(433h) Continuous Multi-Fidelity Bayesian Optimization for Efficient Integrated Process Design and Advanced Control

It has long been recognized that design and control are interconnected activities that should be performed simultaneously to identify processes with a high degree of operational flexibility [1], [2]. Due to the complexity of simultaneously considering long-term “here-and-now” design decisions and the short-term “wait-and-see” control designs, in practice, the design problem is often tackled first with little-to-no consideration of the system dynamics. Although simple, this type of sequential approach can lead to heavily constrained processes with limited degrees of freedom left for control. Even though a large amount of work has been done on so-called integrated design and control (IDC) [3][4], a tractable, flexible, and accurate framework for optimal IDC does not yet exist. Such a framework is needed to help enable the shift to next-generation manufacturing/energy systems including smart grids [5], multi-product chemical plants [6], and combined heat and power systems [7]. Recently, it has been shown that optimal IDC problems can be generally formulated as multistage stochastic programs (MSPs); however, the resulting MSP quickly becomes intractable when one considers a realistic representation of the problem [8]. The following four properties are particularly challenging to handle: (i) relevant dynamics occur on much shorter timescales than the lifetime of the system; (ii) uncertainties are present that are best described by continuous random variables with large variance; (iii) key operational decisions are discrete (e.g., unit commitment); and (iv) a complex “high-fidelity” simulator (with many interacting components) is needed to accurately model the system. Even when we neglect feature (iv), such that a known equation-oriented system model is available, a scenario approximation to the MSP produces an extremely large-scale mixed-integer nonlinear program (MINLP) that is far beyond the capabilities of existing solvers.

Most work on IDC (e.g., [9]–[11]) has focused on making approximations to relax features (i)-(iv); although these approximations make the MSP tractable, they degrade the accuracy of the solution in ways that are often detrimental to performance (and the error is often not quantified). In our previous work [12], we proposed a general framework for IDC that accurately captures features (i)-(iv) based on two important concepts: (a) approximating the complex set of recourse decisions with a high-quality decision rule (DR) that is a function that maps the measured data to the control decisions at every operational period and (b) applying an efficient simulation-based optimization (SO) procedure to co-optimize the design variables and DR parameters. To develop high-quality DRs in (a), we rely on model predictive control (MPC), which is an optimization-based control strategy for large-scale multivariable systems with constraints. MPC is one of the few control strategies that can handle systems with mixed-integer decisions (feature (iv)). The SO procedure in (b) can be thought of as an outer optimization over the design variables and an inner stochastic simulation to evaluate the expected operating costs/constraints that appear in the outer problem. SO is needed since we cannot assume that the system model or DR has a known, differentiable structure; even though this potentially limits the rate of convergence of the optimization algorithm, it enables the required flexibility in the IDC framework.

Our original work applied Bayesian optimization (BO) to develop an efficient SO approach, which is specifically designed for noisy, expensive-to-evaluate, and black-box objective functions. Even though BO greatly reduces the number of evaluations compared to available alternatives (such as evolutionary algorithms), it still requires a single high-fidelity simulation to be performed at every iteration, meaning it remains quite expensive to find near-optimal designs. In our more recent work [13], we overcame this bottleneck by exploiting lower fidelity approximations of the IDC problem to help guide the BO search process. We found that, if the lower fidelity approximations show a reasonable degree of correlation to the high-fidelity simulator, we can use them to quickly eliminate poor designs so that we can reserve the most expensive simulations for the most promising designs only. However, the multi-fidelity BO (MFBO) approach that we used required two assumptions that can often be difficult to satisfy: we have reasonable estimates of the error between each fidelity level, and we can determine a sequence of fidelities that results in successive improvement in accuracy. In practice, these assumptions limit the type and number of fidelities that can be considered in the IDC problem. As opposed to a finite sequence, an interesting alternative view of the multi-fidelity problem is to treat the fidelities as being in a continuous multi-dimensional space. In IDC problems, for example, we have many tuning knobs that independently control accuracy of the process simulator, DR quality, and problem time horizon, each of which vary on a fine scale. In this work, we develop a new continuous MFBO approach for IDC problems with embedded MPC-based DRs. We demonstrate the performance of continuous (versus discrete) MFBO on the design of a solar-powered building heating ventilation and air-conditioning (HVAC) system, with grid and battery support, under uncertain weather and demand conditions that vary at the hour scale for a year-long planning horizon. We compare continuous MFBO to several baseline algorithms, such as traditional BO and random search, and show that it can repeatedly identify more cost-effective designs under a fixed computational budget.

References

[1] V. Sakizlis, J. D. Perkins, and E. N. Pistikopoulos, “Parametric controllers in simultaneous process and control design optimization,” Ind. Eng. Chem. Res., vol. 42, no. 20, pp. 4545–4563, 2003.

[2] T. V. Thomaidis and E. N. Pistikopoulos, “Towards the incorporation of flexibility, maintenance and safety in process design,” Comput. Chem. Eng., vol. 19, no. SUPPL. 1, pp. 687–692, Jun. 1995, doi: 10.1016/0098-1354(95)87115-2.

[3] A. Flores-Tlacuahuac and L. T. Biegler, “Simultaneous mixed-integer dynamic optimization for integrated design and control,” Comput. Chem. Eng., vol. 31, no. 5–6, pp. 588–600, May 2007, doi: 10.1016/j.compchemeng.2006.08.010.

[4] L. F. Fuentes-Cortés, A. W. Dowling, C. Rubio-Maya, V. M. Zavala, and J. M. Ponce-Ortega, “Integrated design and control of multigeneration systems for building complexes,” Energy, vol. 116, pp. 1403–1416, Dec. 2016, doi: 10.1016/J.ENERGY.2016.05.093.

[5] F. Sorourifar, V. M. Zavala, and A. W. Dowling, “Integrated Multiscale Design, Market Participation, and Replacement Strategies for Battery Energy Storage Systems,” IEEE Trans. Sustain. Energy, vol. 11, no. 1, pp. 84–92, Jan. 2020, doi: 10.1109/TSTE.2018.2884317.

[6] M. C. Tang et al., “Systematic approach for conceptual design of an integrated biorefinery with uncertainties,” Clean Technol. Environ. Policy, vol. 15, no. 5, pp. 783–799, Oct. 2013, doi: 10.1007/s10098-013-0582-x.

[7] R. Madlener and C. Schmid, “Combined Heat and Power Generation in Liberalised Markets and a Carbon-Constrained World,” GAIA - Ecol. Perspect. Sci. Soc., vol. 12, no. 2, pp. 114–120, Apr. 2017, doi: 10.14512/gaia.12.2.8.

[8] A. Hakizimana, “Novel Optimization Approaches for Integrated Design and Operation of Smart Manufacturing and Energy Systems,” Clemson University, 2019.

[9] I. E. Grossmann, B. A. Calfa, and P. Garcia-Herreros, “Evolution of concepts and models for quantifying resiliency and flexibility of chemical processes,” Comput. Chem. Eng., vol. 70, pp. 22–34, Nov. 2014, doi: 10.1016/j.compchemeng.2013.12.013.

[10] P. Liu, Y. Fu, and A. Kargarian Marvasti, “Multi-stage stochastic optimal operation of energy-efficient building with combined heat and power system,” Electr. Power Components Syst., vol. 42, no. 3–4, pp. 327–338, Mar. 2014, doi: 10.1080/15325008.2013.862324.

[11] D. K. Varvarezos, L. T. Biegler, and I. E. Grossmann, “Multiperiod design optimization with SQP decomposition,” Comput. Chem. Eng., vol. 18, no. 7, pp. 579–595, Jul. 1994, doi: 10.1016/0098-1354(94)85002-X.

[12] N. A. Choksi and J. A. Paulson, “Simulation-based Integrated Design and Control with Embedded Mixed-Integer MPC using Constrained Bayesian Optimization,” in Proceedings of the American Control Conference, 2021.

[13] F. Sorourifar, N. Choksi, and J. A. Paulson, “Computationally efficient integrated design and predictive control of flexible energy systems using multi-fidelity simulation-based Bayesian optimization,” Optim. Control Appl. Methods, 2021, doi: 10.1002/OCA.2817.