Other Topics

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

    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

    Decision Intelligence for Nationwide Ventilator Allocation

  • Jiajun Xu
  • Suvrajeet Sen
    • Categories Applications - OR and Management Sciences, Basic Sciences Applications, Optimization of Simulated Systems Tags , , , ,

    Many states in the U.S. have faced shortages of medical resources because of the surge in the number of patients suffering from COVID-19. As many projections indicate, the situation will be far worse in coming months. The upcoming challenge is not only due to the exponential growth in cases but also because of inherent uncertainty … Read more

    Multi-criteria Course Mode Selection and Classroom Assignment Under Sudden Space Scarcity

  • Mehran Navabi-Shirazi
  • Mohamed El Tonbari
  • Natashia Boland
  • Dima Nazzal
  • Lauren Steimle
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization, Scheduling Tags , , , ,

    Problem Definition: While physical (or ‘social’) distancing is an important public health intervention during airborne pandemics, physical distancing dramatically reduces the effective capacity of classrooms. During the COVID-19 pandemic, this presented a unique problem to campus planners who hoped to deliver a meaningful amount of in-person instruction in a way that respected physical distancing. This … Read more

    On the exactness of the eps-constraint method for bi-objective integer nonlinear programming

  • Marianna De Santis
  • Daniele Patria
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , , ,

    The eps-constraint method is a well-known scalarization technique used for multiobjective optimization. We explore how to properly define the step size parameter of the method in order to guarantee its exactness when dealing with problems having two nonlinear objective functions and integrality constraints on the variables. Under specific assumptions, we prove that the number of … Read more

    Dual SDDP for risk-averse multistage stochastic programs

  • Bernardo Freitas Paulo da Costa
  • Vincent Leclère
    • Categories Dynamic Programming, Stochastic Programming Tags , , , ,

    Risk-averse multistage stochastic programs appear in multiple areas and are challenging to solve. Stochastic Dual Dynamic Programming (SDDP) is a well-known tool to address such problems under time-independence assumptions. We show how to derive a dual formulation for these problems and apply an SDDP algorithm, leading to converging and deterministic upper bounds for risk-averse problems. … Read more

    Robust Integration of Electric Vehicles Charging Load in Smart Grid’s Capacity Expansion Planning

  • Sajad Aliakbari-Sani
  • Olivier Bahn
  • Erick Delage
  • Rinel Foguen Tchuendom
    • Categories Energy, Game Theory, Robust Optimization Tags , , ,

    Battery charging of electric vehicles (EVs) needs to be properly coordinated by electricity producers to maintain network reliability. In this paper, we propose a robust approach to model the interaction between a large fleet of EV users and utilities in a long-term generation expansion planning problem. In doing so, we employ a robust multi-period adjustable … Read more

    Bishop-Phelps cones given by an equation in Banach spaces

  • Xuan Duc Ha Truong
  • Johannes Jahn
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization, Second-Order Cone Programming Tags , , , ,

    In this work, we study Bishop-Phelps cones (briefly, BP cones) given by an equation in Banach spaces. Due to the special form, these cones enjoy interesting properties. We show that nontrivial BP cones given by an equation form a “large family” in some sense in any Banach space and they can be used to characterize … Read more

    A primal heuristic to compute an upper bound set for multi-objective 0-1 linear optimisation problems

  • Xavier Gandibleux
  • Guillaume Gasnier
  • Said Hanafi
    • Categories Branch and Cut Algorithms, Integer Programming, Multi-Criteria Optimization

    This paper presents an algorithm aiming to compute an upper bound set for a multi-objective linear optimisation problem with binary variables (p-01LP). Inspired by the well known « Feasibility Pump » algorithm in single objective optimisation, it belongs to the class of primal heuristics. The proposed algorithm, named « Gravity Machine », aims to deal … Read more

    A Vectorization Scheme for Nonconvex Set Optimization Problems

  • Gabriele Eichfelder
  • Ernest Quintana
  • Stefan Rocktäschel
    • Categories Convex and Nonsmooth Optimization, Multi-Criteria Optimization Tags , , , ,

    In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from multiobjective optimization. Our strategy consists of deriving a parametric family of multiobjective optimization problems whose optimal solution … Read more