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: 

[1] X. Lin, S. L. Janak, and C. A. Floudas. "A New Robust Optimization Approach for Scheduling under Uncertainty: I. Bounded Uncertainty." Comput. Chem. Eng., 28 (2004): 1069--1085.

[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.

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