  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.
