Other Topics

Multi-Echelon Inventory Management for a Non-Stationary Capacitated Distribution Network

  • Alvaro Maggiar
  • Irene Song
  • Alp Muharremoglu
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Supply Chain Management Tags , ,

    We present an inventory management solution for a non-stationary capacitated multi-echelon distribution network involving thousands of products. Assuming backlogged sales, we revisit and leverage the seminal multi-echelon inventory management results in the literature to establish the structural properties of the problem, and derive an efficient and practical solution method. In particular, we describe how the … Read more

    Using Neural Networks to Solve Linear Bilevel Problems with Unknown Lower Level

  • Ioana Molan
  • Martin Schmidt
    • Categories Other Topics Tags , , ,

    Bilevel problems are used to model the interaction between two decision makers in which the lower-level problem, the so-called follower’s problem, appears as a constraint in the upper-level problem of the so-called leader. One issue in many practical situations is that the follower’s problem is not explicitly known by the leader. For such bilevel problems … Read more

    A unified scheme for scalarization in set optimization

  • Xuan Duc Ha Truong
    • Categories Multi-Criteria Optimization Tags , , ,

    In this work, we propose a new scheme for scalarization in set optimization studied with the Kuroiwa set appoach. First, we define an abstract scalarizing function possessing properties such as global Lipschizity, sublinearity, cone monotonicity, cone representation property, cone interior representation property and uniform positivity. Next, we use this function to define the so called … Read more

    Convergence of Trajectory Following Dynamic Programming algorithms for multistage stochastic problems without finite support assumptions

  • Maël Forcier
  • Vincent Leclère
    • Categories Dynamic Programming, Stochastic Programming Tags , ,

    We introduce a class of algorithms, called Trajectory Following Dynamic Programming (TFDP) algorithms, that iteratively refines approximation of cost-to-go functions of multistage stochastic problems with independent random variables. This framework encompasses most variants of the Stochastic Dual Dynamic Programming algorithm. Leveraging a Lipschitz assumption on the expected cost-to-go functions, we provide a new convergence and … Read more

    Solving large-scale unit-commitment problems using dual dynamic programming and open-source solvers

  • Bruno Colonetti
  • Samuel Brito
  • Erlon Finardi
  • Victor M. Zavala
  • Lucas Picarelli
    • Categories 0-1 Programming, Applications - Science and Engineering, Dynamic Programming Tags , , ,

    The astonishing dimensions and complexity of power systems render them impossible to be managed without the help of cutting-edge software. Due to a lack of scalable, reliable and well documented free and open-source solutions, system operators, regulators, and government agencies often rely on proprietary software to provide them information that ultimately will be used to … Read more

    Data Envelopment Analysis of two-stage processes: An alternative (non-conventional) approach

  • Dimitris Despotis
  • Dimitris Sotiros
  • Gregory Koronakos
    • Categories Other Topics Tags , ,

    Network data envelopment analysis (NDEA) is an extension of standard data envelopment analysis that models the efficiency assessment of DMUs by considering their internal structure. While in standard DEA the DMU is regarded as a single process, in NDEA the DMU is viewed as a network of interconnected sub-processes (stages, divisions), where the flow of … Read more

    DiversiTree: A New Method to Efficiently Compute Diverse Sets of Near-Optimal Solutions to Mixed-Integer Optimization Problems

  • Izuwa Ahanor
  • Hugh R. Medal
  • Andrew C. Trapp
    • Categories Applications - Science and Engineering, Integer Programming, Other Topics Tags , , ,

    While most methods for solving mixed-integer optimization problems compute a single optimal solution, a diverse set of near-optimal solutions can often lead to improved outcomes. We present a new method for finding a set of diverse solutions by emphasizing diversity within the search for near-optimal solutions. Specifically, within a branch-and-bound framework, we investigated parameterized node … Read more

    Robust Phi-Divergence MDPs

  • Chin Pang Ho
  • Marek Petrik
  • Wolfram Wiesemann
    • Categories Dynamic Programming, Robust Optimization Tags , ,

    In recent years, robust Markov decision processes (MDPs) have emerged as a prominent modeling framework for dynamic decision problems affected by uncertainty. In contrast to classical MDPs, which only account for stochasticity by modeling the dynamics through a stochastic process with a known transition kernel, robust MDPs additionally account for ambiguity by optimizing in view … Read more

    A Reduced Jacobian Scheme with Full Convergence for Multicriteria Optimization

  • Mounir El Maghri
  • Youssef Elboulqe
    • Categories Constrained Nonlinear Optimization, Linear Programming, Multi-Criteria Optimization Tags , , , , ,

    In this paper, we propose a variant of the reduced Jacobian method (RJM) introduced by El Maghri and Elboulqe in [JOTA, 179 (2018) 917–943] for multicriteria optimization under linear constraints. Motivation is that, contrarily to RJM which has only global convergence to Pareto KKT-stationary points in the classical sense of accumulation points, this new variant … Read more

    A Proximal Gradient Method for Multi-objective Optimization Problems Using Bregman Functions

  • Md Abu Talhamainuddin Ansary
  • Joydeep Dutta
    • Categories Convex Optimization, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , ,

    In this paper, a globally convergent proximal gradient method is developed for convex multi-objective optimization problems using Bregman distance. The proposed method is free from any kind of a priori chosen parameters or ordering information of objective functions. At every iteration of the proposed method, a subproblem is solved to find a descent direction. This … Read more