Efficient User-Oriented Pareto Fronts And Pareto Archives Based On Spatial Data Structures

YEfficient manipulation of Pareto fronts and Pareto archives involves non-trivial data structures and algorithms. Because of this complexity, researchers and programmers might recur to naive strategies based on linear lists, where most operations require expensive pairwise comparisons between all elements. The lack of a functional container type for Pareto fronts and archives reduces their usefulness in multi-objective optimization, simulations in economics, decision making, data analysis, or any application that caches objects based on multiple criteria. Despite the existence of some frameworks for multi-objective optimization, there is no user-oriented solution focused exclusively on efficient implementations of dynamic fronts and archives as abstract data types with their fundamental operations for insertion, removal, searching, reference points, hyperbox queries, nearest points, and indicators. This paper describes such a library based on spatial data structures for Pareto fronts and archives with specialized algorithms to perform all of these operations with low asymptotic complexity. At a negligible integration cost, the results confirm this implementation achieves notable performance gains over naive methods for fronts of all sizes and dimensions.