A New Approach for Optimization under Uncertainty
Stacy Janak
Chemical Engineering, Princeton University
Uncertainty is prevalent in many problems due to inaccurate process models and
variability of process and environmental data. It can be shown that optimal
solutions of Mixed-Integer Linear Programming (MILP) problems may become
severely infeasible if the nominal data are slightly perturbed. Our objective
then is to develop a methodology to generate "reliable" solutions,
which are, in a sense, immune to uncertainty in the parameters of MILP problems
[1]. This methodology produces "robust" solutions that remain feasible
in the presence of uncertainty. Robust optimization techniques are developed for
several forms of uncertain data and applied to two different types of MILP
problems. First is the problem of scheduling multipurpose batch chemical plants
in the presence of uncertainty. Utilizing the continuous-time short-term
scheduling model proposed by [2], three of the most common sources of
uncertainty in scheduling problems are addressed, namely processing times of
tasks, market demands for products, and prices of products and raw materials.
The robust optimization formulation is also applied to the problem of
elucidating the complex network connectivity of the signaling pathways in yeast
based on the global gene expression data from the DNA microarray experiments.
Using the mathematical model presented in [3], we consider different forms of
uncertainty in the lumped kinetic parameters and experimental data to show that
feasible MILP solutions for the network topology can become severely infeasible
if the nominal data is perturbed.
RELATED READING: [2] M.G. Ierapetritou and C.A. Floudas. "Effective Continuous-Time Formulation for Short-Term Scheduling: 1. Multipurpose Batch Processes." Ind. Eng. Chem. Res., 37 (1998): 4341-4359. [3] X. Lin, C. A. Floudas, Y. Wang, and J. R. Broach. "Theoretical and Computational Studies of the Glucose Signaling Pathways in Yeast Using Global Gene Expression Data." Biotechnol. Bioeng., 84 (2003): 864--886. |