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An efficient approach to unbounded bi-objective archives -: introducing the mak_tree algorithm

Given the prominence of elite archiving in contemporary multiobjective optimisation research and the limitations inherent in bounded population sizes, it is unusual that the vast majority of popular techniques aggressively truncate the capacity of archives and are based upon inefficient list representations. By forming better data structures and algorithms for the storage of archival members, the need for truncation is reduced and unbounded elite sets become viable. While work does exist in this vein, it is always of a general nature and significant improvements can be made in the bi-objective case. As such, this paper elucidates the unique properties of two-dimensional non-dominated sets and capitalises on these notions to develop the highly efficient and specialised bi-objective Mak_Tree algorithm. Theoretical results indicate that the specialised approach is preferable to pre-existing general techniques, while empirical analysis illustrates improved performance over both unbounded and bounded list techniques.