Multi-Criteria Optimization

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 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

    On Vectorization Strategies in Set Optimization

  • Gabriele Eichfelder
  • Tobias Gerlach
    • Categories Multi-Criteria Optimization Tags , , ,

    In this paper, we investigate solution approaches in set optimization that are based on so-called vectorization strategies. Thereby, the original set-valued problems are reformulated as multi-objective optimization problems, whose optimal solution sets approximate those of the original ones in a certain sense. We consider both infinite-dimensional and finite-dimensional vectorization approaches. In doing so, we collect … 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

    ASMOP: Additional sampling stochastic trust region method for multi-objective problems

  • Nataša Krklec Jerinkić
  • Luka Rutešić
    • Categories Multi-Criteria Optimization, Optimization of Systems modeled by PDEs, Stochastic Programming Tags , , , , ,

    We consider an unconstrained multi-criteria optimization problem with finite sum objective functions. The proposed algorithm belongs to a non-monotone trust-region framework where additional sampling approach is used to govern the sample size and the acceptance of a candidate point. Depending on the problem, the method can result in a mini-batch or an increasing sample size … Read more

    A stochastic gradient method for trilevel optimization

  • Tommaso Giovannelli
  • Griffin D. Kent
  • Luis Nunes Vicente
    • Categories Multi-Criteria Optimization Tags , , ,

    With the success that the field of bilevel optimization has seen in recent years, similar methodologies have started being applied to solving more difficult applications that arise in trilevel optimization. At the helm of these applications are new machine learning formulations that have been proposed in the trilevel context and, as a result, efficient and … Read more

    Steepest descent method using novel adaptive stepsizes for unconstrained nonlinear multiobjective programming

  • Pham Thi Hoai
    • Categories Convex Optimization, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    We propose new adaptive strategies to compute stepsizes for the steepest descent method to solve unconstrained nonlinear multiobjective optimization problems without employing any linesearch procedure. The resulting algorithms can be applied to a wide class of nonconvex unconstrained multi-criteria optimization problems satisfying a global Lipschitz continuity condition imposed on the gradients of all objectives. In … 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