On the adaptation of reference sets using niching and pair-potential energy functions for multi-objective optimization
Flowchart of our adaptation method plugged into a MOEA that employs a predefined WVRS.
Archive maintenance mechanism based on niching and PPFs on DTLZ1-1. (a) Each solution from the archive is associated to a weight vector from the original WVRS using the perpendicular distance. (b) The weight vectors with a niche count greater than zero are detected as useful weight vectors. (c) The nearest solution to each useful weight vector is selected. (d) The worst contributing solution from the remaining solutions is iteratively deleted until the cardinality of the archive is reduced to the population size.
Generation process of the adapted WVRS on DTLZ1-1. (a) The useful weight vectors were detected from the association procedure. (b) An archive with cardinality equal to the population size $N$ is obtained from the archive maintenance mechanism based on niching and PPFs. (c) The surviving solutions from PPFs selection are converted into weight vectors. (d) The adapted WVRS is generated by combining useful weight vectors and the recently generated weight vectors. It is worth noting that the solutions selected using niching are not converted into weight vectors. Instead, the useful weight vectors are included in the adapted WVRS as they represent the aspiration points of such solutions.
Project information
- Category: Multi-Objective Optimization
- Project date: 12 January, 2023
- Project URL: On the adaptation of reference sets using niching and pair-potential energy functions for multi-objective optimization
- Project Code: AdaK
Project Description
In this paper, we proposed a pluggable reference set adaptation method based on niching and pair-potential energy functions (PPFs), called AdaK, to enhance the performance of different Multi-Objective Evolutionary Algorithms (MOEAs) on Multi-Objective Problems (MOPs) with irregular pareto front (PF) shapes while maintaining their good behavior on MOPs with regular PF shapes.
Our adaptation method was validated by plugging it into three well-known MOEAs that use a predefined weight vector-based reference set. We perform an empirical study using different PPFs for our adaptation method on the DTLZ, WFG, Minus-DTLZ, Minus-WFG, IMOP, and VNT test suites.
Our experimental results show the capability of our adaptation method to promote an invariant performance regardless of the PF shape. Additionally, we show that MOEAs with our adaptation method have a competitive performance against state-of-the-art MOEAs.