PAES-25: Local Search, Archiving, and Multi/Many-Objective Pseudo-Boolean Functions

Joshua D. Knowles, Arnaud Liefooghe

Abstract: Twenty-five years on from the original Pareto archived evolution strategy (PAES), we present and investigate an updated version (PAES-25), revisiting the algorithmic components of the mutation operator, acceptance criterion, and archiver, focusing on bit-string represented multi- and many- objective optimization problems. The original PAES, particularly the (1+1)-PAES, was intended as a “baseline” algorithm against which EMO algorithms (emerging at the time) with more parameters and the use of a population might be compared. PAES-25, which remains very simple, may serve similar purposes today, and may also help in developing our understanding of local search dynamics on multi-objective landscapes. Using LOTZ as a benchmark, and introducing three multi/many-objective variants, LITZ, sLITZ and FRITZ (up to 8 objectives here), the best performing PAES-25 configuration emerges as one using the multilevel grid archiver, a 1/n per-bit standard mutation, and original acceptance criterion (which accepts “neutral” search moves). We find no need for the use of hypervolume-based archiving, which is more computationally expensive, and generally recommend against an unbounded archive. Just as the original (1+1)-PAES has proven useful in developing purely Pareto-based hybrid EMO algorithms, as well as Pareto optimization local search algorithms like simulated annealing and tabu search variants, so should PAES-25, while now benefiting from an archiving component suitable for many-objective problems. We publish our functions, code, and results to facilitate future community benchmarking efforts.