This paper presents a new heuristic to solve efficiently the problem of dimension- ing large-size hybrid optoelectronic networks with grooming. It is modeled as a large Mixed Integer Program which cannot be solved to optimality in a reasonable amount of time for networks larger than 10 nodes. The heuristic is based on concepts borrowed from genetic algorithm, tabu search and simulated annealing. The definition of the populations and neighborhoods are discussed in depth along with the intensification and diversification procedures. An application of this heuristic to networks of up to 50 nodes has shown excellent results: The computational time is low and the average optimality gap is generally under 7%.