Profile and wave front optimization by metaheuristic algorithms for efficient finite element analysis

Abstract

To efficiently solve the equations that arise from finite element analysis, the stiffness matrix of a model should lx-structured. This can be achieved by reducing the profile or wavefront of the corresponding graph matrix of a structure depending on whether the skyline or frontal method is used. One of the efficient methods for achieving this goal is the method of King, extended by Sloan. In this paper, the coefficients of the priority function utilized in the generalized Sloan's method are optimized using the recently developed motahouristic algorithm, called vibrating particles system. The results are compared with t hose of other met alien l ist ic algorithms consisting of the particle swarm optimization, colliding bodies optimization, enhanced colliding bodies optimization, and tug of war optimization. These met alien ristics are used for optimum nodal numbering of the graph models of the finite element meshes to reduce the profile and wavefront of the corresponding sparse mat rices. The comparison of t he results of the metahouristic algorithms and those of t he King and Sloan demonstrates the efficiency of the new metahouristic algorit hm utilized for profile and wavefront optimization.