Line-prioritized environmental selection and normalization scheme for many-objective optimization using reference-lines-based framework

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.