multiobjective optimization

On Supportedness-Promoting Image Space Transformations in Multiobjective Optimization

  • Felix Neussel
  • Oliver Stein
    • Categories Multi-Criteria Optimization Tags , , , ,

    We study the supportedness of nondominated points of multiobjective optimization problems, that is, whether they can be obtained via weighted sum scalarization. One key question is how supported points behave under an efficiency-preserving transformation of the original problem. Under a differentiability assumption, we characterize the transformations that preserve both efficiency and supportedness as the component-wise … Read more

    Properties of Enclosures in Multiobjective Optimization

  • Gabriele Eichfelder
  • Daniel Hoff
    • Categories Global Optimization, Multi-Criteria Optimization, Nonlinear Optimization Tags , ,

    A widely used approximation concept in multiobjective optimization is the concept of enclosures. These are unions of boxes defined by lower and upper bound sets that are used to cover optimal sets of multiobjective optimization problems in the image space. The width of an enclosure is taken as a quality measure. In this paper, we … Read more

    On the Structure of the Inverse-Feasible Region of a Multiobjective Integer Program

  • Tyler Perini
    • Categories Combinatorial Optimization, Integer Programming, Multi-Criteria Optimization Tags , ,

    Many optimization problems are made more challenging due to multiple, conflicting criteria. The subjective nature of balancing these criteria motivates techniques for inverse optimization. This study establishes foundations for an exact representation of the inverse feasible region of a multiobjective integer program. We provide the first insights into its exact structure, as well as two … Read more

    On Bivariate Achievement Scalarizing Functions

  • Philip de Castro
    • Categories Multi-Criteria Optimization Tags , ,

    Achievement Scalarizing Functions (ASFs) are a class of scalarizing functions for multiobjective optimization problems that have been successfully implemented in many applications due to their mathematical elegance and decision making utility. However, no formal proofs of the fundamental properties of ASFs have been presented in the literature. Furthermore, developments of ASFs, including the construction of … Read more

    Worst-Case Complexity of High-Order Algorithms for Pareto-Front Reconstruction

  • Andrea Cristofari
  • Marianna De Santis
  • Giampaolo Liuzzi
  • Stefano Lucidi
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags , ,

    In this paper, we are concerned with a worst-case complexity analysis of a-posteriori algorithms for unconstrained multiobjective optimization. Specifically, we propose an algorithmic framework that generates sets of points by means of $p$th-order models regularized with a power $p+1$ of the norm of the step. Through a tailored search procedure, several trial points are generated … Read more

    Quadratic Convex Reformulations for MultiObjective Binary Quadratic Programming

  • Marianna De Santis
  • Lucas Létocart
  • Yue Zhang
    • Categories (Mixed) Integer Nonlinear Programming, 0-1 Programming, Multi-Criteria Optimization Tags , , ,

    Multiobjective binary quadratic programming refers to optimization problems involving multiple quadratic – potentially non-convex – objective functions and a feasible set that includes binary constraints on the variables. In this paper, we extend the well-established Quadratic Convex Reformulation technique, originally developed for single-objective binary quadratic programs, to the multiobjective setting. We propose a branch-and-bound algorithm … Read more

    Pareto Leap: An Algorithm for Biobjective Mixed-Integer Programming

  • Philip de Castro
  • Margaret Wiecek
    • Categories (Mixed) Integer Nonlinear Programming, Integer Programming, Multi-Criteria Optimization Tags , , ,

    Many real-life optimization problems need to make decisions with discrete variables and multiple, conflicting objectives. Due to this need, the ability to solve such problems is an important and active area of research. We present a new algorithm, called Pareto Leap, for identifying the (weak) Pareto slices of biobjective mixed-integer programs (BOMIPs), even when Pareto … Read more

    Local Upper Bounds Based on Polyhedral Ordering Cones

  • Gabriele Eichfelder
  • Firdevs Ulus
    • Categories Multi-Criteria Optimization Tags , , ,

    The concept of local upper bounds plays an important role for numerical algorithms in nonconvex, integer, and mixed-integer multiobjective optimization with respect to the componentwise partial ordering, that is, where the ordering cone is the nonnegative orthant. In this paper, we answer the question on whether and how this concept can be extended to arbitrary … Read more

    Scaled Proximal Gradient Methods for Multiobjective Optimization: Improved Linear Convergence and Nesterov’s Acceleration

  • Jian Chen
    • Categories Multi-Criteria Optimization Tags , , ,

    Over the past two decades, descent methods have received substantial attention within the multiobjective optimization field. Nonetheless, both theoretical analyses and empirical evidence reveal that existing first-order methods for multiobjective optimization converge slowly, even for well-conditioned problems, due to the objective imbalances. To address this limitation, we incorporate curvature information to scale each objective within … Read more