Soft-computing approach to solve ill-posed inverse problems: application to random materials and imperfect cylindrical shells

In this work a soft-computing approach, based on a hybrid stochastic optimization (HSO) tool, is suggested to solve numerically inverse problems. These problems are formulated and solved using optimization methods. The HSO tool combines genetic algorithms, simulated annealing and taboo list. One of the key features of the proposed approach is the possibility of identifying multiple solutions that satisfy the 'forward' model. The HSO tool has been applied to reconstruct the microstructural configurations of random materials. The ill-posed inverse problem associated with the reconstruction process, i.e. the identification of the microstructural configurations, can be seen as an optimization problem where a set of target correlation functions is prescribed and the reconstruction method proceeds to identify realizations of the random material that best match the prescribed set of target correlation functions. The proposed approach is highly parallelizable, flexible and scalable and it can be, in principle, adopted to solve other types of optimization problems as well.