A hybrid global optimization method for inverse estimation of hydraulic parameters: Annealing-simplex method

Inverse estimation of unsaturated hydraulic parameters is often a highly nonlinear optimization problem with multiple parameters. The objective functions involved are often topographically complex and may contain many local minima. Because of these reasons, the inverse solutions are commonly very sensitive to the initial guess of the parameters when conventional optimizers are used. This paper presents an annealing-simplex method that incorporates simulated annealing strategies into a classical downhill simplex method. An upward infiltration experiment was used as an example of inverse estimation to test the method. Numerical experiments of both minimizing an algebraic function and inversion of upward infiltration data showed that the new method successfully converged to the global minimum En all cases, irrespective of the initial hydraulic parameter estimates, while the classical downhill method often converged to unfavorable local minima. The CPU times needed for the annealing-simplex method to estimate 5 and 7 hydraulic parameters simultaneously are about a half hour and 1 hour on a PC, respectively. Additionally, no special requirements are imposed on the objective function, and the method is independent of the details of the simulation submodel. Therefore the proposed method should be applicable to other optimization problems in water resources when it is important to have a robust global search capability.