We propose a hybrid approach for multi-objective assignment problem which combines genetic algorithm and mathematical programming techniques. This method is based on the dominance cost variant of the multi-objective genetic algorithm hybridized with exact method. The initial population is generated by solving a series of mono-objective assignment problems obtained by a suitable choice of a set of weights. The crossover operator solves a reduced mono-objective problem where the weights are chosen to identify an unexplored region. Numerical experiments show the efficiency of our approach.