Should Multi-objective Evolutionary Algorithms Use Always Best Non-dominated Solutions as Parents?

The generational model maintaining both parent and offspring populations is frequently employed for designing multi-objective evolutionary algorithms. The archive population of non-dominated solutions acquired during the search is also often incorporated, especially for real-world problems that cannot lose any valuable information obtained. Although both the parent and archive populations should maintain good solutions, repeated generations may cause solutions in the parent population to be dominated by ones in the archive. This means that the parent population at the final generation cannot be the best solution set throughout the search. This is not problematic if the parent population, with lower optimality than the archive, is beneficial for offspring generation. However, if solutions with the highest optimality are useful for offspring generation, the archive should be used for it. This paper aims to investigate whether the parent population should always be the best non-dominated solution set. As a research methodology, this paper picks NSGA-II, NSGA-III, IBEA, NSGA-II-SDR, and
$\boldsymbol{\theta}$
-DEA, employing the generational model and re-selecting the parent population from the archive in every certain generation to make the parent population the best. The generational interval of the re-selection is a parameter that adjusts the optimality of the parent population. The shorter the interval, the higher the optimality in the parent population. Experimental results using the knapsack problems with 2–6 objectives show that the highest parent optimality with the shortest re-selection interval maximizes the search performance for many algorithms and problems, while the highest parent optimality does not necessarily maximize the search performance for some algorithms and problems.