Nature-Inspired Optimization Algorithms for the 3D Reconstruction of Porous Media

Abstract

One of the most challenging problems that are still open in the field of materials science is the 3D reconstruction of porous media using information from a single 2D thin image of the original material. Such a reconstruction is only feasible subject to some important assumptions that need to be made as far as the statistical properties of the material are concerned. In this study, the aforementioned problem is investigated as an explicitly formulated optimization problem, with the phase of each porous material point being decided such that the resulting 3D material model shows the same statistical properties as its corresponding 2D version. Based on this problem formulation, herein for the first time, several traditional (genetic algorithms—GAs, particle swarm optimization—PSO, differential evolution—DE), as well as recently proposed (firefly algorithm—FA, artificial bee colony—ABC, gravitational search algorithm—GSA) nature-inspired optimization algorithms were applied to solve the 3D reconstruction problem. These algorithms utilized a newly proposed data representation scheme that decreased the number of unknowns searched by the optimization process. The advantages of addressing the 3D reconstruction of porous media through the application of a parallel heuristic optimization algorithm were clearly defined, while appropriate experiments demonstrating the greater performance of the GA algorithm in almost all the cases by a factor between 5%–84% (porosity accuracy) and 3%–15% (auto-correlation function accuracy) over the PSO, DE, FA, ABC, and GSA algorithms were undertaken. Moreover, this study revealed that statistical functions of a high order need to be incorporated into the reconstruction procedure to increase the reconstruction accuracy.