PSO : an efficient algorithm to solve geophysical inverse problems. The 1D-DC case

Most of the geophysical inverse problems are ill-posed. In the VES (Vertical Electrical Sounding) case this fact is known as the equivalence or suppression problem: the shape of the objective function is that of the bottom of a narrow, elongated valley with almost null gradients and many localized "sinkholes". Flat outer areas with ridges also prevent access from local minima to the bottom of the valley. These features become insurmountable difficulties for local optimization methods, since they are not able to discriminate among the multiple models consistent with the end criteria, driving to unpredictable results. Global optimization methods are a good alternative in such situations due to their probabilistic nature. PSO algorithm is an evolutionary technique inspired in social behavior in nature. By means of a fruitful mechanical analogy we analyze its convergence properties, giving some criteria to choose the PSO parameters. This approach allows a family of PSO variants to be proposed, some of them with better properties to cope with the VES difficulties. Finally, performance of PSO variants against Simulated Annealing and Genetic Algorithms is done for a salt water intrusion in a coastal aquifer in South Spain.