Optimization with Probabilistic Constraints

Abstract

Many important planning and design applications in uncertain environments involve service level or reliability requirements. These include emergency planning, telecommunication network design, cancer therapy planning, and financial optimization. Such requirements give rise to probabilistic or chance constraints. The stochasticity and nonconvexity associated with such constraints make the underlying optimization problem extremely challenging. Current approaches for probabilistically constrained optimization problems are either not able to handle realistic problems or provide much too conservative solutions. In this work: (i) We integrated sampling theory with mixed-integer programming schemes to effectively and efficiently solve large classes of such problems, (ii) We developed new formulations for a wide class of probabilistic set covering problems by exploiting sumodularity properties, (iii) We developed new algorithmic techniques for probabilistic constraints with coefficient uncertainties.

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Document Details

Document Type
Technical Report
Publication Date
Feb 16, 2011
Accession Number
ADA567240

Entities

People

  • Shabbir Ahmed

Organizations

  • Georgia Tech

Tags

Communities of Interest

  • Air Platforms
  • Sensors

DTIC Thesaurus Topics

  • Coefficients
  • Communication Systems
  • Computer Programming
  • Coverings
  • Emergencies
  • Environment
  • Integer Programming
  • Mathematical Programming
  • Operations Research
  • Optimization
  • Reliability
  • Sampling
  • Statistical Analysis
  • Systems Engineering
  • Uncertainty

Fields of Study

  • Computer science

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Operations Research