This paper proposes an original bi-objective optimization approach around the key feature of local conservation of the Pareto stationnarity along the gradient axes (LCPS). The proposed algorithm consists of two steps. The decomposition step starts with the anchor points, generate N evenly points on the axes relating the anchor points to the utopia point. Then, the corresponding nearest reference points on the Pareto front are generated. In the path-relinking step, we carry out a path-relinking in the objective space, between each pair of Pareto solutions, following the best direction among the gradients axes. The SPIDER algorithm largely outperforms state-of-the-art and popular evolutionary algorithms both in terms of the quality of the obtained Pareto fronts (convergence, cardinality, diversity) and the search time.