Other Topics

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

    Cooperative vs Noncooperative Scenarios in multi-objective Potential games: the multi-portfolio context

  • Valerio Giuseppe Sasso
  • Lorenzo Lampariello
  • Simone Sagratella
    • Categories Convex Optimization, Game Theory Tags , , ,

    We focus on multi-agent, multi-objective problems, particularly on those where the objectives admit a potential structure. We show that the solution to the potential multi-objective problem is always a noncooperative optimum for the multi-agent setting. Furthermore, we identify a class of problems for which every noncooperative solution can be computed via the potential problem. We … Read more

    Investment and Operational Planning for an electric market with massive entry of renewable energy

  • Matías Vera
  • Alejandro Jofré
  • Nicolas Hernández-Santibáñez
    • Categories Dynamic Programming, Network Optimization, Stochastic Programming Tags

    In this paper, we study a joint problem in which the Independent System Operator (ISO) intends to minimize the joint cost of operation and investment in a network structure. The problem is formulated through operational and investment control variables; we discuss the hierarchy between them and use the so-called Day Ahead Problem to find an … Read more

    Teaching Statistics Using Facility Location Modeling: A Course-based Undergraduate Research Experience

  • Abel Sapirstein
  • Lauren Steimle
    • Categories Applications - OR and Management Sciences, Other Topics Tags , , , ,

    There is a growing need to expand and strengthen the industrial engineering/operations research workforce. Undergraduate research experiences are an effective way to build in-demand skills and to attract people to science, technology, engineering, and mathematics fields, such as industrial engineering/operations research. However, the traditional apprenticeship model of an undergraduate research experience limits the number of … Read more

    A first-order method for nonconvex-nonconcave minimax problems under a local Kurdyka-Łojasiewicz condition

  • Zhaosong Lu
  • Xiangyuan Wang
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Other Topics Tags , , , ,

    We study a class of nonconvex–nonconcave minimax problems in which the inner maximization problem satisfies a local Kurdyka–Łojasiewicz (KL) condition that may vary with the outer minimization variable. In contrast to the global KL or Polyak–Łojasiewicz (PL) conditions commonly assumed in the literature—which are significantly stronger and often too restrictive in practice—this local KL condition … 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

    Best-Response Dynamics for Large-Scale Integer Programming Games with Applications to Aquatic Invasive Species Prevention

  • Hyunwoo Lee
  • Robert Hildebrand
  • Wenbo Cai
  • I. Esra Buyuktahtakin Toy
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Game Theory Tags , , , ,

    This paper presents a scalable algorithm for computing the best pure Nash equilibrium (PNE) in large-scale integer programming games (IPGs). While recent advances in IPG algorithms are extensive, existing methods are limited to a small number of players, typically 𝑛 = 2, 3. Motivated by a county-level aquatic invasive species (AIS) prevention problem involving 84 … Read more