mixed-integer programming

A Unified Approach to Mixed-Integer Optimization Problems With Logical Constraints

  • Dimitris Bertsimas
  • Ryan Cory-Wright
  • Jean Pauphilet
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches Tags , , ,

    We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic optimization, sparse principal component analysis and sparse learning problems. These problems exhibit logical relationships between continuous and discrete variables, which are usually reformulated linearly … Read more

    Globalized Robust Optimization with Gamma-Uncertainties

  • Andreas Bärmann
  • Christina Büsing
  • Frauke Liers
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization, Robust Optimization Tags , , ,

    Globalized robust optimization has been proposed as a generalization of the standard robust optimization framework in order to allow for a controlled decrease in protection depending on the distance of the realized scenario from the predefined uncertainty set. In this work, we specialize the notion of globalized robustness to Gamma-uncertainty in order to extend its … Read more

    Portfolio Optimization with Irreversible Long-Term Investments in Renewable Energy under Policy Risk: A Mixed-Integer Multistage Stochastic Model and a Moving-Horizon Approach

  • Nadine Gatzert
  • Martin Schmidt
  • Alexander Martin
  • Benjamin Seith
  • Nikolai Vogl
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Stochastic Programming Tags , , , ,

    Portfolio optimization is an ongoing hot topic of mathematical optimization and management science. Due to the current financial market environment with low interest rates and volatile stock markets, it is getting more and more important to extend portfolio optimization models by other types of investments than classical assets. In this paper, we present a mixed-integer … Read more

    Adaptive Two-stage Stochastic Programming with an Application to Capacity Expansion Planning

  • Shabbir Ahmed
  • Nagi Gebraeel
  • Beste Basciftci
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , , , ,

    Multi-stage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that are fully adapted to the uncertainty. Often, e.g. due to contractual constraints, such flexible and adaptive policies are not desirable, and the decision maker may need to commit to a set of actions for a certain number of … Read more

    Risk-Averse Bi-Level Stochastic Network Interdiction Model for Cyber-Security Risk Management

  • Tanveer Hossain Bhuiyan
  • Mahantesh Halappanavar
  • Hugh R. Medal
  • Apurba Nandi
    • Categories (Mixed) Integer Linear Programming, Network Optimization, Stochastic Programming Tags , , , ,

    Security of cyber networks is crucial; recent severe cyber-attacks have had a devastating effect on many large organizations. The attack graph, which maps the potential attack paths of a cyber network, is a popular tool for analyzing cyber system vulnerability. In this study, we propose a bi-level stochastic network interdiction model on an attack graph … Read more

    Radius of Robust Feasibility for Mixed-Integer Problems

  • Frauke Liers
  • Lars Schewe
  • Johannes Thürauf
    • Categories (Mixed) Integer Linear Programming, Robust Optimization Tags , , ,

    For a mixed-integer linear problem (MIP) with uncertain constraints, the radius of robust feasibility (RRF) determines a value for the maximal “size” of the uncertainty set such that robust feasibility of the MIP can be guaranteed. To the best of our knowledge, the approaches for the RRF presented in the literature are restricted to continuous … Read more

    Stochastic Lipschitz Dynamic Programming

  • Shabbir Ahmed
  • Filipe G. Cabral
  • Bernardo Freitas Paulo da Costa
    • Categories Dynamic Programming, Integer Programming, Stochastic Programming Tags , , ,

    We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to build lower approximations for the non-convex cost to go functions. An example of such a class of cuts are those derived using … Read more

    Planning Out-of-Hours Services for Pharmacies

  • Christina Büsing
  • Arie M.C.A. Koster
  • Timo Gersing
    • Categories 0-1 Programming, Applications - OR and Management Sciences, Scheduling Tags , , , , ,

    The supply of pharmaceuticals is one important factor in a functioning health care system. In the German health care system, the chambers of pharmacists are legally obliged to ensure that every resident can find an open pharmacy at any day and night time within an appropriate distance. To that end, the chambers of pharmacists create … Read more

    Structure-driven fix-and-propagate heuristics for mixed integer programming

  • Timo Berthold
  • Gerald Gamrath
  • Stefan Heinz
  • Michael Winkler
    • Categories (Mixed) Integer Linear Programming Tags , , , ,

    Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They often provide good feasible solutions early and help to reduce the time needed to prove optimality. In this paper, we present a scheme for start heuristics that can be executed without previous knowledge of an LP solution or a previously … Read more

    A Decomposition Heuristic for Mixed-Integer Supply Chain Problems

  • Lars Schewe
  • Martin Schmidt
  • Dieter Weninger
    • Categories (Mixed) Integer Linear Programming, Supply Chain Management Tags , , , ,

    Mixed-integer supply chain models typically are very large but are also very sparse and can be decomposed into loosely coupled blocks. In this paper, we use general-purpose techniques to obtain a block decomposition of supply chain instances and apply a tailored penalty alternating direction method, which exploits the structural properties of the decomposed instances. We … Read more