In this paper, we propose near admissible multiobjective search algorithms to approximate, with performance guarantee, the set of Pareto optimal solution paths in a state space graph. Approximation of Pareto optimality relies on the use of an epsilon-dominance relation between vectors, significantly narrowing the set of non-dominated solutions. We establish correctness of the proposed algorithms, and discuss computational complexity issues. We present numerical experimentations, showing that approximation significantly improves resolution times in multiobjective search problems.