Integer Programming

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

    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

    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

    Co-optimization of Demand Response and Reserve Offers for a Major Consumer

  • Miguel F. Anjos
  • Anthony Downward
  • Michael C. Ferris
  • Mahbubeh Habibian
  • Golbon Zakeri
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Stochastic Programming Tags , ,

    In this paper we present a stochastic optimization problem for a strategic major consumer who has flexibility over its consumption and can offer reserve. Our model is a bi-level optimization model (reformulated as a mixed-integer program) that embeds the optimal power flow problem, in which electricity and reserve are co-optimized. We implement this model for … Read more

    A hybrid approach for Bi-Objective Optimization

  • Kim Allan Andersen
  • Thomas R. Stidsen
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches, Multi-Criteria Optimization

    A large number of the real world planning problems which are today solved using Operations Research methods are actually multi-objective planning problems, but most of them are solved using single-objective methods. The reason for converting, i.e. simplifying, multi- objective problems to single-objective problems is that no standard multi-objective solvers exist and specialized algorithms need to … Read more

    Dantzig Wolfe decomposition and objective function convexification for binary quadratic problems: the cardinality constrained quadratic knapsack case

  • Alberto Ceselli
  • Lucas Létocart
  • Emiliano Traversi
    • Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization, Quadratic Programming Tags , , ,

    The purpose of this paper is to provide strong reformulations for binary quadratic problems. We propose a first methodological analysis on a family of reformulations combining Dantzig-Wolfe decomposition and Quadratic Convex Reformulation principles. As a representative case study, we apply them to a cardinality constrained quadratic knapsack problem, providing extensive experimental insights. We show that … Read more