Chance Constrained Optimization with Robust and Sampling Approximation

  • Author / Creator
    Li, Zhuangzhi
  • Uncertainty is pervasive in various process operations problems. Its appearance spans from the detailed process description of multi-site manufacturing. In practical applications, there is a need for making optimal and reliable decisions in the presence of uncertainties. Asking for constraint satisfaction at some level of probability is reasonable in many applications, which calls for the utilization of chance constraints. This thesis studies the approximation methods for solving the chance constrained optimization problems. Two approximation methods were considered: Robust optimization approximation and Sample average approximation. For the robust optimization approximation method, an optimal uncertainty set size identification algorithm is proposed, which can find the smallest possible uncertainty set size that leads to the least conservative robust optimization approximation. For the sample average approximation method, a new linear programming based scenario reduction method is proposed, which can reduce the number of samples used in the sample average approximation problem, thus lead to reduction of computational complexity. Furthermore, the proposed scenario reduction method is computationally more efficient than the existing methods. The effectiveness of the proposed methods is demonstrated by several case studies.

  • Subjects / Keywords
  • Graduation date
    Fall 2015
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.