3 Presentations

• 
  03:30 PM - 03:55 PM

  A Trust-Region-Based Bayesian Optimization Method for Mixed-Variable Spaces

  • Meisseme Kadri, presenter,
  • Youssef Diouane, Polytechnique Montréal
  • Amina Lamghari, Université du Québec à Trois-Rivières
  • Issmail El Hallaoui, Polytechnique Montréal

  Hyper-parameter tuning is a critical yet computationally demanding Black-Box Optimization (BBO) problem, particularly in relation to deep learning tasks. Existing BBO techniques, including Bayesian Optimization (BO), often struggle with mixed-variable search spaces that include continuous, integer, and categorical variables. In this work, we introduce a mixed-variable framework for BO, integrating a Trust-Region (TR) mechanism to allow alternating between local (within the vicinity of the trust region) and global (exploring regions beyond the trust region) BO steps. The proposed framework not only enhances performance but also ensures asymptotic convergence. The proposed approach constructs a Gaussian Process tailored for mixed-variables and optimizes the acquisition function over the mixed-variable domain to ensure an efficient exploration of the mixed search space. The potential of the proposed framework is first illustrated on a set of analytical test cases. The framework is then tested on a deep learning-related task, where we aim to tune the hyper-parameters of MobileNetV2—a lightweight convolutional neural network—on a garbage classification dataset. Our framework demonstrates improved computational efficiency and model performance compared to classical BO methods.

• 
  03:55 PM - 04:20 PM

  CatMADS: categorical variables with the MADS algorithm

  • Edward Hallé-Hannan, presenter, Polytechnique
  • Charles Audet, GERAD - Polytechnique Montréal
  • Sébastien Le Digabel, GERAD, Polytechnique Montréal
  • Youssef Diouane, Polytechnique Montréal
  • Christophe Tribes, GERAD-Polytechnique

  Solving optimization problems where functions lack explicit expressions and variables involve different types poses significant theoretical and algorithmic challenges. Nevertheless, such settings often occur in simulation-based engineering design and machine learning. In this talk, the mesh adaptive direct search (MADS) algorithm is extended to mixed-variable problems. MADS is a robust derivative-free optimization framework with a well-established convergence analysis for constrained quantitative problems. CatMADS generalizes MADS by incorporating categorical variables, handled via distance-induced neighborhoods. Different types of local minima are introduced for the class of problems and developing theoretical results. An exhaustive convergence analysis of CatMADS is provided, with flexible choices balancing computational cost and local optimality strength. CatMADS integrates the progressive barrier strategy for handling constraints with guarantees. An instance of CatMADS employs cross-validation to construct problem-specific categorical distances. The instance is benchmarked against state-of-the-art solvers on 32 new mixed-variable problems, half of which are constrained. Data profiles show CatMADS achieves the best results, demonstrating that the framework is empirically efficient in addition to having strong theoretical foundations.

• 
  04:20 PM - 04:45 PM

  Blackbox Optimization for Loss Minimization in Power Distribution Networks using Feeder Reconfiguration

  • Christina G. Soldati, presenter, Polytechnique Montréal, GERAD
  • Sébastien Le Digabel, GERAD, Polytechnique Montréal
  • Antoine Lesage-Landry, Polytechnique Montréal

  Modern power distribution networks (DNs) incorporate a growing number of active distribution network (ADN) technologies, such as distributed energy resources (DERs) and remotely activated switches. As a DN is a naturally unbalanced system due to the multi-phased highly fluctuating demand, DERs which can lead to bi-directional power flow amplify the phase imbalance, reducing system reliability and efficiency. The proposed network topology reconfiguration method uses tie and sectionalizing switches to minimize power losses in a three-phase unbalanced DN equipped with DERs. Strict, practical feasibility of the solution is ensured by using a high-accuracy load-flow simulator, and by formulating the problem as a blackbox optimization (BBO) problem, solved with the NOMAD software package. To circumvent the computational burden of BBO, combinatorial optimization-inspired algorithms are introduced and adapted to the DN context, namely the variable neighbourhood search (VNS) metaheuristic and the branch-and-bound (BB) framework. VNS incorporates a random component, thus potentially leading to faster progress toward a good solution. BB approximates the mechanisms underlying the exact branch-and-bound method used in mixed-integer programming, though its performance remains highly sensitive to the choice of initial point. Consequently, three methods using various combinations of a standalone BBO problem, a VNS, and a BB, are tested and compared. Each optimization technique being the warm start for the next induces constant improvement on the solution quality. These methods are tested on the modified IEEE 34-bus and 136-bus test feeders, both integrating DERs. The final solution typically results in a network topology that differs from the initial configuration, and the power losses are considerably diminished, illustrating the direct impact of combining local generation and network reconfiguration to improve the DN efficiency.