Integer Programming

Quadratic Convex Reformulations for MultiObjective Binary Quadratic Programming

  • Marianna De Santis
  • Lucas Létocart
  • Yue Zhang
    • Categories (Mixed) Integer Nonlinear Programming, 0-1 Programming, Multi-Criteria Optimization Tags , , ,

    Multiobjective binary quadratic programming refers to optimization problems involving multiple quadratic – potentially non-convex – objective functions and a feasible set that includes binary constraints on the variables. In this paper, we extend the well-established Quadratic Convex Reformulation technique, originally developed for single-objective binary quadratic programs, to the multiobjective setting. We propose a branch-and-bound algorithm … Read more

    Optimization over Trained (and Sparse) Neural Networks: A Surrogate within a Surrogate

  • Hung Pham
  • Zhiyi Ren
  • Jiatai Tong
  • Thiago Serra
    • Categories (Mixed) Integer Linear Programming, Integer Programming

    In constraint learning, we use a neural network as a surrogate for part of the constraints or of the objective function of an optimization model. However, the tractability of the resulting model is heavily influenced by the size of the neural network used as a surrogate. One way to obtain a more tractable surrogate is … Read more

    The 1-persistency of the clique relaxation of the stable set polytope: a focus on some forbidden structures

  • Lucía Moroni
  • Diego Delle Donne
  • Mariana Escalante
  • Pablo Fekete
    • Categories Combinatorial Optimization, Graphs and Matroids, Integer Programming Tags , ,

    A polytope $P\subseteq [0,1]^n$ is said to have the \emph{persistency} property if for every vector $c\in \R^{n}$ and every $c$-optimal point $x\in P$, there exists a $c$-optimal integer point $y\in P\cap \{0,1\}^n$ such that $x_i = y_i$ for each $i \in \{1,\dots,n\}$ with $x_i \in \{0,1\}$. In this paper, we consider a relaxation of the … Read more

    Data-driven robust menu planning for food services: Reducing food waste by using leftovers

  • Marloes Remijnse
  • Marjolein Buisman
  • Ahmadreza Marandi
  • S.U.K Rohmer
  • Tom Van Woensel
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Robust Optimization Tags , , , ,

    With food waste levels of about 30%, mostly caused by overproduction, reducing food waste poses an important challenge in the food service sector. As food is prepared in advance rather than on demand, there is a significant risk that meals or meal components remain uneaten. Flexible meal planning can promote the reuse of these leftovers … Read more

    Global Optimization of Gas Transportation and Storage: Convex Hull Characterizations and Relaxations

  • Bahar Okumusoglu
  • Burak Kocuk
    • Categories (Mixed) Integer Linear Programming, Energy, Global Optimization Tags , , ,

    Gas transportation and storage has become one of the most relevant and important optimization problems in energy systems. This problem inherently includes highly nonlinear and nonconvex aspects due to gas physics, and discrete aspects due to the control decisions of active network elements. Obtaining even locally optimal solutions for this problem presents significant mathematical and … Read more

    A Survey on the Applications of Stochastic Dual Dynamic Programming and its Variants

  • Bonn Kleiford Seranilla
  • Nils Löhndorf
    • Categories Dynamic Programming, Integer Programming, Stochastic Programming Tags , , ,

    Stochastic Dual Dynamic Programming (SDDP) is widely recognized as the predominant methodology for solving large-scale multistage stochastic linear programming (MSLP) problems. This paper aims to contribute to the extant literature by conducting a comprehensive survey of the literature on SDDP within the realm of practical applications. We systematically identify and analyze the various domains where … Read more

    Strong Formulations and Algorithms for Regularized A-Optimal Design

  • Yongchun Li
    • Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization Tags , , , ,

    We study the Regularized A-Optimal Design (RAOD) problem, which selects a subset of \(k\) experiments to minimize the inverse of the Fisher information matrix, regularized with a scaled identity matrix. RAOD has broad applications in Bayesian experimental design, sensor placement, and cold-start recommendation. We prove its NP-hardness via a reduction from the independent set problem. … Read more

    Rank-one convexification for convex quadratic optimization with step function penalties

  • Andrés Gómez
  • Shaoning Han
    • Categories (Mixed) Integer Nonlinear Programming, Data Science Applications, Semi-definite Programming Tags ,

    We investigate convexification in convex quadratic optimization with step function penalties. Such problems can be cast as mixed-integer quadratic optimization problems, where binary variables are used to encode the non-convex step function. First, we derive the convex hull for the epigraph of a quadratic function defined by a rank-one matrix. Using this rank-one convexification, we … Read more

    An interactive optimization framework for incorporating a broader range of human feedback into stochastic multi-objective mixed integer linear programs

  • Damsara Jayarathne
  • Jennifer Pazour
  • John E. Mitchell
    • Categories (Mixed) Integer Linear Programming, Multi-Criteria Optimization, Stochastic Programming Tags , , , ,

    Interactive optimization leverages the strengths of optimization frameworks alongside the expertise of human users. Prior research in this area tends to either ask human users for the same type of information, or when varying information is requested, users must manually modify the optimization model directly. These limitations restrict the incorporation of wider human knowledge into … Read more

    Pareto Leap: An Algorithm for Biobjective Mixed-Integer Programming

  • Philip de Castro
  • Margaret Wiecek
    • Categories (Mixed) Integer Nonlinear Programming, Integer Programming, Multi-Criteria Optimization Tags , , ,

    Many real-life optimization problems need to make decisions with discrete variables and multiple, conflicting objectives. Due to this need, the ability to solve such problems is an important and active area of research. We present a new algorithm, called Pareto Leap, for identifying the (weak) Pareto slices of biobjective mixed-integer programs (BOMIPs), even when Pareto … Read more