Multi-Criteria Optimization

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

    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

    A study of Liu-Storey conjugate gradient methods for vector optimization

  • Max L. N. Gonçalves
  • Leandro Fonseca Prudente
  • F. S. Lima
    • Categories Multi-Criteria Optimization, Unconstrained Optimization Tags , , ,

    This work presents a study of Liu-Storey (LS) nonlinear conjugate gradient (CG) methods to solve vector optimization problems. Three variants of the LS-CG method originally designed to solve single-objective problems are extended to the vector setting. The first algorithm restricts the LS conjugate parameter to be nonnegative and use a sufficiently accurate line search satisfying … Read more

    An Upper Bound on the Hausdorff Distance Between a Pareto Set and its Discretization in Bi-Objective Convex Quadratic Optimization

  • Burla E. Ondes
  • Susan R. Hunter
    • Categories Multi-Criteria Optimization, Optimization of Simulated Systems Tags , ,

    We provide upper bounds on the Hausdorff distances between the efficient set and its discretization in the decision space, and between the Pareto set (also called the Pareto front) and its discretization in the objective space, in the context of bi-objective convex quadratic optimization on a compact feasible set. Our results imply that if t … Read more

    Parallel Strategies for Direct Multisearch

  • C. P. Brás
  • Ana Luisa Custódio
  • S. Tavares
  • V. Duarte
  • P. Medeiros
    • Categories Bound-constrained Optimization, Multi-Criteria Optimization, Parallel Algorithms

    Direct Multisearch (DMS) is a Derivative-free Optimization class of algorithms suited for computing approximations to the complete Pareto front of a given Multiobjective Optimization problem. It has a well-supported convergence analysis and simple implementations present a good numerical performance, both in academic test sets and in real applications. Recently, this numerical performance was improved with … Read more

    A Multiobjective Approach for Sector Duration Optimization in Stereotactic Radiosurgery Treatment Planning

  • Oylum Şeker
  • Mucahit Cevik
  • Merve Bodur
  • Young Lee-Bartlett
  • Mark Ruschin
    • Categories Biomedical Applications, Multi-Criteria Optimization Tags , , , ,

    Sector duration optimization (SDO) is a problem arising in treatment planning for stereotactic radiosurgery on Gamma Knife. Given a set of isocenter locations, SDO aims to select collimator size configurations and irradiation times thereof such that target tissues receive prescribed doses in a reasonable amount of treatment time, while healthy tissues nearby are spared. We … Read more

    Limit sets in global multiobjective optimization

  • Gabriele Eichfelder
  • Oliver Stein
    • Categories Global Optimization Theory, Multi-Criteria Optimization Tags , , , , ,

    Inspired by the recently introduced branch-and-bound method for continuous multiobjective optimization problems from G. Eichfelder, P. Kirst, L. Meng, O. Stein, A general branch-and-bound framework for continuous global multiobjective optimization, Journal of Global Optimization, 80 (2021) 195-227, we study for a general class of branch-and-bound methods in which sense the generated terminal enclosure and the … Read more