Genetic Programming For Cellular Automata Urban Inundation Modelling

Abstract

Recent advances in Cellular Automata (CA) represent a new, computationally efficient method of simulating flooding in urban areas. A number of recent publications in this field have shown that CAs can be much more computationally efficient than methods than using standard shallow water equations (Saint Venant/Navier-Stokes equations). CAs operate using local state-transition rules that determine the progression of the flow from one cell in the grid to another cell, in many publications the Manning’s Formula is used as a simplified local state transition rule. Through the distributed interactions of the CA, computationally simplified urban flooding can be processed, although these methods are limited by the approximation represented by the Manning’s formula. Literature demonstrates that the viability of the Manning’s formula will break down with too large a time step, flow rates, too small a cell size, or too smooth roughness factor; Therefore further increases in computational efficiency could be gained with a better approximation, or rather one capable of producing the required simulation with enough accuracy at larger time steps, smaller cells sizes, smoother roughness factors. Genetic programming has the potential to be used to optimise state transition rules to maximise accuracy and minimise computation time. In this paper we present some preliminary findings on the use of genetic programming (GP) for deriving these rules automatically. The experimentation compares GP-derived rules with human created solutions based on the Mannings formula and findings indicate that the GP rules can improve on these approaches