  Optimization models with decision variables in multiple time scales are
widely used across various fields such as integrated planning and scheduling.
To address scalability challenges in these models, we present the Parametric
Autotuning Multi-Time Scale Optimization (PAMSO) algorithm. PAMSO tunes
parameters in a low-fidelity model to assist in solving a higher-fidelity
multi-time scale optimization model. These parameters represent the mismatch
between the two models. PAMSO defines a black-box function with tunable
parameters as inputs and multi-scale cost as output, optimized using
Derivative-Free Optimization methods. This scalable algorithm allows optimal
parameters from one problem to be transferred to similar problems. Case studies
demonstrate its effectiveness on an MINLP model for integrated design and
scheduling in a resource task network with around 67,000 variables and an MILP
model for integrated planning and scheduling of electrified chemical plants and
renewable resources with around 26 million variables.
