On the various local solutions to a two-input dynamic optimization problem

- Multi-input dynamic optimization could have close optimal solutions.
- Analytical method of resolution is best suited to distinguish between them.
- The general structure of the global optimal solution does not change with variations.

Solving a multi-input dynamic optimization of a batch processes is a complex problem involving interactions between input variables and constraints over time. The problem gets more difficult due to the presence of local solutions that have almost the same cost but widely varying structures. This paper studies various local optimal solutions for a non-isothermal semi-batch reactor with the feed rate and temperature as inputs and a heat removal constraint. Three solution patterns were studied, all consisting in meeting the heat removal constraint for the first part and seeking the compromise between the main and side reactions in the later part. A sensitivity analysis shows that the best solution pattern among those studied does not change with variations in parameters or initial conditions.