Stability and optimisation of the homotopy method
Auteur(s) |
T. van den Brink
|
R. Mak
|
N. Strachan
|
A. Tahiri
|
M. Versluis
|
M. Vrijhof
|
K. Xiao
Publicatie type | Rapport Deltares
The problem posed by Deltares was to study the Homotopy method applied to the Hoogheemschap van Rijnland water system. The goal of the project was twofold. The first aim was to decrease the runtime of the model. To this end, we introduced two methods. The SmartSeed method uses the computation of the previous hour as a seed for the computation of the next hour. This method allows us to skip two computation steps. When tested, the method decreased runtimes by 60%. The second method we introduced is a semi-linearized model. It only solves the complete model for the first 24 hours and uses a linearization for predictions further in the future. We expected quite significant runtime improvements but were not able to demonstrate this.
The second goal of the project was to investigate the theoretical foundations of current methods with regard to stability. The current methods are based on an article by J. Baayen that deals with slightly simpler systems than those needed at Deltares: in the article, water levels are optimized for only one objective. Since water management often comes with several, possibly conflicting, objectives, we tried to shape the ideas of said article into the context of multi-objective optimization. The major task here was to define the different notions of stability in the context of multi-objective optimization and see which results from the article could still be carried over to the new setup. Most results carry over, but finding a global optimum requires further research.