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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 16, 2011
- Accession Number
- ADA567240
Entities
People
- Shabbir Ahmed
Organizations
- Georgia Tech