Anya Castillo

Decomposing Optimization-Based Bounds Tightening Problems Via Graph Partitioning

  • Michael Lee Bynum
  • Anya Castillo
  • Bernard Knueven
  • Carl D. Laird
  • Jean-Paul Watson
  • John D. Siirola
    • Categories Global Optimization

    Bounds tightening or domain reduction is a critical refinement technique used in global optimization algorithms for nonlinear and mixed-integer nonlinear programming problems. Bounds tightening can strengthen convex relaxations and reduce the size of branch and bounds trees. An effective but computationally intensive bounds tightening technique is optimization-based bounds tightening (OBBT). In OBBT, each variable is … Read more

    A Computationally Efficient Algorithm for Computing Convex Hull Prices

  • Anya Castillo
  • Bernard Knueven
  • James Ostrowski
  • Jean-Paul Watson
    • Categories Applications - OR and Management Sciences Tags , , , ,

    Electricity markets worldwide allow participants to bid non-convex production offers. While non-convex offers can more accurately reflect a resource’s capabilities, they create challenges for market clearing processes. For example, system operators may be required to execute side payments to participants whose costs are not covered through energy sales as determined via traditional locational marginal pricing … Read more

    Tightening McCormick Relaxations Toward Global Solution of the ACOPF Problem

  • Michael Lee Bynum
  • Anya Castillo
  • Carl D. Laird
  • Jean-Paul Watson
    • Categories Global Optimization Applications Tags , ,

    We show that a strong upper bound on the objective of the alternating current optimal power flow (ACOPF) problem can significantly improve the effectiveness of optimization-based bounds tightening (OBBT) on a number of relaxations. We additionally compare the performance of relaxations of the ACOPF problem, including the rectangular form without reference bus constraints, the rectangular … Read more

    Global Solution Strategies for the Network-Constrained Unit Commitment Problem With AC Transmission Constraints

  • Anya Castillo
  • Carl D. Laird
  • Jean-Paul Watson
  • Jianfeng Liu
    • Categories Global Optimization, Integer Programming, Nonlinear Optimization Tags , ,

    We propose a novel global solution algorithm for the network-constrained unit commitment problem that incorporates a nonlinear alternating current model of the transmission network, which is a nonconvex mixed-integer nonlinear programming (MINLP) problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. … Read more