Quad-trees: A Data Structure for Storing Pareto-sets in Multi-objective Evolutionary Algorithms with Elitism

In multi-objective evolutionary algorithms (MOEAs) with elitism, the data structures for storing and updating archives may have a great impact on the required computational (CPU) time, especially when optimizing higherdimensional problems with large Pareto-sets. In this chapter, we introduce Quad-trees as an alternative data structure to linear lists for storing Paretosets. In particular, we investigate several variants of Quad-trees and compare them with conventional linear lists. We also study the influence of population size and number of objectives on the required CPU time. These data structures are evaluated and compared on several multi-objective example problems. The results presented show that typically, linear lists perform better for small population sizes and higher-dimensional Pareto-fronts (large archives) whereas Quad-trees perform better for larger population sizes and Pareto-sets of small cardinality.