Profile and wavefront optimization by metaheuristic algorithms for efficient finite element analysis

For an efficient solution of the equations arising from finite element analysis, the stiffness matrix of the model should be structured. This can be done by reducing the profile or wavefront of the corresponding graph matrix of the structure depending on whether skyline or frontal method being used, respectively. One of the efficient methods to achieve this goal is the use of 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 metaheuristic algorithm, so-called vibrating particles system. The results are compared to those of other metaheuristic algorithms consisting of the particle swarm optimization, colliding bodies optimization, enhanced colliding bodies optimization, and tug of war optimization. These metaheuristics, 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 matrices. Comparison of the results achieved by these metaheuristic algorithms and those of the King and Sloan, demonstrates the efficiency of the new metaheuristic utilized for profile and wavefront optimization.