Optimization of large scale engineering computations with biologically inspired algorithms

Abstract

Two optimization problems related to engineering simulations based on Finite Element Method (FEM) are investigated in this thesis. In both cases, biologically inspired algorithms (BIAs) are applied to solve them. In the first case, BIAs are used to minimize the execution time of large engineering simulations that require the power of supercomputers. FEM derivatives, the Finite Element Tearing and Inteconnecting (FETI) methods can utilize these parallel architectures. The presented tool can automatically search for a near-optimal configuration of FETI methods during a transient analysis. The experiments show that basic BIAs with a small population (5 individuals) and a penalty system as protection against incompatible configurations represent an effective solution. One can use them to find the near-optimal configuration of FETI-based methods in lower hundreds of the cost function evaluations. This solution can improve the utilization of expensive hardware resources in modern computational clusters. The second part of the thesis deals with inverse nonlinear problems of elasticity. In contrast to standard numerical simulations, inverse analysis searches for an original unloaded shape of the known deformed shape. The desired unloaded shape should deform to the known deformed shape under the given (known) properties of materials and the acting environment. Due to the present nonlinearity (material or geometric), the behavior of the newly constructed, unloaded shape is hardly predictable in the given environment. In this thesis, I investigate the transformation of a deformed shape into the original one by radial basis function (RBF). In this method, the displacement of all mesh nodes is controlled by several morphing points only. It can reduce the search space size when searching for the unloaded shape. Moreover, the number of morphing points is independent of a particular mesh density. On the other hand, an inappropriate selection of morphing points can make the correct transformation impossible. To prevent improper selection, I introduce automated selection of morphing points by BIAs in two steps - layers. The top layer chooses the morphing points from an initial set. The bottom layer looks for their optimal displacement to construct the desired unloaded shape. The two-layer approach was able to find a desired unloaded shape, leading to a relative error below 5% with only 25 points. The already existing methods would require working with all boundary nodes of the given mesh. The presented solution allows everyone to work with reasonable numbers of unknowns (morphing points and their displacement) that are manageable by modern optimization methods, including BIAs.