Integer Programming

A Machine Learning Approach to Solving Large Bilevel and Stochastic Programs: Application to Cycling Network Design

  • Bo Lin
    • Categories Integer Programming, Stochastic Programming, Transportation Tags , , , ,

    We present a novel machine learning-based approach to solving bilevel programs that involve a large number of independent followers, which as a special case include two-stage stochastic programming. We propose an optimization model that explicitly considers a sampled subset of followers and exploits a machine learning model to estimate the objective values of unsampled followers. … Read more

    Optimizing Vaccine Distribution in Developing Countries under Natural Disaster Risk

  • Bonn Kleiford Seranilla
  • Nils Löhndorf
    • Categories (Mixed) Integer Linear Programming, Dynamic Programming, Stochastic Programming Tags , , ,

    For many developing countries, COVID-19 vaccination roll-out programs are not only slow but vaccination centers are also exposed to the risk of natural disaster, like flooding, which may slow down vaccination progress even further. Policy-makers in developing countries therefore seek to implement strategies that hedge against distribution risk in order for vaccination campaigns to run … Read more

    Dynamic Rebalancing Optimization for Bike-sharing Systems: A Modeling Framework and Empirical Comparison

  • Jiaqi Liang
  • Sanjay Dominik Jena
  • Andrea Lodi
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Transportation Tags , , ,

    Bike-sharing systems have been implemented in multiple major cities, offering a low-cost and environmentally friendly transportation alternative to vehicles. Due to the stochastic nature of customer trips, stations are often unbalanced, resulting in unsatisfied demand. As a remedy, operators employ trucks to rebalance bikes among unbalanced stations. Given the complexity of the dynamic rebalancing planning, … Read more

    A note on quadratic constraints with indicator variables: Convex hull description and perspective relaxation

  • Andrés Gómez
  • Weijun Xie
    • Categories (Mixed) Integer Nonlinear Programming

    In this paper, we study the mixed-integer nonlinear set given by a separable quadratic constraint on continuous variables, where each continuous variable is controlled by an additional indicator. This set occurs pervasively in optimization problems with uncertainty and in machine learning. We show that optimization over this set is NP-hard. Despite this negative result, we … Read more

    Relaxations and Duality for Multiobjective Integer Programming

  • Alex Dunbar
  • Saumya Sinha
  • Andrew J. Schaefer
    • Categories Integer Programming, Multi-Criteria Optimization Tags , , , ,

    Multiobjective integer programs (MOIPs) simultaneously optimize multiple objective func- tions over a set of linear constraints and integer variables. In this paper, we present continuous, convex hull and Lagrangian relaxations for MOIPs and examine the relationship among them. The convex hull relaxation is tight at supported solutions, i.e., those that can be derived via a … Read more

    On the Relation Between Affinely Adjustable Robust Linear Complementarity and Mixed-Integer Linear Feasibility Problems

  • Christian Biefel
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities Tags , , ,

    We consider adjustable robust linear complementarity problems and extend the results of Biefel et al.~(2022) towards convex and compact uncertainty sets. Moreover, for the case of polyhedral uncertainty sets, we prove that computing an adjustable robust solution of a given linear complementarity problem is equivalent to solving a properly chosen mixed-integer linear feasibility problem. Article … Read more

    Explicit convex hull description of bivariate quadratic sets with indicator variables

  • Aida Khajavirad
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory, Integer Programming Tags , , , , ,

    \(\) We consider the nonconvex set \(S_n = \{(x,X,z): X = x x^T, \; x (1-z) =0,\; x \geq 0,\; z \in \{0,1\}^n\}\), which is closely related to the feasible region of several difficult nonconvex optimization problems such as the best subset selection and constrained portfolio optimization. Utilizing ideas from convex analysis and disjunctive programming, … Read more

    Temporal Bin Packing with Half-Capacity Jobs

  • Christopher Muir
  • Luke Marshall
  • Alejandro Toriello
    • Categories (Mixed) Integer Linear Programming, Polyhedra, Scheduling Tags , , , ,

    Motivated by applications in cloud computing, we study a temporal bin packing problem with jobs that occupy half of a bin’s capacity. An instance is given by a set of jobs, each with a start and end time during which it must be processed, i.e., assigned to a bin. A bin can accommodate two jobs … Read more

    A Successive Linear Relaxation Method for MINLPs with Multivariate Lipschitz Continuous Nonlinearities

  • Julia Grübel
  • Richard Krug
  • Martin Schmidt
  • Winnifried Wollner
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Global Optimization Tags , , , ,

    We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate them and that we know their global Lipschitz constants. The algorithm is a successive linear relaxation method in which we alternate … Read more

    Worst-Case Analysis of Heuristic Approaches for the Temporal Bin Packing Problem with Fire-Ups

  • John Martinovic
  • Nico Strasdat
    • Categories (Mixed) Integer Linear Programming, Approximation Algorithms, Scheduling Tags , , , ,

    We consider the temporal bin packing problem with fire-ups (TBPP-FU), a branch of operations research recently introduced in multi-objective cloud computing. In this scenario, any item is equipped with a resource demand and a lifespan meaning that it requires the bin capacity only during that time interval. We then aim at finding a schedule minimizing … Read more