Computation time analysis of centralized and distributed optimization algorithms applied to automated irrigation networks

This paper compares the computation time of two algorithms for solving a structured constrained linear optimal control problem with finite horizon quadratic cost within the context of automated irrigation networks. The first is a standard centralized algorithm based on the active set method that does not exploit problem structure. The second is distributed and is based on a consensus algorithm, not specifically tailored to account for system structure. It is shown that there is a significant advantage in terms of computation overhead (the time spent computing the optimal solution) in using the second algorithm in large-scale networks. Specifically, for a fixed horizon length the computation overhead of the centralized algorithm grows as O(n⁵) with the number n of sub-systems. By contrast, it is observed via a combination of analysis and experiment that given n times resources for computation the computation overhead of the distributed algorithm grows as O(n) with the number n of sub-systems.