Process Optimization Using Slack Variables and Simulation

The patent transforms the static optimization problem into a dynamic one by introducing a moving horizon approach. The optimizer continuously updates the search range based on current process conditions and measured inputs, allowing the solution space to adapt dynamically rather than being constrained by fixed predefined ranges. This enables the system to provide solutions outside traditional limits while maintaining control performance.

The patent changes the parameters of the optimization problem by incorporating slack variables that modify the constraint boundaries. These slack variables allow the optimizer to temporarily violate predefined ranges and limits when beneficial, then correct deviations. This parameter transformation enables flexible adaptation while preserving the core control objectives.

The patent introduces slack variables as intermediary elements between the optimizer and the process constraints. These slack variables act as buffers that absorb constraint violations, allowing the optimizer to explore a broader solution space without directly violating hard constraints. This intermediary mechanism provides flexibility in handling constraints while maintaining computational tractability through standard optimization algorithms.

The patent extends the optimization problem into an additional dimension by incorporating slack variables that represent constraint violation margins. This dimensional extension transforms the problem from a constrained optimization in n-dimensions to an unconstrained (or softly constrained) optimization in n+1 dimensions, providing greater flexibility while maintaining computational simplicity through established mathematical programming techniques.

The patent applies beforehand cushioning by introducing slack variables that anticipate and buffer constraint violations before they occur. These slack variables create a cushioning layer between the optimizer and hard constraints, allowing the system to explore solutions that temporarily exceed predefined ranges while ensuring that actual process constraints are never violated. This approach prevents suboptimal solutions caused by overly restrictive constraint enforcement.

The patent employs partial or excessive action by allowing the optimizer to temporarily exceed predefined ranges and limits through slack variables. Rather than strictly enforcing constraints at all times, the system permits controlled excesses when beneficial for optimization, then corrects deviations. This partial relaxation of constraints enables discovery of superior solutions while maintaining overall constraint satisfaction through feedback control.