Multi-Criteria Optimization

Objective-Function Free Multi-Objective Optimization: Rate of Convergence and Performance of an Adagrad-like algorithm

  • Marianna De Santis
  • Gabriele Eichfelder
  • Margherita Porcelli
    • Categories Multi-Criteria Optimization, Unconstrained Optimization Tags , ,

    We propose an Adagrad-like algorithm for multi-objective unconstrained optimization that relies on the computation of a common descent direction only. Unlike classical local algorithms for multi-objective optimization, our approach does not rely on the dominance property to accept new iterates, which allows for a flexible and function-free optimization framework. New points are obtained using an … Read more

    An adaptive line-search-free multiobjective gradient method and its iteration-complexity analysis

  • Max L. N. Gonçalves
  • Geovani Nunes Grapiglia
  • Jefferson Gonçalves Melo
    • Categories Multi-Criteria Optimization, Unconstrained Optimization Tags , , ,

    This work introduces an Adaptive Line-Search-Free Multiobjective Gradient (AMG) method for solving smooth multiobjective optimization problems. The proposed approach automatically adjusts stepsizes based on steepest descent directions, promoting robustness with respect to stepsize choice while maintaining low computational cost. The method is specifically tailored to the multiobjective setting and does not rely on function evaluations, … Read more

    First-order Methods for Unconstrained Vector Optimization Problems: A Unified Majorization-Minimization Perspective

  • Jian Chen
    • Categories Multi-Criteria Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , ,

    In this paper, we develop a unified majorization-minimization scheme and convergence analysis with first-order surrogate functions for unconstrained vector optimization problems (VOPs). By selecting different surrogate functions, the unified method can be reduced to various existing first-order methods. The unified convergence analysis reveals that the slow convergence of the steepest descent method is primarily attributed … Read more

    An active-set method for box-constrained multiobjective optimization

  • N. S. Fazzio
  • Leandro Fonseca Prudente
  • María Laura Schuverdt
    • Categories Multi-Criteria Optimization Tags , , ,

    We propose an active-set algorithm for smooth multiobjective optimization problems subject to box constraints. The method works on one face of the feasible set at a time, treating it as a lower-dimensional region on which the problem simplifies. At each iteration, the algorithm decides whether to remain on the current face or to move to … Read more

    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