Analysis of Evolutionary Diversity Optimization for Permutation Problems

Generating diverse populations of high-quality solutions has gained interest as a promising extension to the traditional optimization tasks. This work contributes this line research with an investigation on evolutionary diversity for three most well-studied permutation problems: Traveling Salesperson Problem (TSP), both symmetric and asymmetric variants, Quadratic Assignment (QAP). It includes analysis worst-case performance simple mutation-only algorithm different mutation operators, using established measure. Theoretical results show that many operators these problems guarantee convergence maximally sufficiently small size within cubic quartic expected runtime. On other hand, regarding QAP suggest strong mutations give poor performance, strength exponentially Additionally, experiments are carried out QAPLIB synthetic instances in unconstrained constrained settings, reveal much more optimistic practical performances while corroborating theoretical findings strength. These should serve baseline future studies.