# (635a) A Scalable Stochastic Programming Approach for Designing Flexible Systems

#### AIChE Annual Meeting

#### 2019

#### 2019 AIChE Annual Meeting

#### Computing and Systems Technology Division

#### Design and Operations Under Uncertainty

#### Thursday, November 14, 2019 - 8:00am to 8:19am

The stochastic flexibility (SF) index is a flexibility measure that exactly quantifies the probability of finding feasible operation and thus avoids the conservative behavior associated with uncertainty sets [8]. Specifically, it models uncertain parameters as random variables with an associated probability density function that can be integrated over the feasible region to determine the probability of satisfying system constraints (i.e., having feasible operation). It can be computed rigorously by evaluating the feasibility of Monte Carlo samples [9]. The SF index can be used as a metric to guide the design of flexible systems. Such a design problem would seek a design that minimizes a design cost while ensuring that the system remains feasible with a given SF index. This approach gives rise to a joint chance constraint problem that is computationally challenging to solve. In particular, the joint chance constraint often needs to be reformulated by using binary variables [10].

In this presentation, we demonstrate the utility of this design problem and provide a more scalable approach to reformulate the joint chance constraint using continuous variables. The approach relies on the observation that the joint chance constraint problem provides a Pareto solution for the conflict resolution (multi-objective) problem that seeks to minimize cost and maximize the SF index. We will demonstrate that we can recover the Pareto set for this problem to high accuracy by solving a continuous formulation. This thus provides a scalable approach to solve large-scale design problems that would otherwise be intractable. Furthermore, this approach has implications for general joint chance constraint problems that have been traditionally bottle-necked by binary reformulations.

References:

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