Integer Programming

Minotaur: A Mixed-Integer Nonlinear Optimization Toolkit

  • Sven Leyffer
  • Jeff Linderoth
  • James R. Luedtke
  • Ashutosh Mahajan
  • Todd S. Munson
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Optimization Software and Modeling Systems Tags , ,

    We present a flexible framework for general mixed-integer nonlinear programming (MINLP), called Minotaur, that enables both algorithm exploration and structure exploitation without compromising computational efficiency. This paper documents the concepts and classes in our framework and shows that our implementations of standard MINLP techniques are efficient compared with other state-of-the-art solvers. We then describe structure-exploiting … Read more

    Convexification of Queueing Formulas by Mixed-Integer Second-Order Cone Programming: An Application to a Discrete Location Problem with Congestion

  • Ahmadi-Javid Amir
  • Pooya Hoseinpour
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Second-Order Cone Programming

    Mixed-Integer Second-Order Cone Programs (MISOCPs) form a nice class of mixed-inter convex programs, which can be solved very efficiently due to the recent advances in optimization solvers. Our paper bridges the gap between modeling a class of optimization problems and using MISOCP solvers. It is shown how various performance metrics of M/G/1 queues can be … Read more

    Enhanced Pseudo-Polynomial Formulations for Bin Packing and Cutting Stock Problems

  • Maxence Delorme
  • Manuel Iori
    • Categories (Mixed) Integer Linear Programming Tags , , , , ,

    We study pseudo-polynomial formulations for the classical bin packing and cutting stock problems. We first propose an overview of dominance and equivalence relations among the main pattern-based and pseudo-polynomial formulations from the literature. We then introduce reflect, a new formulation that uses just half of the bin capacity to model an instance and needs significantly … Read more

    A New Exact Algorithm to Optimize a Linear Function Over the Set of Efficient Solutions for Bi-objective Mixed Integer Linear Programs

  • Hadi Charkhgard
  • Alvaro Sierra-Altamiranda
    • Categories (Mixed) Integer Linear Programming, Multi-Criteria Optimization Tags , , ,

    We present the first (criterion space search) algorithm for optimizing a linear function over the set of efficient solutions of bi-objective mixed integer linear programs. The proposed algorithm is developed based on the Triangle Splitting Method (Boland et al. 2015b) which can find a full representation of the nondominated frontier of any bi-objective mixed integer … Read more

    A multi-period production and distribution optimization model for radiopharmaceuticals

  • Ioannis G. Akrotirianakis
  • Amit Chakraborty
    • Categories (Mixed) Integer Nonlinear Programming, Biomedical Applications, Production and Logistics Tags , , ,

    This paper addresses the manufacturing and distribution of short-lived radio-pharmaceuticals which are mainly used in diagnostic imaging studies. We develop a mixed integer nonlinear optimization model that is flexible enough to capture the complex underlying nuclear physics of the production process of fludeoxyglucose (FDG), which is widely used in oncology and cardiology, as well as … Read more

    Compact Representation of Near-Optimal Integer Programming Solutions

  • John Hooker
  • Thiago Serra
    • Categories 0-1 Programming

    It is often useful in practice to explore near-optimal solutions of an integer programming problem. We show how all solutions within a given tolerance of the optimal value can be efficiently and compactly represented in a weighted decision diagram, once the optimal value is known. The structure of a decision diagram facilitates rapid processing of … Read more

    Lower bounds on the lattice-free rank for packing and covering integer programs

  • Merve Bodur
  • Alberto Del Pia
  • Santanu S. Dey
  • Marco Molinaro
    • Categories Cutting Plane Approaches, Integer Programming Tags , , , , ,

    In this paper, we present lower bounds on the rank of the split closure, the multi-branch closure and the lattice-free closure for packing sets as a function of the integrality gap. We also provide a similar lower bound on the split rank of covering polyhedra. These results indicate that whenever the integrality gap is high, … Read more

    A mixed-integer branching approach for very small formulations of disjunctive constraints

  • Joey Huchette
  • Juan Pablo Vielma
    • Categories (Mixed) Integer Linear Programming Tags , , ,

    We study the existence and construction of very small formulations for disjunctive constraints in optimization problems: that is, formulations that use very few integer variables and extra constraints. To accomplish this, we present a novel mixed-integer branching formulation framework, which preserves many of the favorable algorithmic properties of a traditional mixed-integer programming formulation, including amenability … Read more

    Bi-Perspective Functions for Mixed-Integer Fractional Programs with Indicator Variables

  • Adam N. Letchford
  • Qiang Ni
  • Zhaoyu Zhong
    • Categories (Mixed) Integer Nonlinear Programming, Telecommunications Tags , ,

    Perspective functions have long been used to convert fractional programs into convex programs. More recently, they have been used to form tight relaxations of mixed-integer nonlinear programs with so-called indicator variables. Motivated by a practical application (maximising energy efficiency in an OFDMA system), we consider problems that have a fractional objective and indicator variables simultaneously. … Read more

    Constraints reduction programming by subset selection: a study from numerical aspect

  • Yuan Shen
    • Categories 0-1 Programming, Applications - OR and Management Sciences, Convex Optimization Tags , , , , , ,

    We consider a novel method entitled constraints reduction programming which aims to reduce the constraints in an optimization model. This method is derived from various applications of management or decision making, and has potential ability to handle a wider range of applications. Due to the high combinatorial complexity of underlying model, it is difficult to … Read more