Other Topics

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

    Moulin Mechanism Design for Freight Consolidation

  • Maged M. Dessouky
  • Alejandro Toriello
  • Nelson A. Uhan
  • Wentao Zhang
    • Categories Game Theory, Supply Chain Management, Transportation

    In freight consolidation, a “fair” cost allocation scheme is critical for forming and sustaining horizontal cooperation that leads to reduced transportation cost. We study a cost-sharing problem in a freight consolidation system with one consolidation center and a common destination. In particular, we design a mechanism that collects bids from a set of suppliers, and … Read more

    On cone based decompositions of proper Pareto optimality

  • Marlon Braun
  • Hartmut Schmeck
  • Pradyumn Kumar Shukla
    • Categories Global Optimization, Multi-Criteria Optimization Tags , , ,

    In recent years, the research focus in multi-objective optimization has shifted from approximating the Pareto optimal front in its entirety to identifying solutions that are well-balanced among their objectives. Proper Pareto optimality is an established concept for eliminating Pareto optimal solutions that exhibit unbounded tradeo ffs. Imposing a strict tradeo ff bound allows specifying how many units … Read more

    The proximal point method for locally Lipschitz functions in multiobjective optimization

  • Glaydston Bento
  • João Xavier da Cruz Neto
  • Antoine Soubeyran
  • João Carlos Souza
  • G. López
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , , , , ,

    This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by Bonnel et al. (SIAM J. Optim., 4 (2005), pp. 953-970) is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new approach for convergence analysis of the … Read more

    SCORE Allocations for Bi-objective Ranking and Selection

  • Guy Feldman
  • Susan R. Hunter
    • Categories Global Optimization, Multi-Criteria Optimization, Stochastic Programming Tags , ,

    The bi-objective R&S problem is a special case of the multi-objective simulation optimization problem in which two conflicting objectives are known only through dependent Monte Carlo estimators, the decision space or number of systems is finite, and each system can be sampled to some extent. The solution to the bi-objective R&S problem is a set … Read more