This paper describes an optimization and artificial intelligence-based approach for solving the mesh partitioning problem in parallel finite element analysis. The problem of domain decomposition with reference to the mesh partitioning approach is described. Some current mesh partitioning approaches are discussed with respect to their limitations. The formulation of the optimization problem is presented. The theory for the mesh partitioning approach using an optimization and a predictive module is also described. It is shown that a genetic algorithm linked to a neural network predictive module may be used successfully to limit the computational load and the number of design variables for the decomposition problem. This approach does not suffer from the limitations of some current domain decomposition approaches, where an overall mesh is first generated and then partitioned. It is shown that by partitioning the coarse initial background mesh, near optimal partitions for finer graded (adaptive) meshes may be obtained economically. The use of the genetic algorithm for the optimization module and neural networks as the predictive module is described. Finally, a comparison between some current mesh partitioning algorithms and the proposed method is made with the aid of three examples, thus illustrating the feasibility of the method.