It is of great importance for a solution with high robustness in the real application, not only with good quality. Searching for robust Pareto optimal solutions for multi-objective optimization problems (MOPs) is a challenge, no exception for multi-objective evolutionary algorithms (MOEAs). Recently, as one of the popular approach to search robust Pareto optimal solutions, "effective objective function" based MOEA (Eff-MOEA) can only find solutions which have average robustness and quality, but cannot find solutions which have the highest robustness and best quality. In this paper, we proposed a new methodology for robust Pareto optimal solutions and presented a novel MOEA named MOEA/R, which convert a multi-objective robust optimization problem (MROP) into a bi-objective optimization problem. Each of two objectives represents a sub-MOP, one of which optimizes solutions' quality and another optimizes solutions' robustness. Through the comparison and analysis between MOEA/R, Eff-MOEA and IR can acquire good purposes. The most important contribution of this paper is that MOEA/R explores a novel methodology for searching robust Pareto optimal solutions.