WA9 - Data-Driven Optimization

We develop mixed-integer linear programming formulations for multivariate piecewise-linear surrogate models based on radial-basis-function interpolation and regression. We study interpolation feasibility and surrogate complexity, derive compact MILP formulations expressible as sums of univariate piecewise-linear functions, and demonstrate computational advantages over existing surrogate- and partition-based MILP formulations.

We investigate an online learning problem for resource allocation, where the exact convex cost functions are unknown but noisy post-allocation cost observations are available. This type of problem falls under bandit convex optimization, for which typical algorithms are designed to learn the deterministic optimal policy directly. Different from these approaches, we study the problem from a new perspective of stochastic policies: we use Dirichlet distributions to parameterize resource-allocation policies and reformulate the task from finding the best allocation plan to identifying the optimal Dirichlet parameters. We show that a naive parameterization can lead to a nonconvex optimization problem, but this issue can be addressed by revealing hidden convexity through an appropriate reparameterization. We then propose an online learning algorithm for the resulting parameter-search problem.

Optimal pressure sensor placement is a critical task for leak localization, essential for minimizing potable water losses in water distribution networks and preventing environmental disasters in chemical or wastewater transport systems. An effective placement strategy minimizes the number of sensors required while ensuring the efficient detection of leaks across the entire network. This work proposes a bi-objective formulation, solved using the NSGA-II algorithm, that explicitly accounts for measurement noise and flowrate uncertainty. The algorithm simultaneously minimizes two complementary criteria: (1) a distance-weighted mean error index that quantifies average localization accuracy across all leak scenarios, and (2) a worst-case error index that evaluates the maximum localization failure under severe uncertainty. The methodology relies on hydraulic simulations performed with WNTR, where leak scenarios are generated by varying emitter coefficients and injecting Gaussian measurement noise to simulate real-world hardware limits. The approach is validated on the benchmark Hanoi network and compared against literature. Results demonstrate that the proposed farmwork provides decision-makers with highly interpretable trade-offs between accuracy and reliability, yielding sensor configurations that avoid the blind spots inherent to single-objective solutions. The proposed framework is computationally efficient and scalable to real-world networks.

Underground mining operations rely heavily on rotating machinery, particularly axial fans, whose performance directly impacts energy consumption and operational safety. Such systems are frequently analysed using high-fidelity simulations, but their high computational simulations cost restricts their utility in iterative design and optimisation procedures. A reduced-order modelling (ROM) approach for the effective simulation and optimisation of rotating equipment is presented in this article. The suggested method uses projection-based methods, combining Galerkin projection and the Proper Orthogonal Decomposition (POD) to provide a low-dimensional dynamical model that maintains the unsteady effects and dominant flow characteristics. To investigate how operating parameters affect system performance, the simplified model is included into an optimisation framework. The goal is to reduce computational time while improving important performance metrics. According to preliminary findings, the ROM predicts relevant quantities of interest with adequate accuracy while achieving significant computational savings when compared to high-fidelity simulations. This enables efficient parametric studies and supports the optimization of complex rotating machinery under realistic operating conditions. With special relevance to mining applications, the suggested methodology provides a useful and computationally effective tool for the optimisation of axial fans in industrial settings.