A new kind of multiobjective optimization model is constructed in this paper, which contains various solutions apart from the true Pareto-optimums but hardly dominated. These solutions are defined as dominance resistant solutions (DRSs). It is proved that the evolutionary algorithms based on Paretodominance relationship fail to find the true Pareto fronts for the DRS MOP. Hence a new algorithm based on varepsilon -dominance relationship, called varepsilon -dominance MOEA( EDMOEA), is proposed to improve the DRSs in population effectively. Finally, experiments on a set of DRS MOOPs and other regular test functions are conducted, the EDMOEA outperforms the NSGA-II, and can be applied easily to complex multiobjective optimization problems.
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