Hierarchical planning-scheduling-control -- Optimality surrogates and derivative-free optimization

TL;DR

This paper develops a workflow combining optimality surrogates and derivative-free optimization to solve complex hierarchical planning, scheduling, and control problems in chemical companies, balancing tractability and accuracy.

Contribution

It introduces a methodology that integrates these techniques, leveraging parallelization and tuning, to efficiently solve multi-level formulations with improved scalability and robustness.

Findings

Both methods improve over heuristics but have limitations.

Combining methods enhances solution quality and tractability.

Parallelization and tuning are key to handling complex formulations.

Abstract

Planning, scheduling, and control typically constitute separate decision-making units within chemical companies. Traditionally, their integration is modelled sequentially, but recent efforts prioritize lower-level feasibility and optimality, leading to large-scale, potentially multi-level, hierarchical formulations. Data-driven techniques, like optimality surrogates or derivative-free optimization, become essential in addressing ensuing tractability challenges. We demonstrate a step-by-step workflow to find a tractable solution to a tri-level formulation of a multi-site, multi-product planning-scheduling-control case study. We discuss solution tractability-accuracy trade-offs and scaling properties for both methods. Despite individual improvements over conventional heuristics, both approaches present drawbacks. Consequently, we synthesize our findings into a methodology combining their strengths. Our approach remains agnostic to the level-specific formulations when the linking variables are identified and retains the heuristic sequential solution as fallback option. We advance the field by leveraging parallelization, hyperparameter tuning, and a combination of off- and on-line computation, to find tractable solutions to more accurate multi-level formulations.