Multi-Criteria 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

    generalizing the successive shortest path algorithm to solve the multi-objective assignment problem

  • Antonio Sedeño-Noda
    • Categories Multi-Criteria Optimization, Network Optimization, Other Topics Tags , ,

    We introduce a novel characterization of the efficient solutions to the Multi-objective Assignment Problem (MAP), relying solely on Network Flow theory. This result establishes that the set of efficient assignments restricted to the first $k$ origin-destination pairs in the associated bipartite graph can be derived incrementally from the efficient solutions corresponding to the first $k-1$ … Read more

    Global Multi-Objective Simulation Optimization: Error Bounds and Convergence Rates

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

    Consider the context of solving a multi-objective simulation optimization problem with one or more continuous objective functions to global optimality on a compact feasible set. For a simple algorithm that consists of selecting a finite set of feasible points using a space-filling design, expending the same number of simulation replications at each point to estimate … Read more

    A Multivariate Loss Ratio Approach for Systemic Risk Measurement and Allocation

  • Wei Wang
  • HuifuXu
    • Categories Finance and Economics, Multi-Criteria Optimization, Other Topics Tags , , , ,

    The primary challenges in systemic risk measurement involve determining an overall reserve level of risk capital and allocating it to different components based on their systemic relevance. In this paper, we introduce a multivariate loss ratio measure (MLRM), which is the minimum amount of capital to be injected into a financial system such that the … 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

    Consistent and unbiased estimation of the hypervolume of an unknown true Pareto front

  • Xavier Gandibleux
  • Andrzej Jaszkiewicz
    • Categories Combinatorial Optimization, Meta Heuristics, Multi-Criteria Optimization Tags , ,

    Hypervolume is most likely the most often used set quality indicator in (evolutionary) multi-objective optimization. It may be used to compare the quality of solution sets whose images in the objective space are approximations of the true Pareto front. Although in this way we may compare two or more approximations, our knowledge is limited without … Read more

    On Subproblem Tradeoffs in Decomposition and Coordination of Multiobjective Optimization Problems

  • Philip de Castro
  • Margaret Wiecek
    • Categories Multi-Criteria Optimization

    Multiobjective optimization is widely used in applications for modeling and solving complex decision-making problems. To help resolve computational and cognitive difficulties associated with problems which have more than three or four objectives, we propose a decomposition and coordination methodology to support decision making for large multiobjective optimization problems (MOPs) with global, quasi-global, and local variables. … Read more

    MultiObjectiveAlgorithms.jl: a Julia package for solving multi-objective optimization problems

  • Oscar Dowson
  • Xavier Gandibleux
  • Gökhan Kof
    • Categories Multi-Criteria Optimization, Optimization Software and Modeling Systems Tags , , ,

    We present MultiObjectiveAlgorithms.jl, an open-source Julia library for solving multi-objective optimization problems written in JuMP. MultiObjectiveAlgorithms.jl implements a number of different solution algorithms, which all rely on an iterative scalarization of the problem from a multi-objective optimization problem to a sequence of single-objective subproblems. As part of this work, we extended JuMP to support vector-valued … Read more

    Pareto-optimal trees and Pareto forest: a bi-objective optimization model for binary classification

  • Marianna De Santis
  • Daniele Patria
  • Justo Puerto
    • Categories Data Science Applications, Multi-Criteria Optimization, Optimization in Data Science Tags , ,

    As inherently transparent models, classification trees play a central role in interpretable machine learning by providing easily traceable decision paths that allow users to understand how input features contribute to specific predictions. In this work, we introduce a new class of interpretable binary classification models, named Pareto-optimal trees, which aim at combining the complementary strengths … 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