  We study a multi-objective scheduling problem on two dedicated processors.
The aim is to minimize simultaneously the makespan, the total tardiness and the
total completion time. This NP-hard problem requires the use of well-adapted
methods. For this, we adapted genetic algorithms to multi-objective case. Three
methods are presented to solve this problem. The first is aggregative, the
second is Pareto and the third is non-dominated sorting genetic algorithm II
(NSGA-II). We proposed some adapted lower bounds for each criterion to evaluate
the quality of the found results on a large set of instances. Indeed, these
bounds also make it possible to determine the dominance of one algorithm over
another based on the different results found by each of them. We used two
metrics to measure the quality of the Pareto front: the hypervolume indicator
(HV) and the number of solutions in the optimal front (ND). The obtained
results show the effectiveness of the proposed algorithms.
