Month: August 2021

A hybrid patch decomposition approach to compute an enclosure for multi-objective mixed-integer convex optimization problems

  • Gabriele Eichfelder
  • Leo Warnow
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , ,

    In multi-objective mixed-integer convex optimization multiple convex objective functions need to be optimized simultaneously while some of the variables are only allowed to take integer values. In this paper we present a new algorithm to compute an enclosure of the nondominated set of such optimization problems. More precisely, we decompose the multi-objective mixed-integer convex optimization … Read more

    A two-objective optimization of ship itineraries for a cruise company

  • Gianni Di Pillo
  • Marcello Fabiano
  • Stefano Lucidi
  • Massimo Roma
    • Categories Applications - OR and Management Sciences, Transportation

    This paper deals with the problem of cruise itinerary planning which plays a central role in worldwide cruise ship tourism. In particular, the Day-by-day Cruise Itinerary Optimization (DCIO) problem is considered. Assuming that a cruise has been planned in terms of homeports and journey duration, the DCIO problem consist in determining the daily schedule of … Read more

    On implementation details and numerical experiments for the HyPaD algorithm to solve multi-objective mixed-integer convex optimization problems

  • Gabriele Eichfelder
  • Leo Warnow
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , ,

    In this paper we present insights on the implementation details of the hybrid patch decomposition algorithm (HyPaD) for convex multi-objective mixed-integer optimization problems. We discuss how to implement the SNIA procedure which is basically a black box algorithm in the original work by Eichfelder and Warnow. In addition, we present and discuss results for various … Read more

    Interpretable Policies and the Price of Interpretability in Hypertension Treatment Planning

  • Gian-Gabriel Garcia
  • Wesley Marrero
  • Lauren Steimle
  • Jeremy Sussman
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Dynamic Programming Tags , , , , ,

    Problem definition: Effective hypertension management is critical to reducing consequences of atherosclerotic cardiovascular disease, a leading cause of death in the United States. Clinical guidelines for hypertension can be enhanced using decision-analytic approaches, capable of capturing many complexities in treatment planning. However, model-generated recommendations may be uninterpretable/unintuitive, limiting their acceptability in practice. We address this … Read more

    On Piecewise Linear Approximations of Bilinear Terms: Structural Comparison of Univariate and Bivariate Mixed-Integer Programming Formulations

  • Lukas Hager
  • Robert Burlacu
  • Andreas Bärmann
  • Thomas Kleinert
    • Categories (Mixed) Integer Linear Programming, Global Optimization Theory, Quadratic Programming Tags , , , ,

    Bilinear terms naturally appear in many optimization problems. Their inherent nonconvexity typically makes them challenging to solve. One approach to tackle this difficulty is to use bivariate piecewise linear approximations for each variable product, which can be represented via mixed-integer linear programming (MIP) formulations. Alternatively, one can reformulate the variable products as a sum of … Read more

    Linear Control Policies for Online Vehicle Relocation in Shared Mobility Systems

  • Yuichi Takano
  • Yasuhiro Yoshida
    • Categories Transportation

    In one-way station-based shared mobility systems, where system users share vehicles for making trips between vehicle stations, the accumulation of one-way trips inevitably causes vehicle imbalances between stations. To correct these imbalances, we focus on the effective use of linear control policies for calculating online vehicle relocations from a history of user trips. Our scenario-based … Read more

    Solving Graph Partitioning on Sparse Graphs: Cuts, Projections, and Extended Formulations

  • Demetrios Papazaharias
  • Jose L. Walteros
    • Categories Combinatorial Optimization, Network Optimization Tags , , , ,

    This paper explores new solution approaches for the graph partitioning problem. While the classic formulations for graph partitioning are compact, they either suffer from a poor relaxation, symmetry, or contain a cubic number of constraints regardless of the graph density. These shortcomings often result in poor branch-and-bound performance. We approach this problem from perspective of … Read more

    An abstract convergence framework with application to inertial inexact forward-backward methods

  • Silvia Bonettini
  • Peter Ochs
  • Marco Prato
  • Simone Rebegoldi
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    In this paper we introduce a novel abstract descent scheme suited for the minimization of proper and lower semicontinuous functions. The proposed abstract scheme generalizes a set of properties that are crucial for the convergence of several first-order methods designed for nonsmooth nonconvex optimization problems. Such properties guarantee the convergence of the full sequence of … Read more

    QCQP with Extra Constant Modulus Constraints: Theory and Applications on QoS Constrained Hybrid Beamforming for mmWave MU-MIMO

  • Xin He
    • Categories Constrained Nonlinear Optimization, Quadratic Programming, Telecommunications Tags , , , , , , , ,

    The constant modulus constraint is widely used in analog beamforming, hybrid beamforming, intelligent reflecting surface design, and radar waveform design. The quadratically constrained quadratic programming (QCQP) problem is also widely used in signal processing. However, the QCQP with extra constant modulus constraints was not systematically studied in mathematic programming and signal processing. For example, the … Read more

    Linear relaxation based branch-and-bound for multi-objective integer programming with warm-starting

  • Nicolas Forget
  • Sune Lauth Gadegaard
  • Lars Relund Nielsen
    • Categories Multi-Criteria Optimization

    In this paper we propose a generic branch-and-bound algorithm for solving multi-objective integer linear programming problems. % In the recent literature, competitive frameworks has been proposed for bi-objective 0-1 problems, and many of these frameworks rely on the use of the linear relaxation to obtain lower bound sets. When increasing the number of objective functions, … Read more