Abstract: Grid-based measure is commonly used to maintain diversity in many MOEAs.The ε-MOEA，which is based on the ε-dominance concept，is essentially based on grid-strategy.Though often gaining an appropriate tradeoff between the aspects of the performance，the ε-MOEA has its inherent vice and behaves unacceptably sometimes.That is，when the slope to one dimension of the PF_true changes a lot along it，the algorithm loses many extreme or representative individuals，which has a severely influence on the diversity of the solution set.In order to solve this problem，a new δ-dominance concept and suppositional optimum point concept is defined，then a new grid-based elitist-reserving strategy is proposed，finally it is applied in an EMO archive algorithm（δ-MOEA）.The experimental results illustrate δ-MOEA’s good performance，which is much better especially at the diversity than NSGA2 and ε-MOEA.

Key words: grid, archive set, ε-dominance, δ-dominance, suppositional optimum point, grid-based elitist-reserving strategy, δ-MOEA

摘要： 网格方法被多个进化算法用来保持解集的分布性。基于ε支配概念的ε-MOEA本质上也是基于网格策略的。虽然ε-MOEA通常情况下都能在算法性能的各方面之间取得较为合理的折衷，但是由于其存在固有缺陷，很多时候表现出不容忽视的问题——当PF_true对某一维的变化率在该维不同区域的差异较大时，解集中边界个体或代表性个体丢失——严重影响解集的分布性。针对这一问题，定义了一种新的δ支配概念和虚拟“最优点”的概念，提出了一种新的网格存优策略，并将之应用于更新进化多目标归档算法的归档集。实验结果显示，基于新的存优策略的进化多目标归档算法（δ-MOEA）具有良好的性能，尤其在分布性方面比NSGA2和ε-MOEA好得多。

关键词: 网格, 归档集, ε支配, δ支配, 虚拟“最优点”, 网格存优策略, δ-MOEA, ,