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Stochastic mesh adaptive direct search for blackbox optimization using probabilistic estimates

  • Charles Audet
  • Kwassi Joseph Dzahini
  • Michael Kokkolaras
  • Sébastien Le Digabel
    • Categories Nonlinear Optimization, Other Topics, Unconstrained Optimization Tags , , , ,

    We present a stochastic extension of the mesh adaptive direct search (MADS) algorithm originally developed for deterministic blackbox optimization. The algorithm, called StoMADS, considers the unconstrained optimization of an objective function f whose values can be computed only through a blackbox corrupted by some random noise following an unknown distribution. The proposed method is based … Read more

    Objective Selection for Cancer Treatment: An Inverse Optimization Approach

  • Temitayo Ajayi
  • Andrew J. Schaefer
  • Taewoo Lee
    • Categories Biomedical Applications, Convex and Nonsmooth Optimization, Multi-Criteria Optimization Tags , , , , , ,

    In radiation therapy treatment-plan optimization, selecting a set of clinical objectives that are tractable and parsimonious yet effective is a challenging task. In clinical practice, this is typically done by trial and error based on the treatment planner’s subjective assessment, which often makes the planning process inefficient and inconsistent. We develop the objective selection problem … Read more

    Risk-Averse Optimal Control

  • Alois Pichler
  • Ruben Schlottter
    • Categories Dynamic Programming, Stochastic Programming Tags , ,

    In the context of multistage stochastic optimization, it is natural to consider nested risk measures, which originate by repeatedly composing risk measures, conditioned on realized observations. Starting from this discrete time setting, we extend the notion of nested risk measures to continuous time by adapting the risk levels in a time dependent manner. This time … Read more

    Representation of the Pareto front for heterogeneous multi-objective optimization

  • Gabriele Eichfelder
  • Jana Thomann
    • Categories Multi-Criteria Optimization, Unconstrained Optimization Tags , , ,

    Optimization problems with multiple objectives which are expensive, i.e. where function evaluations are time consuming, are difficult to solve. Finding at least one locally optimal solution is already a difficult task. In case only one of the objective functions is expensive while the others are cheap, for instance analytically given, this can be used in … Read more

    On the intrinsic core of convex cones in real linear spaces

  • Ali P. Farajzadeh
  • Christian Günther
  • Christiane Tammer
  • Bahareh Khazayel
    • Categories Convex Optimization, Multi-Criteria Optimization Tags , , , , , , ,

    Convex cones play an important role in nonlinear analysis and optimization theory. In particular, specific normal cones and tangent cones are known to be convex cones, and it is a crucial fact that they are useful geometric objects for describing optimality conditions. As important applications (especially, in the fields of optimal control with PDE constraints, … Read more

    Computational Enhancement in the Application of the Branch and Bound Method for Linear Integer Programs and Related Models

  • Ali Al-Hasani
  • Andrew C. Eberhard
  • Masar Al-Rabeeah
  • Santosh Kumar
  • Elias Munapo
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , , , , ,

    In this paper, a reformulation that was proposed for a knapsack problem has been extended to single and bi-objective linear integer programs. A further reformulation by adding an upper bound constraint for a knapsack problem is also proposed and extended to the bi-objective case. These reformulations significantly reduce the number of branch and bound iterations … Read more

    Methods for multiobjective bilevel optimization

  • Gabriele Eichfelder
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization

    This paper is on multiobjective bilevel optimization, i.e. on bilevel optimization problems with multiple objectives on the lower or on the upper level, or even on both levels. We give an overview on the major optimality notions used in multiobjective optimization. We provide characterization results for the set of optimal solutions of multiobjective optimization problems … Read more

    Integer Programming, Constraint Programming, and Hybrid Decomposition Approaches to Discretizable Distance Geometry Problems

  • Merve Bodur
  • Moira MacNeil
    • Categories Branch and Cut Algorithms, Integer Programming, Other Topics Tags , , , ,

    Given an integer dimension K and a simple, undirected graph G with positive edge weights, the Distance Geometry Problem (DGP) aims to find a realization function mapping each vertex to a coordinate in K-dimensional space such that the distance between pairs of vertex coordinates is equal to the corresponding edge weights in G. The so-called … Read more

    RaBVIt-SG, an algorithm for solving Feedback Nash equilibria in Multiplayers Stochastic Differential Games

  • Jorge Herrera de la Cruz
  • Benjamin Ivorra
  • Ángel M. Ramos
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Marketing Tags , , ,

    In a previous work, we have introduced an algorithm, called RaBVItG, used for computing Feedback Nash equilibria of deterministic multiplayers Differential Games. This algorithm is based on a sequence of Game Iterations (i.e., a numerical method to simulate an equilibrium of a Differential Game), combined with Value Iterations (i.e, a numerical method to solve a … Read more

    Multi-Module Capacitated Lot-Sizing Problem, and its Generalizations with Two-Echelons and Piecewise Concave Production Costs

  • Kartik Kulkarni
  • Manish Bansal
    • Categories 0-1 Programming, Dynamic Programming, Production and Logistics Tags , , , , ,

    We study new generalizations of the classical capacitated lot-sizing problem with concave production (or transportation), holding, and subcontracting cost functions in which the total production (or transportation) capacity in each time period is the summation of capacities of a subset of n available modules (machines or vehicles) of different capacities. We refer to this problem … Read more