Integer Programming

A fully mixed-integer linear programming formulation for economic dispatch with valve-point effects, transmission loss and prohibited operating zones

  • Huangyue Chen
  • Jinbao Jian
  • Shanshan Pan
  • Linfeng Yang
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering Tags , , , , ,

    Economic dispatch (ED) problem considering valve-point effects (VPE), transmission loss and prohibited operating zones (POZ) is a very challenging issue due to its intrinsic non-convex, non-smooth and non-continuous natures. To achieve a near globally solution, a fully mixed-integer linear programming (FMILP) formulation is proposed for such an ED problem. Since the original loss function is … Read more

    Intersection disjunctions for reverse convex sets

  • James R. Luedtke
  • Eli Towle
    • Categories (Mixed) Integer Nonlinear Programming, Constrained Nonlinear Optimization, Global Optimization Theory Tags , , , ,

    We present a framework to obtain valid inequalities for optimization problems constrained by a reverse convex set, which is defined as the set of points in a polyhedron that lie outside a given open convex set. We are particularly interested in cases where the closure of the convex set is either non-polyhedral, or is defined … Read more

    A Tutorial on Formulating and Using QUBO Models

  • Yu Du
  • Fred Glover
  • Gary Kochenberger
    • Categories 0-1 Programming, Combinatorial Optimization Tags , ,

    The Quadratic Unconstrained Binary Optimization (QUBO) model has gained prominence in recent years with the discovery that it unifies a rich variety of combinatorial optimization problems. By its association with the Ising problem in physics, the QUBO model has emerged as an underpinning of the quantum computing area known as quantum annealing and has become … Read more

    Interdiction of a Mixed-Integer Linear System

  • Ross Baldick
  • Bowen Hua
  • Kevin Wood
    • Categories Applications - OR and Management Sciences, Integer Programming Tags , ,

    A system-interdiction problem can be modeled as a bilevel program in which the upper level models interdiction decisions and the lower level models system operation. This paper studies MILSIP, a mixed-integer linear system interdiction problem, which assumes binary interdiction decisions and models system operations through a mixed-integer linear program. To solve large-scale instances of MILSIP, … Read more

    Submodularity in conic quadratic mixed 0-1 optimization

  • Alper Atamturk
  • Andrés Gómez
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches Tags , , , , , , ,

    We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. These inequalities can be utilized for solving numerous practical nonlinear discrete optimization problems from value-at-risk minimization to queueing system design, from robust interdiction to assortment optimization through appropriate conic quadratic mixed 0-1 relaxations. The inequalities exploit the submodularity of the binary restrictions and … Read more

    Successive Quadratic Upper-Bounding for Discrete Mean-Risk Minimization and Network Interdiction

  • Alper Atamturk
  • Carlos Deck
  • Hyemin Jeon
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization Tags , , , ,

    The advances in conic optimization have led to its increased utilization for modeling data uncertainty. In particular, conic mean-risk optimization gained prominence in probabilistic and robust optimization. Whereas the corresponding conic models are solved efficiently over convex sets, their discrete counterparts are intractable. In this paper, we give a highly effective successive quadratic upper-bounding procedure … Read more

    The Noncooperative Fixed Charge Transportation Problem

  • Simone Sagratella
  • Marcel Stefan Schmidt
  • Nathan Sudermann-Merx
    • Categories (Mixed) Integer Linear Programming, Game Theory Tags , ,

    We introduce the noncooperative fixed charge transportation problem (NFCTP), which is a game-theoretic extension of the fixed charge transportation problem. In the NFCTP, competing players solve coupled fixed charge transportation problems simultaneously. Three versions of the NFCTP are discussed and compared, which differ in their treatment of shared social costs. This may be used from … Read more

    Adaptive Large Neighborhood Search for Mixed Integer Programming

  • Gregor Hendel
    • Categories (Mixed) Integer Linear Programming

    Large Neighborhood Search (LNS) heuristics are among the most powerful but also most expensive heuristics for mixed integer programs (MIP). Ideally, a solver learns adaptively which LNS heuristics work best for the MIP problem at hand in order to concentrate its limited computational budget. To this end, this work introduces Adaptive Large Neighborhood Search (ALNS) … Read more

    Large-scale Influence Maximization via Maximal Covering Location

  • Evren Güney
  • Markus Leitner
  • Mario Ruthmair
  • Markus Sinnl
    • Categories Applications - OR and Management Sciences, Integer Programming, Stochastic Programming Tags , , ,

    Influence maximization aims at identifying a limited set of key individuals in a (social) network which spreads information based on some propagation model and maximizes the number of individuals reached. We show that influence maximization based on the probabilistic independent cascade model can be modeled as a stochastic maximal covering location problem. A reformulation based … Read more

    Weighted Thresholding Homotopy Method for Sparsity Constrained Optimization

  • Jianli Chen
  • Wenxing Zhu
  • Huating Huang
  • Lanfan Jiang
    • Categories Integer Programming Tags , , ,

    Weighted or reweighted strategies have not been considered for sparsity constrained optimization. In this paper, we reformulate the sparsity constraint as an equivalent weighted l1-norm constraint in the sparsity constrained optimization problem. To solve the reformulated problem, we investigate the problem in the Lagrange dual framework, and prove that the strong duality property holds. Then … Read more