Gurobi-machinelearning is an open-source python package to formulate trained regression models in a gurobipy model that can then be solved with the Gurobi solver. We will present this package with a focus on trained neural networks. Representing such as constraints in a MIP leads to large models. Optimization based bound tightening (OBBT) can be used to improve performance for solving such models. We will discuss how Gurobi has been extended to perform OBBT tailored to NN models and present performance results.

Neural networks have been traditionally overlooked in critical sectors, e.g., energy. Even though they tend to be successful nonlinear predictors, their lack of interpretability, limited performance guarantees, complex training procedures as well as high susceptibility to data corruption and other adversarial attacks have labelled them as unreliable. Many solutions have been proposed in the past decade to guide and frame their training as much as possible, e.g., hyperparameter optimization, adversarial defense procedures, post-training verification frameworks, and tight MLOps lifecycle management. Still, these advances add up to training complexity and don't scale easily. In this work, we leverage recent results from distributionally robust optimization and convex learning to propose a new Wasserstein distributionally robust shallow convex neural network (WaDiRo-SCNN) with out-of-sample performance guarantees and simple low-stochasticity training. The training is formulated as a convex optimization problem efficiently solvable with open-source solvers. We first benchmark our model with a numerical study in a controlled synthetic environment. Lastly, we apply our approach to distribution feeder-specific impact prediction of commercial buildings enrolled in a demand response program

This paper presents a methodology for integrating machine learning techniques into metaheuristics for solving combinatorial optimization problems. Namely, we propose a general machine learning framework for neighbor generation in metaheuristic search. We first define an efficient neighborhood structure constructed by applying a transformation to a selected subset of variables from the current solution. Then, the key of the proposed methodology is to generate promising neighbors by selecting a proper subset of variables that contains a descent of the objective in the solution space. To learn a good variable selection strategy, we formulate the problem as a classification task that exploits structural information from the characteristics of the problem and from high-quality solutions. We validate our methodology on two metaheuristic applications: a Tabu Search scheme for solving a Wireless Network Optimization problem and a Large Neighborhood Search heuristic for solving Mixed-Integer Programs. The experimental results show that our approach is able to achieve a satisfactory trade-offs between the exploration of a larger solution space and the exploitation of high-quality solution regions on both applications.

Optimizing industrial mining complexes (mineral supply/value chains), from extraction to end-product delivery, presents significant challenges due to non-linearities and multiple sources of uncertainty, including in supply and demand. The two-stage stochastic integer program results in formulations with tens of millions of variables and nonlinear constraints, challenging the computational limits of state-of-the-art solvers. To address this computational complexity and streamline the optimization process, a novel distributionally robust warm-starting framework is introduced.

Leveraging historical solutions, a graph-based predictive model is trained to learn connectivity probabilities of mining blocks. Subsequently, resource-constrained min-cost max-flow problems are solved to establish initial production schedules that adhere to operational constraints and capture uncertainties related to both the optimization problem and the predictive model. An ambiguity set, constructed from historical connectivities, shifts the warm-start from a deterministic single point estimate -common in mining- to a distributionally robust optimization approach.

The framework captures the spatial distribution and inherent uncertainty of mining operations, yielding a diverse solution set for different scenarios and/or a singular risk-aware solution informed by block connectivity probabilities. Theoretical analysis and computational experiments demonstrate significant computational efficiencies and enhanced decision-making robustness. We discuss these findings, potential limitations, and future research directions for developing robust, reasoning, and responsible decision support systems for large-scale industrial applications under uncertainty.