2022 Annual Meeting

(185h) Data-Driven Techniques Towards the Efficient Integration of Planning, Scheduling and Control

Authors

Shah, N., Imperial College London
del Rio Chanona, A., Imperial College London
Enterprise-wide optimization (EWO) aims to coordinate all decision-making within companies and thus increase their competitiveness [1]. Mathematical optimization is key to the hierarchical integration of process operations - a key aspect of EWO - ranging from process and supply chain design down to planning, scheduling, and control. Traditionally, upper-level decisions are taken while disregarding lower-level considerations, and then fed as setpoints to the lower levels. Ensuring lower-level feasibility or optimality however leads to large-scale, potentially multilevel, formulations which are not just computationally intractable, but also mathematically difficult [2]. We present data-driven methods that address these computational shortcomings, and how mathematical and organisational considerations inform the choice of which technique to use.

There are two main options to decrease the computational burden: We can exploit 1) the mathematical structure of the optimization problem in decomposition or distributed optimization schemes, or 2) specific surrogate modelling schemes (i.e. trust region frameworks) that do not need to sacrifice solution accuracy if given enough time. While there is some research into the intersection of data-driven techniques and decomposition algorithms [3], the problem of surrogate modelling is inherently 'data-driven’, and as such has been studied widely across many fields under different names [4-8]. The potential of Gaussian processes, neural networks, and decision trees in particular have been thoroughly investigated in EWO and process systems engineering (PSE) as a whole [9,10].

To integrate hierarchical levels of decision-making, we can leverage data-driven techniques in a bottom-up or top-down approach. In the bottom-up approach, we could for example construct surrogates that map a certain combination of upper-level scheduling decisions to a feasibility or optimality evaluation of the control problem [11,12]. Derivative-free optimization (DFO), also known as black-box or data-driven optimization, can be used when gradient expressions cannot be cheaply obtained and exploited in traditional gradient-based optimization solvers. DFO algorithms have been benchmarked on PSE applications [13] and in the data-driven coordination of EWO subproblems [14]. DFO has also been introduced to solve multilevel problems in a top-down approach by finding the upper-level planning variables that optimize an upper-level objective while treating the lower-level optimization problem as a black-box constraint [15].

While there are numerous examples of how data-driven techniques can be used in EWO, the literature is missing an exposition into how operational considerations affect mathematical optimization structure, and how this informs the ideal choice of how data-driven techniques can be efficiently exploited for the task at hand. To this end, we present variations on a multi-agent, stochastic integrated planning, scheduling, and control case study, which is difficult to solve tractably by traditional means without sacrificing solution accuracy. We then show how we can combine DFO and surrogate modelling techniques to find a tractable solution to the tri-level optimization problem.

We construct feasibility and optimality surrogates for the lower-level control problem offline which are included as constraints in the middle scheduling problem. As such, we have collapsed the two lower levels of scheduling and control into a single level. Then, we use derivative-free optimization to find the upper-level planning variables. DFO iteratively proposes a set of planning-level variables which are fixed and fed to the lower-level integrated scheduling-control problem. The lower-level is then solved using traditional optimization software (Pyomo) and returns the corresponding upper-level objective to be optimized by the upper-level DFO. As such, we manage to find a tractable solution with little optimality gap to an otherwise intractable trilevel integrated planning, scheduling, and control problem. We argue that DFO stands out as a data-driven alternative to using decomposition schemes like Benders decomposition that solve for complicating variables in the outer problem, and discuss how this relates to the treatment of considerations such as stochasticity and privacy. Finally, we illustrate how DFO and surrogate modelling can adaptively leverage data in practice to efficiently solve the integrated problem on a monthly basis.



References

  1. C. E. Gounaris, I. E. Grossmann, 2019, A preface to the special issue on enterprise-wide optimization, Optimization and Engineering 20(4), 965–968
  2. Y. Chu, F. You, 2015, Model-based integration of control and operations: Overview, challenges, advances, and opportunities, Computers & Chemical Engineering 83, 2–20
  3. Y. Bengio, A. Lodi, A. Prouvost, 2021, Machine learning for combinatorial optimization: A methodological tour d’horizon, European Journal of Operational Research 290(2), 405–421
  4. J. P.Eason, L. T. Biegler, 2016, A trust region filter method for glass box/black box optimization, AIChE Journal 62(9), 3124–3136
  5. R. R. Barton, M. Meckesheimer, 2006, Chapter 18 Metamodel-Based Simulation Optimization, Simulation
  6. L. Ljung, 2008, Perspectives on System Identification, IFAC Proceedings Volumes 41(2), 7172–7184
  7. A. Chiuso, G. Pillonetto, 2019, System Identification: A Machine Learning Perspective, Annual Review of Control, Robotics, and Autonomous Systems 2(1), 281–304
  8. S. Amaran, N. V. Sahinidis, B. Sharda, S. J. Bury, 2014, Simulation optimization: a review of algorithms and applications, 4OR 12(4), 301–333
  9. Savage, T., Zhang, D., Mowbray, M., & Río Chanona, E. A. D. (2021). Model-free safe reinforcement learning for chemical processes using Gaussian processes. IFAC-PapersOnLine, 54(3), 504–509
  10. F. Ceccon, J. Jalving, J. Haddad, A. Thebelt, C. Tsay, C. D. Laird, R. Misener, 2022, OMLT: Optimization & Machine Learning Toolkit. ArXiv, abs/2202.02414
  11. A. Bhosekar, M. Ierapetritou, 2018, Advances in surrogate based modeling, feasibility analysis, and optimization: A review, Computers & Chemical Engineering 108, 250–267
  12. S. Avraamidou, E. N. Pistikopoulos, 2019, A Bi-Level Formulation And Solution Method For The Integration Of Process Design And Scheduling. Proceedings of the 9th International Conference on Foundations of Computer-Aided Process Design 47, 17-22
  13. D. van de Berg, T. Savage, P. Petsagkourakis, D. Zhang, N. Shah, E. A. del Rio-Chanona, 2022, Data-driven optimization for process systems engineering applications. Chemical Engineering Science 248, 117135
  14. D. van de Berg, P. Petsagkourakis, N. Shah, E. A. del Rio-Chanona, 2022, Data-driven distributed optimization for systems consisting of expensive black-box subproblems, 14th International Symposium on Process Systems Engineering (accepted)
  15. B. Beykal, S. Avraamidou, E. N. Pistikopoulos, 2022, Data-driven optimization of mixed-integer bi-level multi-follower integrated planning and scheduling problems under demand uncertainty, Computers & Chemical Engineering 156, 107551