the use of state-of-the-art mixed integer linear programming solvers, for instance, has the potential to exactly train an NN while avoiding computing-intensive training and hyperparameter tuning and simultaneously training and sparsifying the network. We study the case of few-bit discrete-valued neural networks, both binarized neural networks (BNNs) whose values are restricted to 61 and integer-valued neural networks (INNs) whose values lie in the range {―P, ::: , P}. Few-bit NNs receive increasing recognition because of their lightweight architecture and ability to run on low-power devices: for example, being implemented using Boolean operations. This paper proposes new methods to improve the training of BNNs and INNs. Our contribution is a multiobjective ensemble approach based on training a single NN for each possible pair of classes and applying a majority voting scheme to predict the final output. Our approach results in the training of robust sparsified networks whose output is not affected by small perturbations on the input and whose number of active weights is as small as possible. We empirically compare this BeMi approach with the current state of the art in solver-based NN training and with traditional gradient-based training, focusing on BNN learning in few-shot contexts. We compare the benefits and drawbacks of INNs versus BNNs, bringing new light to the distribution of weights over the {―P, ::: , P} interval. Finally, we compare multiobjective versus single-objective training of INNs, showing that robustness and network simplicity can be acquired simultaneously, thus obtaining better test performances. Although the previous state-of-the-art approaches achieve an average accuracy of 51:1% on the Modified National Institute of Standards and Technology data set, the BeMi ensemble approach achieves an average accuracy of 68.4% when trained with 10 images per class and 81.8% when trained with 40 images per class while having up to 75.3% NN links removed.

Future energy markets for low voltage AC and DC distribution systems will facilitate prosumer participation in the market. To comply with market regulations and grid constraints, a tailored market design reflecting (DC) operational requirements is needed. Our previous work identified a locational energy market design. However, its real-life implementation faces challenges due to uncertainties in system operation, prosumer preferences, and bidding strategies. This article tests the market design under uncertain scenarios. To this end, we develop an agent-based model that simulates typical electric vehicle user preferences and bidding strategies, influenced by varying degrees of range anxiety. The market design is tested in challenging scenarios with a high share of solar panels and electric vehicles, modelled using the high-resolution Pecan Street database. Simulations indicate that the proposed market design maintains both economic efficiency and system reliability under real-life uncertainties. This in turn indicates the practical feasibility of locational energy markets in helping to integrate renewable generation sources and bidirectional power flows.

Carbon capture and sequestration initiatives make new demands on modern reservoir simulators. To find optimal locations and volumes of CO2 to inject into a subsurface to maximize CO2 storage, we must simulate a large ensemble of injection cases. One possible solution to the computational complexity of this task is to employ machine-learning models which, after a one-off overhead cost of training, can infer and predict future states of a reservoir several orders of magnitude faster than traditional methods. Most previous work in the literature has primarily focused on either convolution-based methods or, more recently, neural operator-based methods, to predict the evolution of state variables. These architectures have shown promise in predicting on structured reservoir grids but lack the capability to extend the same level of accuracy to unstructured grids. Graph neural networks (GNNs) overcome this bottleneck by incorporating inductive biases arising from local message-passing mechanisms, facilitating convolution operations over complex graphs and meshes. In this work, we present a novel autoregressive GNN autoencoder to predict time-varying state variables for an ensemble of CO2 injection cases. We implement a graph convolution network for the message-passing protocol and incorporate physics-informed edge weights between cell connections to guide flow. An exhaustive set of node features are used to train the model on the hyperbolic evolution of phase saturations while preserving the ellipticity in the pressure. We test the performance of the GNN model for (1) its ability to predict state variables for varying injection rates of CO2, (2) for the post-injection phase, and (3) under different unseen geological configurations. Training and testing are performed by constructing ensembles of 2D, 3D, and real field cases that best represent these scenarios. For the 2D regular grid case, we observe that the model can capture pressure and saturation values accurately, even for highly varying injection rates and with only a limited amount of data. This performance is maintained in the post-injection phase. A key advantage of GNNs is that they show a distinct ability for transfer learning on ensembles of unseen geological configurations. We observe that the model can predict the shape and intensity of wavefronts of certain cases with no prior exposure to the specific static properties during training. Similar results are produced for 3D grids and real field cases.

The way how the uncertainties are represented by sets plays a vital role in the performance of robust optimization (RO). This paper presents a novel approach leveraging machine learning (ML) techniques to construct data-driven uncertainty sets from historical uncertainty data for RO problems. The proposed method integrates Density-Based Spatial Clustering of Applications with Noise (DBSCAN), Gaussian Mixture Model (GMM), and Principle Component Analysis (PCA) systematically to eliminate the influence of uncertainty scenarios with low occurrence probability and generate a nonconvex uncertainty set that is a union of multiple basic subsets (box or ellipsoid) without sacrificing its computational tractability. In addition to presenting a comprehensive algorithm for uncertainty set development, this paper offers detailed guidelines for parameter tuning and performance analysis. By harnessing the well-established ML packages scikit-learn, a Python-based toolkit for implementing the proposed approach is also provided. Furthermore, a computationally efficient solution for a two-stage linear RO problem with the proposed data-driven uncertainty set is derived, alongside establishing a probabilistic guarantee of constraint satisfaction for out-of-sample uncertainties. Extensive numerical experiments, conducted on both synthetic and real-world datasets as well as an optimization-based control problem, are performed to demonstrate the efficacy of the proposed methodology.