A NEW HYBRID OPTIMIZATION APPROACH USING PSO, NELDER-MEAD SIMPLEX AND K-MEANS CLUSTERING ALGORITHMS FOR 1D FULL WAVEFORM INVERSION
Full waveform inversion, Derivative free optimization, Computational cost.
Full Waveform Inversion (FWI) is formulated as a nonlinear optimization problem that traditionally uses derivative-based local minimization methods to find the scalar field of subsurface physical properties that best represents the field seismic data. However, these methods have a high computational cost and an accuracy limited to local minima, in addition to suffering from a slow convergence rate (Cycle Skipping). Therefore, was developed in this work a two-phase hybrid optimization algorithm based on Derivative-Free Optimization (DFO) algorithms. Where in the first phase it uses global minimization and clustering technique, and in the second it uses local minimization. In phase 1, were adopted the modified Particle Swarm Optimization (PSO) algorithm and the Kmeans, and in phase 2, the Nelder-Mead Adaptive Simplex (ANMS). The new hybrid algorithm was called the PSO-Kmeans-ANMS. Where the K-means is responsible for dividing the swarm of particles into 2 clusters at each instant. This strategy aims to automatically balance the exploration and exploitation mechanisms of the parameter search space, allowing to find more accurate solutions and consequently improve convergence. The proposed hybrid algorithm was validated on the set of 12 benchmark functions and then applied to the FWI 1D problem. The PSO-Kmeans-ANMS results were compared with the classic PSO, modified PSO, and ANMS algorithms. The metrics used were the average execution time and the success rate (being accepted error of up to ±4% of the optimal solution). In all validation experiments and the FWI application, the PSO-Kmeans-ANMS performed well in terms of robustness and computational efficiency. In the case of FWI, there was a significant reduction in computational cost, thus presenting a relevant result.