Applications – Science and Engineering

AI Hilbert: From Data and Background Knowledge to Automated Scientific Discovery

  • Ryan Cory-Wright
  • Bachir El Khadir
  • Sanjeeb Dash
    • Categories Basic Sciences Applications, Global Optimization Applications, Semi-definite Programming Tags , , ,

    The discovery of scientific formulae that parsimoniously explain natural phenomena and align with existing background theory is a key goal in science. Historically, scientists have derived natural laws by manipulating equations based on existing knowledge, forming new equations, and verifying them experimentally. In recent years, data-driven scientific discovery has emerged as a viable competitor in settings with … Read more

    Routing a fleet of unmanned aerial vehicles: a trajectory optimisation-based framework

  • Walton P. Coutinho
  • Jörg Fliege
  • Maria Battarra
  • Anand Subramanian
    • Categories (Mixed) Integer Nonlinear Programming, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags , , ,

    We consider the problem in which a fleet of unmanned aerial gliders is required to visit a number of locations and then land in one of the available landing sites while optimising some performance criteria, subject to operational constraints and flight dynamics. Such problems frequently occur in disaster mitigation, where fast aerial reconnaissance of points … Read more

    Switching Time Optimization for Binary Quantum Optimal Control

  • Xinyu Fei
  • Lucas Brady
  • Jeffrey Larson
  • Sven Leyffer
  • Siqian Shen
    • Categories (Mixed) Integer Nonlinear Programming, Basic Sciences Applications, Control Applications Tags , ,

    Quantum optimal control is a technique for controlling the evolution of a quantum system and has been applied to a wide range of problems in quantum physics. We study a binary quantum control optimization problem, where control decisions are binary-valued and the problem is solved in diverse quantum algorithms. In this paper, we utilize classical … Read more

    A Multicut Approach to Compute Upper Bounds for Risk-Averse SDDP

  • Joaquim Dias Garcia
  • Mario Pereira
    • Categories Dynamic Programming, Energy, Stochastic Programming Tags , , , ,

    Stochastic Dual Dynamic Programming (SDDP) is a widely used and fundamental algorithm for solving multistage stochastic optimization problems. Although SDDP has been frequently applied to solve risk-averse models with the Conditional Value-at-Risk (CVaR), it is known that the estimation of upper bounds is a methodological challenge, and many methods are computationally intensive. In practice, this … Read more

    A Polynomial Algorithm for the Lossless Battery Charging Problem

  • James Ostrowski
    • Categories Applications - Science and Engineering, Energy, Network Optimization Tags , ,

    This study presents a polynomial time algorithm to solve the lossless battery charging problem. In this problem the optimal charging and discharging schedules are chosen to maximize total profit. Traditional solution approaches have relied on either approximations or exponential algorithms. By studying the optimality conditions of this problem, we are able to reduce it to … Read more

    Sharpness and well-conditioning of nonsmooth convex formulations in statistical signal recovery

  • Lijun Ding
  • Alex L. Wang
    • Categories Nonsmooth Optimization, Optimization in Data Science, Statistics Tags , , , , ,

    \(\) We study a sample complexity vs. conditioning tradeoff in modern signal recovery problems where convex optimization problems are built from sampled observations. We begin by introducing a set of condition numbers related to sharpness in \(\ell_p\) or Schatten-p norms (\(p\in[1,2]\)) based on nonsmooth reformulations of a class of convex optimization problems, including sparse recovery, … Read more

    Improved Rank-One-Based Relaxations and Bound Tightening Techniques for the Pooling Problem

  • Mosayeb Jalilian
  • Burak Kocuk
    • Categories Applications - Science and Engineering Tags , , ,

    The pooling problem is a classical NP-hard problem in the chemical process and petroleum industries. This problem is modeled as a nonlinear, nonconvex network flow problem in which raw materials with different specifications are blended in some intermediate tanks, and mixed again to obtain the final products with desired specifications. The analysis of the pooling … Read more

    A Tailored Derivative Instrument to Mitigate the Price-and-Quantity Risk faced by Wind Power Companies

  • Maria de Fatima Lacerda Barbosa
  • Alexandre Street
  • Bruno F. Santos
    • Categories Energy, Finance and Economics Tags , , , , ,

    The intermittent nature of wind generation combined with the well-known volatility of electricity spot prices expose Wind Power Companies (WPCs) committed to long-term forward contracts to the so-called price-and-quantity risk. Several instruments were designed in the past years to mitigate this risk exposure. However, most of them were mainly constructed to cope with only one … Read more

    Accreditation, Performance, and Credit Risk in Electricity Capacity Markets

  • Jacob Mays
    • Categories Energy, Finance and Economics Tags , , , ,

    Many liberalized electricity markets use capacity mechanisms to ensure that sufficient resources will be available in advance of operations. Recent events have called into question the ability of capacity mechanisms to provide sufficient incentives for reliability. A core resource adequacy challenge is that, given the high value of reliable electricity, penalties for non-performance on capacity … Read more

    Compressed Sensing: A Discrete Optimization Approach

  • Dimitris Bertsimas
  • Nicholas A. G. Johnson
    • Categories (Mixed) Integer Nonlinear Programming, Second-Order Cone Programming, Statistics Tags , , , ,

    We study the Compressed Sensing (CS) problem, which is the problem of finding the most sparse vector that satisfies a set of linear measurements up to some numerical tolerance. CS is a central problem in Statistics, Operations Research and Machine Learning which arises in applications such as signal processing, data compression and image reconstruction. We … Read more