Data structures for non-dominated sets: implementations and empirical assessment of two decades of advances

Abstract

Many data structures have been developed over the last two decades for the storage and efficient update of unconstrained sets of mutually non-dominating solutions. Typically, analysis has been provided in the original works for these data structures in terms of worst/average case complexity performance. Often, however, other aspects such as rebalancing costs of underlying data structures, cache sizes, etc., can also significantly affect behaviour. Empirical performance comparison has often (but not always) been limited to run-time comparison with a basic linear list. No comprehensive comparison between the different specialised data structures proposed in the last two decades has thus far been undertaken. We take significant strides in addressing this here. Eight data structures from the literature are implemented within the same overarching open source Java framework. We additionally highlight and rectify some errors in published work --- and offer additional efficiency gains. Run-time performances are compared and contrasted, using data sequences embodying a number of different characteristics. We show that in different scenarios different data structures are preferable, and that those with the lowest big O complexity are not always the best performing. We also find that performance profiles can vary drastically with computational architecture, in a non-linear fashion.