In this paper, a digital planar curve approximation method based on a multi-objective genetic algorithm is proposed. In this method, the optimization/exploration algorithm locates breakpoints on the digital curve by minimizing simultaneously the number of breakpoints and the approximation error. Using such an approach, the algorithm proposes a set of solutions at its end. The user may choose his own solution according to its objective. The proposed approach is evaluated on curves issued from the literature and compared successfully with many classical approaches.