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

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

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