Results are reported of the use of genetic algorithms for the variable ordering problem in Reed-Muller binary decision diagrams. Tests carried out on benchmark examples and randomly generated functions are very encouraging and compare favourably with other non-exhaustive algorithms. The results show significant reduction in the number of nodes and gates for multi-level designs. The work is confined to single output fixed polarity Reed-Muller expansions: the method will be developed further to extend to other forms and to multi-outputs.