A Branch and Bound Algorithm for Biobjective Mixed Integer Quadratic Programs

  • Pubudu L.W. Jayasekara Merenchige
  • Margaret Wiecek
    • Categories (Mixed) Integer Nonlinear Programming, Integer Programming, Multi-Criteria Optimization Tags , , , , ,

    Multiobjective quadratic programs (MOQPs) are appealing since convex quadratic programs have elegant mathematical properties and model important applications. Adding mixed-integer variables extends their applicability while the resulting programs become global optimization problems. We design and implement a branch and bound (BB) algorithm for biobjective mixed-integer quadratic programs (BOMIQPs). In contrast to the existing algorithms in … Read more

    Second-order Partial Outer Convexification for Switched Dynamical Systems

  • Christoph Plate
  • Sebastian Sager
  • Martin Stoll
  • Manuel Tetschke
    • Categories Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , ,

    Mixed-integer optimal control problems arise in many practical applications combining nonlinear, dynamic, and combinatorial features. To cope with the resulting complexity, several approaches have been suggested in the past. Some of them rely on solving a reformulated and relaxed control problem, referred to as partial outer convexification. Inspired by an efficient algorithm for switching time … Read more

    A comparison of different approaches for the vehicle routing problem with stochastic demands

  • Matheus Jun Ota
  • Ricardo Fukasawa
    • Categories Branch and Cut Algorithms, Production and Logistics, Stochastic Programming Tags , ,

    The vehicle routing problem with stochastic demands (VRPSD) is a well studied variant of the classic (deterministic) capacitated vehicle routing problem (CVRP) where the customer demands are given by random variables. Two prominent approaches for solving the VRPSD model it either as a chance-constraint program (CC-VRPSD) or as a two-stage stochastic program (2S-VRPSD). In this … Read more

    On Generalization and Regularization via Wasserstein Distributionally Robust Optimization

  • Jonathan Yu-Meng Li
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Wasserstein distributionally robust optimization (DRO) has found success in operations research and machine learning applications as a powerful means to obtain solutions with favourable out-of-sample performances. Two compelling explanations for the success are the generalization bounds derived from Wasserstein DRO and the equivalency between Wasserstein DRO and the regularization scheme commonly applied in machine learning. … Read more

    Handling Symmetries in Mixed-Integer Semidefinite Programs

  • Christopher Hojny
  • Marc E. Pfetsch
    • Categories (Mixed) Integer Nonlinear Programming, Semi-definite Programming Tags , ,

    Symmetry handling is a key technique for reducing the running time of branch-and-bound methods for solving mixed-integer linear programs. In this paper, we generalize the notion of (permutation) symmetries to mixed-integer semidefinite programs (MISDPs). We first discuss how symmetries of MISDPs can be automatically detected by finding automorphisms of a suitably colored auxiliary graph. Then … Read more

    Handling Sub-symmetry in Integer Programming using Activation Handlers

  • Christopher Hojny
  • Tom Verhoeff
  • Sten Wessel
    • Categories Integer Programming Tags , ,

    Symmetry in integer programs (IPs) can be exploited in order to reduce solving times. Usually only symmetries of the original IP are handled, but new symmetries may arise at some nodes of the branch-and-bound tree. While symmetry-handling inequalities (SHIs) can easily be used to handle original symmetries, handling sub-symmetries arising later on is more intricate. … Read more

    Decremental State-Space Relaxations for the Basic Traveling Salesman Problem with a Drone

  • Marcos Blufstein
  • Gonzalo Lera-Romero
  • Francisco J. Soulignac
    • Categories Dynamic Programming, Transportation Tags , , , , ,

    Truck-and-drone routing problems have become an important topic of research in the last decade due to their applications for last-mile deliveries. Despite the large number of publications in this area, the most efficient exact algorithms designed thus far struggle to solve the benchmark instances with 39 or more customers. This fact is true even for … Read more

    On enhanced KKT optimality conditions for smooth nonlinear optimization

  • Roberto Andreani
  • María Laura Schuverdt
  • Leonardo D. Secchin
    • Categories Nonlinear Optimization Tags , , , ,

    The Fritz-John (FJ) and KKT conditions are fundamental tools for characterizing minimizers and form the basis of almost all methods for constrained optimization. Since the seminal works of Fritz John, Karush, Kuhn and Tucker, FJ/KKT conditions have been enhanced by adding extra necessary conditions. Such an extension was initially proposed by Hestenes in the 1970s … Read more

    CDOpt: A Python Package for a Class of Riemannian Optimization

  • Nachuan Xiao
  • Xiaoyin Hu
  • Xin Liu
  • Kim-Chuan Toh
    • Categories Nonlinear Optimization, Optimization Software and Modeling Systems

    Optimization over the embedded submanifold defined by constraints $c(x) = 0$ has attracted much interest over the past few decades due to its wide applications in various areas, including computer vision, signal processing, numerical linear algebra, and deep learning. Plenty of related optimization packages have been developed based on Riemannian optimization approaches, which rely on … Read more

    Optimization of the first Dirichlet Laplacian eigenvalue with respect to a union of balls

  • Ernesto G. Birgin
  • Lucas Fernandez
  • Gabriel Haeser
  • Antoine
    • Categories Nonlinear Optimization, Optimization of Systems modeled by PDEs Tags , ,

    The problem of minimizing the first eigenvalue of the Dirichlet Laplacian with respect to a union of m balls with fixed identical radii and variable centers in the plane is investigated in the present work. The existence of a minimizer is shown and the shape sensitivity analysis of the eigenvalue with respect to the centers’ … Read more