Evolutionary Mesh Numbering: Preliminary Results

TL;DR

This paper explores using Evolutionary Algorithms to improve mesh numbering in Finite Element Methods, achieving 12-20% efficiency gains over standard heuristics, but with mixed success in crossover and hybridization strategies.

Contribution

It demonstrates that evolutionary algorithms can enhance mesh numbering efficiency beyond traditional methods, with specific insights into their performance and interactions.

Findings

Improved mesh numbering results by 12-20% over standard heuristics

Crossover operators tested did not prove useful in this context

Hybridization with other methods did not yield success in preliminary experiments

Abstract

Mesh numbering is a critical issue in Finite Element Methods, as the computational cost of one analysis is highly dependent on the order of the nodes of the mesh. This paper presents some preliminary investigations on the problem of mesh numbering using Evolutionary Algorithms. Three conclusions can be drawn from these experiments. First, the results of the up-to-date method used in all FEM softwares (Gibb's method) can be consistently improved; second, none of the crossover operators tried so far (either general or problem specific) proved useful; third, though the general tendency in Evolutionary Computation seems to be the hybridization with other methods (deterministic or heuristic), none of the presented attempt did encounter any success yet. The good news, however, is that this algorithm allows an improvement over the standard heuristic method between 12% and 20% for both the 1545 and 5453-nodes meshes used as test-bed. Finally, some strange interaction between the selection scheme and the use of problem specific mutation operator was observed, which appeals for further investigation.