A strength pareto evolutionary algorithm based on adaptive reference points for solving irregular fronts.

Evolutionary algorithms have proven to be extremely effective at tackling multi-objective optimization problems (MOPs). However, when dealing with many-objective optimization problems (MaOPs), their performance frequently degrades, especially when the Pareto marking irregular shapes. The population pressure to choose the Pareto optimal front and address the generalizability of different Pareto front shapes becomes more challenging as the number of objectives increases. We present a strength Pareto evolutionary algorithm based on adaptive reference points (SPEA/ARP) to address this problem. First, the reference points are updated using current and historical population information. The angles between the current demographic information and the predefined uniform reference points are used to select the active reference points, and the adaptive reference points are selected from the historical population information projected onto the reference plane. Second, the fitness function values are applied to classify the environmental selection criteria into two categories: 1) The angle distance scaling function using adaptive reference points is utilized to increase selection pressure, and the diversity of non-dominated solutions is balanced using the angle-based secondary selection technique. 2) Otherwise, the fitness function values are employed to choose the next generation of non-dominated solutions. Third, an aggregate fitness r-value generated by the angle distance scaling function is employed to construct matching pools that produce valid offsprings. Finally, extensive experiments are carried out to demonstrate SPEA/ARP performance by comparing it with six state-of-the-art many-objective evolutionary algorithms on 5-, 10-, 15-objective of 31 benchmark MaOPs. The experiments show that SPEA/ARP outperforms the compared algorithms.