Other Topics

A parametric programming approach to redefine the global configuration of resource constraints of 0-1-Integer Linear Programming problems.

  • Alejandro Crema
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , , , ,

    A mathematical programming approach to deal with the global configuration of resource constraints is presented. A specialized parametric programming algorithm to obtain the pareto set for the biobjective problem that appears to deal with the global configuration for 0-1-Integer Linear Programing problems is presented and implemented. Computational results for Multiconstrained Knapsack problems and Bounded Knapsack … Read more

    A Copositive Approach for Two-Stage Adjustable Robust Optimization with Uncertain Right-Hand Sides

  • Samuel Burer
  • Guanglin Xu
    • Categories Dynamic Programming, Linear, Cone and Semidefinite Programming, Robust Optimization Tags , , , , ,

    We study two-stage adjustable robust linear programming in which the right-hand sides are uncertain and belong to a convex, compact uncertainty set. This problem is NP-hard, and the affine policy is a popular, tractable approximation. We prove that under standard and simple conditions, the two-stage problem can be reformulated as a copositive optimization problem, which … Read more

    Optimal Deterministic Algorithm Generation

  • Ioannis G. Kevrekidis
  • Alexander Mitsos
  • Jaromił Najman
    • Categories Applications - Science and Engineering, Global Optimization, Other Topics Tags , ,

    A formulation for the automated generation of algorithms via mathematical programming (optimization) is proposed. The formulation is based on the concept of optimizing within a parameterized family of algorithms, or equivalently a family of functions describing the algorithmic steps. The optimization variables are the parameters – within this family of algorithms- that encode algorithm design: … Read more

    An Effective Dynamic Programming Algorithm for the Minimum-Cost Maximal Knapsack Packing

  • Fabio Furini
  • Ivana Ljubić
  • Markus Sinnl
    • Categories Combinatorial Optimization, Dynamic Programming, Integer Programming

    Given a set of n items with profits and weights and a knapsack capacity C, we study the problem of finding a maximal knapsack packing that minimizes the profit of selected items. We propose for the first time an effective dynamic programming (DP) algorithm which has O(nC) time complexity and O(n+C) space complexity. We demonstrate … Read more

    Optimization with stochastic preferences based on a general class of scalarization functions

  • Nilay Noyan
  • Gabor Rudolf
    • Categories Multi-Criteria Optimization, Stochastic Programming

    It is of crucial importance to develop risk-averse models for multicriteria decision making under uncertainty. A major stream of the related literature studies optimization problems that feature multivariate stochastic benchmarking constraints. These problems typically involve a univariate stochastic preference relation, often based on stochastic dominance or a coherent risk measure such as conditional value-at-risk (CVaR), … Read more

    Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes

  • Isabel Beckenbach
  • Leon Eifler
  • Ambros Gleixner
  • Andreas Grever
  • Jakob Witzig
  • Konstantin Fackeldey
  • Marcus Weber
    • Categories (Mixed) Integer Linear Programming, Chemical Engineering, Optimization of Simulated Systems

    In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to … Read more

    Decomposition of loosely coupled integer programs: A multiobjective perspective

  • Shabbir Ahmed
  • Merve Bodur
  • Natashia Boland
  • George L. Nemhauser
    • Categories Integer Programming, Multi-Criteria Optimization Tags , , ,

    We consider integer programming (IP) problems consisting of (possibly a large number of) subsystems and a small number of coupling constraints that link variables from different subsystems. Such problems are called loosely coupled or nearly decomposable. Motivated by recent developments in multiobjective programming (MOP), we develop a MOP-based decomposition algorithm to solve loosely coupled IPs. … Read more

    Exact algorithms for bi-objective ring tree problems with reliability measures

  • Alessandro Hill
  • Silvia Schwarze
    • Categories Branch and Cut Algorithms, Multi-Criteria Optimization, Network Optimization Tags , , , , ,

    We introduce bi-objective models for ring tree network design with a focus on network reliability within telecommunication applications. Our approaches generalize the capacitated ring tree problem (CRTP) which asks for a partially reliable topology that connects customers with different security requirements to a depot node by combined ring and tree graphs. While the CRTP aims … Read more

    On a Practical Notion of Geoffrion Proper Optimality in Multicriteria Optimization

  • Kalyanmoy Deb
  • Joydeep Dutta
  • Poonam Kesarwani
  • Pradyumn Kumar Shukla
    • Categories Multi-Criteria Optimization, Nonlinear Optimization

    Geoffrion proper optimality is a widely used optimality notion in multicriteria optimization that prevents exact solutions having unbounded trade-offs. As algorithms for multicriteria optimization usually give only approximate solutions, we analyze the notion of approximate Geoffrion proper optimality. We show that in the limit, approximate Geoffrion proper optimality may converge to solutions having unbounded trade-offs. … Read more

    On the Existence of Ideal Solutions in Multi-objective 0-1 Integer Programs

  • Natashia Boland
  • Hadi Charkhgard
  • Martin Savelsbergh
    • Categories 0-1 Programming, Multi-Criteria Optimization Tags , , ,

    We study conditions under which the objective functions of a multi-objective 0-1 integer linear program guarantee the existence of an ideal point, meaning the existence of a feasible solution that simultaneously minimizes all objectives. In addition, we study the complexity of recognizing whether a set of objective functions satisfies these conditions: we show that it … Read more