Applications – Science and Engineering

Sparse Multiple Kernel Learning: Alternating Best Response and Semidefinite Relaxations

  • Dimitris Bertsimas
  • Caio de Próspero Iglesias
  • Nicholas A. G. Johnson
    • Categories Convex Optimization, Semi-definite Programming, Statistics Tags , , , ,

    We study Sparse Multiple Kernel Learning (SMKL), which is the problem of selecting a sparse convex combination of prespecified kernels for support vector binary classification. Unlike prevailing \(\ell_1\)‐regularized approaches that approximate a sparsifying penalty, we formulate the problem by imposing an explicit cardinality constraint on the kernel weights and add an \(\ell_2\) penalty for robustness. … Read more

    An Optimal Solution is Not Enough: Alternative Solutions and Optimal Power Systems

  • Matthew Viens
  • William E. Hart
  • Michael C. Ferris
    • Categories Applications - Science and Engineering, Energy, Optimization Software and Modeling Systems Tags , , , ,

    Power systems modeling and planning has long leveraged mathematical programming for its ability to provide optimality and feasibility guarantees. One feature that has been recognized in the optimization literature since the 1970s is the existence and meaning of multiple exact optimal and near-optimal solutions, which we call alternative solutions. In power systems modeling, the use … Read more

    An alternating optimization approach for robust optimal control in chromatography

  • Dominik H. Cebulla
  • Andrea Gilch
  • Jan Hendrik Rolfes
  • Christian Kirches
  • Frauke Liers
    • Categories Optimization of Systems modeled by PDEs, Robust Optimization Tags , ,

    Chromatographic separation plays a vital role in various areas, as this technique can deliver high-quality products both in lab- and industrial-scale processes. Economical and also ecological benefits can be expected when optimizing such processes with mathematical methods. However, even small perturbations in the operating conditions can result in significantly altered results, which may lead to … Read more

    Stronger cuts for Benders’ decomposition for stochastic Unit Commitment Problems based on interval variables

  • Azema
  • Vincent Leclère
  • Wim van Ackooij
    • Categories (Mixed) Integer Linear Programming, Energy, Stochastic Programming Tags , ,

    The Stochastic Unit Commitment (SUC) problem models the scheduling of power generation units under uncertainty, typically using a two-stage stochastic program with integer first-stage and continuous second-stage variables. We propose a new Benders decomposition approach that leverages an extended formulation based on interval variables, enabling decomposition by both unit and time interval under mild technical … Read more

    Faster Solutions to the Interdiction Defense Problem using Suboptimal Solutions

  • Joshua Ong
    • Categories (Mixed) Integer Linear Programming, Energy Tags ,

    The interdiction defense (ID) problem solves a defender-attacker-defender model where the defender and attacker share the same set of components to harden and target. We build upon the best response intersection (BRI) algorithm by developing the BRI with suboptimal solutions (BRI-SS) algorithm to solve the ID problem. The BRI-SS algorithm utilizes off-the-shelf optimization solvers that … Read more

    Two-Stage Data-Driven Contextual Robust Optimization: An End-to-End Learning Approach for Online Energy Applications

  • Carlos Gamboa
  • Alexandre Street
  • Davi Valladão
  • Bernardo K. Pagnoncelli
    • Categories Energy, Robust Optimization, Stochastic Programming Tags , , ,

    Traditional end-to-end contextual robust optimization models are trained for specific contextual data, requiring complete retraining whenever new contextual information arrives. This limitation hampers their use in online decision-making problems such as energy scheduling, where multiperiod optimization must be solved every few minutes. In this paper, we propose a novel Data-Driven Contextual Uncertainty Set, which gives … Read more

    Towards robust optimal control of chromatographic separation processes with controlled flow reversal

  • Dominik H. Cebulla
  • Christian Kirches
  • Andreas Potschka
    • Categories Chemical Engineering, Robust Optimization, Systems governed by Differential Equations Optimization Tags , ,

    Column liquid chromatography is an important technique applied in the production of biopharmaceuticals, specifically for the separation of biological macromolecules such as proteins. When setting up process conditions, it is crucial that the purity of the product is sufficiently high, even in the presence of perturbations in the process conditions, e.g., altered buffer salt concentrations. … Read more

    Optimal participation of energy communities in electricity markets under uncertainty. A multi-stage stochastic programming approach

  • Albert Solà Vilalta
  • Ignasi Mañé Bosch
  • F.-Javier Heredia
    • Categories Energy, Stochastic Programming Tags , , ,

    We propose a multi-stage stochastic programming model for the optimal participation of energy communities in electricity markets. The multi-stage aspect captures the different times at which variable renewable generation and electricity prices are observed. This results in large-scale optimization problem instances containing large scenario trees with 34 stages, to which scenario reduction techniques are applied. … Read more

    Solution of Stochastic Facility Location Problems with Combinatorially many Decision-Dependent Distributions

  • Giovanni Pantuso
    • Categories Combinatorial Optimization, Facility Planning and Design, Stochastic Programming

    This article describes a model and an exact solution method for facility location problems with decision-dependent uncertainties. The model allows characterizing the probability distribution of the random elements as a function of the choice of open facilities. This, in turn, generates a combinatorial number of potential distributions of the random elements. Though general in the … Read more

    Measuring the Economic Value of Wind–Solar Complementarity in Europe Using Chance Constraints

  • Montree Jaidee
  • Bismark Singh
    • Categories Energy, Stochastic Programming Tags , , , ,

    The variability of wind and solar photovoltaic (PV) generation poses significant risks for producers in day-ahead electricity markets, where commitments must be made before actual output is realized. A common mitigation strategy is to invest in storage, but an alternative is to exploit the natural complementarity between wind and solar resources. We evaluate this economic … Read more