Application of Global Optimization Algorithms to a Salt Water Intrusion Problem
Juan Luis Fernández‐Martínez, Heidi Anderson Kuzma, Esperanza García–Gonzalo, Julio Manuel Fernandez-Diaz, José Paulino Fernández-Álvarez, César O. Menéndez-Pérez · 2009
Geophysical inverse problems are ill-posed: the objective function has its minimum in a flat elongated valley or surrounded by many local minima. Local optimization methods give unpredictable results if no prior information is available. Traditionally this has generated mistrust on the use of geophysical inverse methods (equivalence problem in VES). Stochastic approach of inverse problems consists in shifting attention to the probability of existence of certain interesting subsurface structures instead of “looking for the true model”. Also, inverse problems are ill-conditioned and observed data noisy. Thus, with no regularization methods (priors) these uncertainties are transmitted to the model parameters by the optimization algorithm. Global optimization methods can be used to sample efficiently the model space and are very robust since they don't solve the optimization problem. In this contribution we apply different algorithms -Particle Swarm (PSO), Binary Genetic Algorithms (BGA), Simulated Annealing (SA) and Differential Evolution (DE)- to model a salt water intrusion problem, analyzing how the solution depends on the algorithm. This comparison gives important clues about the use of VES in hydrogeology.