The Pareto-dominance-based multi-objective evolutionary algorithms (MOEAs) have been successful in solving many test problems and other engineering optimization problems. However, their performance gets affected when solving more than 3-objective optimization problems due to lack of sufficient selection pressure. Many attempts have been made by the researchers toward improving the environmental selection of those MOEAs. One such attempt is selecting solutions using the reference-lines-based framework. In this paper, an efficient environmental selection and normalization scheme are proposed for this framework. The environmental selection operator is developed to equally prioritize solutions associated with different lines drawn from the origin and the reference points. A normalization scheme is also suggested in which the extreme point is used which gets updated on the designed rules. The framework is referred to as LEAF, and it is tested on 3-, 5-, 10-, and 15-objective DTLZ and WFG test instances. LEAF demonstrates its outperformance on almost all DTLZ instances and shows better performance on most of WFG instances over six MOEAs from the literature.

基于帕累托支配的多目标进化算法（MOEA）已成功解决了许多测试问题和其他工程优化问题。但是，由于缺乏足够的选择压力，在解决3个以上目标的优化问题时，它们的性能会受到影响。研究人员已进行了许多尝试，以改善这些MOEA的环境选择。一种这样的尝试是使用基于参考线的框架来选择解决方案。本文针对该框架提出了一种有效的环境选择和归一化方案。开发环境选择算子的目的是对与从原点和参考点绘制的不同线相关联的解决方案进行同等优先级划分。还提出了一种归一化方案，其中使用了极端点，该极端点会根据设计的规则进行更新。该框架称为LEAF，并且已在3、5、10和15个目标DTLZ和WFG测试实例上进行了测试。LEAF在几乎所有DTLZ实例上都表现出优异的性能，并且在文献中的六个MOEA上，在大多数WFG实例上都表现出更好的性能。