Integer Programming

A Branch-and-Cut Algorithm for Mixed Integer Bilevel Linear Optimization Problems and Its Implementation

  • S.T. DeNegre
  • Ted K. Ralphs
  • S. Tahernejad
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Optimization Software and Modeling Systems Tags , , ,

    In this paper, we describe an algorithmic framework for solving mixed integer bilevel linear optimization problems (MIBLPs) by a generalized branch-and-cut approach. The framework presented merges features from existing algorithms (for both traditional mixed integer linear optimization and MIBLPs) with new techniques to produce a flexible and robust framework capable of solving a wide range … Read more

    Generation techniques for linear and integer programming instances with controllable properties

  • Davaatseren Baatar
  • Hans D Mittelmann
  • Simon Bowly
  • Kate Smith-Miles
    • Categories (Mixed) Integer Linear Programming, Optimization Software and Modeling Systems Tags , ,

    This paper addresses the problem of generating synthetic test cases for experimentation in linear programming. We propose a method which maps instance generation and instance space search to an alternative encoded space. This allows us to develop a generator for feasible bounded linear programming instances with controllable properties. We show that this method is capable … Read more

    Small and Strong Formulations for Unions of Convex Sets from the Cayley Embedding

  • Juan Pablo Vielma
    • Categories (Mixed) Integer Nonlinear Programming, 0-1 Programming

    There is often a significant trade-off between formulation strength and size in mixed integer programming (MIP). When modeling convex disjunctive constraints (e.g. unions of convex sets), adding auxiliary continuous variables can sometimes help resolve this trade-off. However, standard formulations that use such auxiliary continuous variables can have a worse-than-expected computational effectiveness, which is often attributed … Read more

    MIP-Based Instantaneous Control of Mixed-Integer PDE-Constrained Gas Transport Problems

  • Martin Gugat
  • Günter Leugering
  • Martin Schmidt
  • Mathias Sirvent
  • David Wintergerst
  • Alexander Martin
    • Categories (Mixed) Integer Nonlinear Programming, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags , , , ,

    We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations … Read more

    Lifted Polymatroid Inequalities for Mean-Risk Optimization with Indicator Variables

  • Alper Atamturk
  • Hyemin Jeon
    • Categories (Mixed) Integer Nonlinear Programming, Stochastic Programming Tags , , , ,

    We investigate a mixed 0-1 conic quadratic optimization problem with indicator variables arising in mean-risk optimization. The indicator variables are often used to model non-convexities such as fixed charges or cardinality constraints. Observing that the problem reduces to a submodular function minimization for its binary restriction, we derive three classes of strong convex valid inequalities … Read more

    FiberSCIP – A shared memory parallelization of SCIP

  • Stefan Heinz
  • Yuji Shinano
  • Stefan Vigerske
  • Michael Winkler
    • Categories Integer Programming, Parallel Algorithms

    Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving Constraint Integer Programs), which is a MIP solver and constraint integer programming framework available in source code. There … Read more

    Optimal Installation for Electric Vehicle Wireless Charging Lanes

  • Mashrur Chowdhury
  • MD Zadid Khan
  • Ilya Safro
  • Hayato Ushijima-Mwesigwa
    • Categories 0-1 Programming, Civil and Environmental Engineering, Transportation

    Range anxiety, the persistent worry about not having enough battery power to complete a trip, remains one of the major obstacles to widespread electric-vehicle adoption. As cities look to attract more users to adopt electric vehicles, the emergence of wireless in-motion car charging technology presents itself as a solution to range anxiety. For a limited … Read more

    Error bounds for monomial convexification in polynomial optimization

  • Warren Adams
  • Akshay Gupte
  • Yibo Xu
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory Tags , , , , ,

    Convex hulls of monomials have been widely studied in the literature, and monomial convexifications are implemented in global optimization software for relaxing polynomials. However, there has been no study of the error in the global optimum from such approaches. We give bounds on the worst-case error for convexifying a monomial over subsets of $[0,1]^n$. This … Read more

    Location of charging stations in electric car sharing systems

  • Georg Brandstätter
  • Markus Leitner
  • Ivana Ljubić
    • Categories (Mixed) Integer Linear Programming, Transportation Tags , , , , ,

    Electric vehicles are a prime candidate for use within an urban car sharing system, both from an economic and environmental perspective. However, their relatively short range necessitates frequent and rather time-consuming recharging throughout the day. Thus, charging stations must be built throughout the system’s operational area where cars can be charged between uses. In this … Read more

    Determining optimal locations for charging stations of electric car-sharing systems under stochastic demand

  • Georg Brandstätter
  • Michael Kahr
  • Markus Leitner
    • Categories (Mixed) Integer Linear Programming, Transportation Tags , , , , ,

    In this article, we introduce and study a two-stage stochastic optimization problem suitable to solve strategic optimization problems of car-sharing systems that utilize electric cars. By combining the individual advantages of car-sharing and electric vehicles, such electric car-sharing systems may help to overcome future challenges related to pollution, congestion, or shortage of fossil fuels. A … Read more