(710f) Design for Flexibility: An Adjustable Robust Optimization Approach

Flexibility is a key consideration when designing an industrial system to allow for safe and effective operation despite plausible uncertainties in the system conditions. With the increasing use of intermittent resources, more stringent safety and environmental regulations, and volatile market conditions, it becomes vital to incorporate flexibility requirements in the operation and design of chemical processes. In traditional flexibility analysis [1-3], a flexibility index is used to quantify the level of flexibility for a given design. This scalar flexibility index corresponds to the largest size of a hyperrectangular uncertainty set for which the operation of the system is guaranteed to be feasible. Conversely, one can also optimize the design for a given flexibility index, i.e. a required level of flexibility [4].

In this work, we propose a new design approach to directly determine the design that maximizes the flexibility of the system. Here, we consider a more general, polyhedral uncertainty set that is parametrized using a vector of flexibility parameters instead of just one scalar flexibility index; this allows for more complex structures and the incorporation of multiple flexibility measures. The overall level of flexibility is expressed as a function of these flexibility parameters. It can be directly maximized or incorporated into a multi-objective optimization framework with cost as the other objective function, which can provide insights into the trade-off between cost and flexibility. We show that such a design problem can be formulated as a two-stage adjustable robust optimization problem with endogenous, i.e. decision-dependent, uncertainty [5]. Here, the design decisions and flexibility parameters are the first-stage variables while the operational variables (or control variables) constitute the second-stage decisions. The endogenous uncertainty is of type 1 since the flexibility parameters alter the shape and size of the uncertainty set [6]. To solve this problem, we employ a parametric cutting plane method, which is an extension of the cutting plane method [7] used for traditional robust optimization problems with decision-independent uncertainty sets. We demonstrate the key features and efficacy of the proposed flexible design approach with illustrative examples as well as a larger case study related to the design of a power-intensive process participating in demand response.

References

[1] Swaney, R. E., & Grossmann, I. E. (1985). An index for operational flexibility in chemical process design. Part I: Formulation and theory. AIChE Journal, 31(4), 621-630.

[2] Grossmann, I. E., Calfa, B. A., & Garcia-Herreros, P. (2014). Evolution of concepts and models for quantifying resiliency and flexibility of chemical processes. Computers & Chemical Engineering, 70, 22-34.

[3] Bhosekar, A., & Ierapetritou, M. (2018). Advances in surrogate based modeling, feasibility analysis, and optimization: A review. Computers & Chemical Engineering, 108, 250-267.

[4] Zhang, Q., Grossmann, I. E., & Lima, R. M. (2016). On the relation between flexibility analysis and robust optimization for linear systems. AIChE Journal, 62(9), 3109-3123.

[5] Lappas, N. H., & Gounaris, C. E. (2018). Robust optimization for decision-making under endogenous uncertainty. Computers & Chemical Engineering, 111, 252-266.

[6] Zhang, Q., & Feng, W. (2020). A unified framework for adjustable robust optimization with endogenous uncertainty. AIChe Journal, 66(12), e17047.

[7] Mutapcic, A., & Boyd, S. (2009). Cutting-set methods for robust convex optimization with pessimizing oracles. Optimization Methods & Software, 24(3), 381-406.