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In this paper, we propose new depth-first heuristic search algorithms to approximate the set of Pareto optimal solutions in multi-objective constraint optimization. Our approach builds upon recent advances in multi-objective heuristic search over weighted AND/OR search spaces and uses an ε-dominance relation between cost vectors to significantly reduce the set of non-dominated solutions. Our empirical evaluation on various benchmarks demonstrates the power of our scheme which improves the resolution times dramatically over recent state-of-the-art competitive approaches.