2016 Optimization Days

HEC Montréal, Québec, Canada, May 2 — 4, 2016

Schedule Authors My Schedule
Cal add eabad1550a3cf3ed9646c36511a21a854fcb401e3247c61aefa77286b00fe402

MA5 Theory and Application of Robust Optimization

May 2, 2016 10:30 AM – 12:10 PM

Location: Marie-Husny

Chaired by Erick Delage

3 Presentations

  • Cal add eabad1550a3cf3ed9646c36511a21a854fcb401e3247c61aefa77286b00fe402
    10:30 AM - 10:55 AM

    Stability and continuity in robust linear and robust linear semi-infinite optimization

    • Timothy C.Y. Chan, University of Toronto
    • Philip Allen Mar, presenter, University of Toronto

    We present novel results on the stability of Robust Optimization (RO) problems with respect to perturbations in their uncertainty sets. We focus on Robust Linear and Robust Linear Semi-Infinite Optimization (LSIO) problems under cost function and constraint uncertainty, and prove Lipschitz continuity of the optimal value, and present results on the stability of the optimal solution set mapping and the ϵ-approximate optimal solution set mapping, all with respect to the Hausdorff distance between their uncertainty sets. Given the surge of interest in constructing data-driven uncertainty sets, our work provides an essential analysis of how the uncertainty set topology affects the optimal value and optimal solution set of a Robust Optimization problem.

  • Cal add eabad1550a3cf3ed9646c36511a21a854fcb401e3247c61aefa77286b00fe402
    10:55 AM - 11:20 AM

    Practicable robust optimization for decomposable functions

    • Erick Delage, presenter, GERAD, HEC Montréal
    • Luca Giovanni Gianoli, Polytechnique Montréal
    • Brunilde Sansò, GERAD, Polytechnique Montréal

    Robust optimization (RO) is a powerful means to handle optimization problems where there is a set of parameters that are uncertain. The effectiveness of the method is especially noticeable when these parameters are only known to lie inside some uncertainty region. Unfortunately, there are important computational considerations that have prevented the methodology from being fully adopted in fields of practice where the cost function that needs to be "robustified" is nonlinear with respect to such parameters. In this paper, we propose a new robust optimization formulation that circumvent the computational burden in problems where the cost decomposes as the sum of convex costs for each decision variable. This is done by exploiting the fact that in this formulation the worst-case cost function can be expressed as a convex combination between a nominal and an upper-bound cost function. One can still control the conservatism of the robust solution by adjusting how many terms of the total cost function can simultaneously reach their respective most pessimistic value. In order to demonstrate the potential of our "practicable robust counterpart" formulation, we present how it can be employed on the robust optimization of packet routing on a telecommunication network with congestion.

  • Cal add eabad1550a3cf3ed9646c36511a21a854fcb401e3247c61aefa77286b00fe402
    11:20 AM - 11:45 AM

    Robust optimization in R&D project selection

    • Aurelie Thiele, presenter, Lehigh University
    • Ruken Duzgun, Marriott International
    • Shuyi Wang, Lehigh University

    We discuss robust optimization models in the context of R&D project selection. The first part of the talk describes how tractable approximations to chance constraints can be used to develop an insightful RO framework. The second part of the talk focuses on designing and analyzing mathematical approaches that balance incremental and radical innovation.

Back