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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

    Optimality of Linear Policies in Distributionally Robust Linear Quadratic Control

  • Bahar Taskesen
  • Dan Iancu
  • Çağıl Koçyiğit
  • Daniel Kuhn
    • Categories Other Topics

    We study a generalization of the classical discrete-time, Linear-Quadratic-Gaussian (LQG) control problem where the noise distributions affecting the states and observations are unknown and chosen adversarially from divergence-based ambiguity sets centered around a known nominal distribution. For a finite horizon model with Gaussian nominal noise and a structural assumption on the divergence that is satisfied … Read more

    Inspection Games with Incomplete Information and Heterogeneous Resources

  • Bobak McCann
  • Mathieu Dahan
    • Categories Game Theory, Linear Programming, Stochastic Programming Tags , , , ,

    We study a two-player zero-sum inspection game with incomplete information, where an inspector deploys resources to maximize the expected damage value of detected illegal items hidden by an adversary across capacitated locations. Inspection and illegal resources differ in their detection capabilities and damage values. Both players face uncertainty regarding each other’s available resources, modeled via … Read more

    On Parametric Linear Programming Duality

  • Benjamin Hamlin
  • Nathan Adelgren
  • Margaret Wiecek
    • Categories Linear Programming, Other Topics Tags , , ,

    Recognizing the strength of parametric optimization to model uncertainty, we extend the classical linear programming duality theory to a parametric setting. For linear programs with parameters in general locations, we prove parametric weak and strong duality theorems and parametric complementary slackness theorems. ArticleDownload

    Collection points placement in urban delivery: A game-theoretic analysis of public and competitive strategies

  • Fabio Mercurio
  • Margarida Carvalho
  • S.U.K Rohmer
  • Loe Schlicher
  • Tom Van Woensel
    • Categories Facility Planning and Design, Game Theory Tags , , , ,

    Collection point networks are rapidly expanding as delivery companies and public authorities promote their implementation to consolidate deliveries and reduce urban congestion. However, rather than catering to public interest by maximizing accessibility, the placement of collection points remains primarily driven by competition among delivery companies, which seek to maximize their market share. This paper thus … 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

    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