mixed-integer programming

Matching Algorithms and Complexity Results for Constrained Mixed-Integer Optimal Control with Switching Costs

  • Felix Bestehorn
  • Christian Kirches
    • Categories (Mixed) Integer Nonlinear Programming, Approximation Algorithms Tags , , , ,

    We extend recent work on the performance of the combinatorial integral approximation decomposition approach for Mixed-Integer Optimal Control Problems (MIOCPs) in the presence of combinatorial constraints or switching costs on an equidistant grid. For the time discretized problem, we reformulate the emerging rounding problem in the decomposition approach as a matching problem on a bipartite … Read more

    Bicriteria approaches for an optimal balance between resilience and cost-effectiveness of supply chains

  • Heiner Ackermann
  • Erik Diessel
    • Categories Multi-Criteria Optimization, Supply Chain Management Tags , , ,

    In supply chain optimization multiple objectives are considered simultaneously, for example to increase resilience and reduce costs. In this paper we discuss the corresponding bicriteria problems to find a good balance between these two objectives. We give a general model for supply chain resilience that integrates strategic decisions with the operational level. This modular model … Read more

    Precise control of approximation quality in multicriteria optimization

  • Erik Diessel
    • Categories Multi-Criteria Optimization Tags , , ,

    Although many algorithms for multicriteria optimization provide good approximations, a precise control of their quality is challenging. In this paper we provide algorithmic tools to obtain exact approximation quality values for given approximations and develop a new method for multicriteria optimization guided by this quality. We show that the well-established “-indicator measure is NP-hard to … Read more

    Accelerating Domain Propagation: an Efficient GPU-Parallel Algorithm over Sparse Matrices

  • Ambros Gleixner
  • Sebastian Pokutta
  • Boro Sofranac
    • Categories Integer Programming Tags , , , ,

    Fast domain propagation of linear constraints has become a crucial component of today’s best algorithms and solvers for mixed integer programming and pseudo-boolean optimization to achieve peak solving performance. Irregularities in the form of dynamic algorithmic behaviour, dependency structures, and sparsity patterns in the input data make efficient implementations of domain propagation on GPUs and, … Read more

    Mixed-integer Linear Programming Models and Algorithms for Generation and Transmission Expansion Planning of Power Systems

  • Antonio Conejo
  • Ignacio E. Grossmann
  • Can Li
  • Peng Liu
  • Benjamin Omell
  • John D. Siirola
    • Categories Applications - Science and Engineering, Energy Tags , , , ,

    With the increasing penetration of renewable generating units, especially in remote areas not well connected with load demand, there are growing interests to co-optimize generation and transmission expansion planning (GTEP) in power systems. Due to the volatility in renewable generation, a planner needs to include the operating decisions into the planning model to guarantee feasibility. … Read more

    Distributionally Robust Facility Location with Bimodal Random Demand

  • Karmel S. Shehadeh
  • Ece Sanci
    • Categories (Mixed) Integer Linear Programming, Facility Planning and Design, Stochastic Programming Tags , , , ,

    In this paper, we consider a decision-maker who wants to determine a subset of locations from a given set of candidate sites to open facilities and accordingly assign customer demand to these open facilities. Unlike classical facility location settings, we focus on a new setting where customer demand is bimodal, i.e., display, or belong to, … Read more

    A Unified Approach to Solve Convex Hull Pricing and Average Incremental Cost Pricing

  • Yonghong Chen
  • Pete Whitman
  • Richard O'Neill
    • Categories Applications - OR and Management Sciences Tags , , , , ,

    This paper introduces a unified approach to solving convex hull pricing (CHP) and average incremental cost (AIC) pricing problems. By developing a convex hull and convex envelope formulation for individual resources, a CHP model that minimizes uplift can be solved by linear programming (LP) using relaxation of the binary terms of the security constrained unit … Read more

    Efficient Formulations and Decomposition Approaches for Power Peak Reduction in Railway Traffic via Timetabling

  • Andreas Bärmann
  • Alexander Martin
  • Oskar Schneider
    • Categories Cutting Plane Approaches, Polyhedra, Scheduling Tags , , , ,

    Over the last few years, optimization models for the energy-efficient operation of railway traffic have received more and more attention, particularly in connection with timetable design. In this work, we study the effect of load management via timetabling. The idea is to consider trains as time-flexible consumers in the railway power supply network and to … Read more

    Inverse Mixed Integer Optimization: Polyhedral Insights and Trust Region Methods

  • Merve Bodur
  • Timothy C.Y. Chan
  • Ian Yihang Zhu
    • Categories Integer Programming Tags , , , , ,

    Inverse optimization – determining parameters of an optimization problem that render a given solution optimal – has received increasing attention in recent years. While significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision-making. In this paper, … Read more

    An Adaptive Patch Approximation Algorithm for Bicriteria Convex Mixed Integer problems

  • Erik Diessel
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , , ,

    Pareto frontiers of bicriteria continuous convex problems can be efficiently computed and optimal theoretical performance bounds have been established. In the case of bicriteria mixed-integer problems, the approximation of the Pareto frontier becomes, however, significantly harder. In this paper, we propose a new algorithm for approximating the Pareto frontier of bicriteria mixed-integer programs with convex … Read more