Integer Programming

The two-echelon location-routing problem with time windows: Formulation, branch-and-price, and clustering

  • M. Saleh Farham
  • Cem Iyigun
  • Haldun Sural
    • Categories (Mixed) Integer Linear Programming, Transportation

    In this study, we consider the two-echelon location-routing problem with time windows (2E-LRPTW) to address the strategic and tactical decisions of the urban freight transportation. In the rst echelon, freights are delivered from city distribution centers (CDCs) to intermediate facilities, called satellites, in large batches. In the second echelon, goods are consolidated into smaller vehicles … Read more

    Testing Copositivity via Mixed-Integer Linear Programming

  • Kurt M. Anstreicher
    • Categories (Mixed) Integer Linear Programming, Global Optimization Theory Tags , ,

    We describe a simple method to test if a given matrix is copositive by solving a single mixed-integer linear programming (MILP) problem. This methodology requires no special coding to implement and takes advantage of the computational power of modern MILP solvers. Numerical experiments demonstrate that the method is robust and efficient. Citation Dept. of Business … Read more

    Exact and Heuristic Algorithms for the Carrier-Vehicle Traveling Salesman Problem

  • Gunes Erdogan
  • E. Alper Yildirim
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences Tags , ,

    This paper presents new structural properties for the Carrier-Vehicle Traveling Salesman Problem. The authors provide a new mixed integer second order conic optimization formulation, with associated optimality cuts based on the structural properties, and an Iterated Local Search (ILS) algorithm. Computational experiments on instances from the literature demonstrate the superiority of the new formulation to … Read more

    Multistage Distributionally Robust Mixed-Integer Programming with Decision-Dependent Moment-Based Ambiguity Sets

  • Siqian Shen
  • Xian Yu
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Stochastic Programming Tags , , , ,

    We study multistage distributionally robust mixed-integer programs under endogenous uncertainty, where the probability distribution of stage-wise uncertainty depends on the decisions made in previous stages. We first consider two ambiguity sets defined by decision-dependent bounds on the first and second moments of uncertain parameters and by mean and covariance matrix that exactly match decision-dependent empirical … Read more

    Safe screening rules for L0-Regression

  • Alper Atamturk
  • Andrés Gómez
    • Categories (Mixed) Integer Nonlinear Programming, Statistics Tags , , ,

    We give safe screening rules to eliminate variables from regression with L0 regularization or cardinality constraint. These rules are based on guarantees that a feature may or may not be selected in an optimal solution. The screening rules can be computed from a convex relaxation solution in linear time, without solving the L0 optimization problem. … Read more

    Learning Optimal Classification Trees: Strong Max-Flow Formulations

  • Sina Aghaei
  • Andrés Gómez
  • Phebe Vayanos
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization, Statistics Tags , , ,

    We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in mixed-integer programming (MIP) technology. Yet, existing approaches from the literature do not leverage the power of MIP to its full extent. Indeed, … Read more

    Solving Binary-Constrained Mixed Complementarity Problems Using Continuous Reformulations

  • Steven A. Gabriel
  • Martin Schmidt
  • Marina Leal
    • Categories (Mixed) Integer Nonlinear Programming, Complementarity and Variational Inequalities, Transportation Tags , , ,

    Mixed complementarity problems are of great importance in practice since they appear in various fields of applications like energy markets, optimal stopping, or traffic equilibrium problems. However, they are also very challenging due to their inherent, nonconvex structure. In addition, recent applications require the incorporation of integrality constraints. Since complementarity problems often model some kind … Read more

    Evaluating on-demand warehousing via dynamic facility location models

  • Kaan Unnu
  • Jennifer Pazour
    • Categories (Mixed) Integer Linear Programming, Supply Chain Management, Transportation Tags , , , , , ,

    On-demand warehousing platforms match companies with underutilized warehouse and distribution capabilities with customers who need extra space or distribution services. These new business models have unique advantages, in terms of reduced capacity and commitment granularity, but also have different cost structures compared to traditional ways of obtaining distribution capabilities. This research is the first quantitative … Read more

    Mixed-Integer Optimal Control Problems with switching costs: A shortest path approach

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

    We investigate an extension of Mixed-Integer Optimal Control Problems (MIOCPs) by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, consisting of solving a partial outer convexification to obtain a relaxed solution and using rounding schemes to obtain a discrete-valued control can still be applied, but the … Read more

    Learning Generalized Strong Branching for Set Covering, Set Packing, and 0-1 Knapsack Problems

  • Yu Yang
  • Natashia Boland
  • Bistra Dilkina
  • Martin Savelsbergh
    • Categories (Mixed) Integer Linear Programming, Integer Programming Tags , ,

    Branching on a set of variables, rather than on a single variable, can give tighter bounds at the child nodes and can result in smaller search trees. However, selecting a good set of variables to branch on is even more challenging than selecting a good single variable to branch on. Generalized strong branching extends the … Read more