Runtime Analysis for Permutation-based Evolutionary Algorithms - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Algorithmica Année : 2024

Runtime Analysis for Permutation-based Evolutionary Algorithms

Résumé

While the theoretical analysis of evolutionary algorithms (EAs) has made significant progress for pseudo-Boolean optimization problems in the last 25 years, only sporadic theoretical results exist on how EAs solve permutation-based problems. To overcome the lack of permutation-based benchmark problems, we propose a general way to transfer the classic pseudo-Boolean benchmarks into benchmarks defined on sets of permutations. We then conduct a rigorous runtime analysis of the permutation-based (1 + 1) EA proposed by Scharnow, Tinnefeld, and Wegener (2004) on the analogues of the LeadingOnes and Jump benchmarks. The latter shows that, different from bit-strings, it is not only the Hamming distance that determines how difficult it is to mutate a permutation σ into another one τ , but also the precise cycle structure of στ −1. For this reason, we also regard the more symmetric scramble mutation operator. We observe that it not only leads to simpler proofs, but also reduces the runtime on jump functions with odd jump size by a factor of Θ(n). Finally, we show that a heavy-tailed version of the scramble operator, as in the bit-string case, leads to a speed-up of order m Θ(m) on jump functions with jump size m. A short empirical analysis confirms these findings, but also reveals that small implementation details like the rate of void mutations can make an important difference.
Fichier principal
Vignette du fichier
new_journal_arxiv_v3.pdf (617.7 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04006938 , version 1 (27-02-2023)
hal-04006938 , version 2 (26-07-2023)

Identifiants

Citer

Benjamin Doerr, Yassine Ghannane, Marouane Ibn Brahim. Runtime Analysis for Permutation-based Evolutionary Algorithms. Algorithmica, 2024, 86 (1), pp.90-129. ⟨10.1007/s00453-023-01146-8⟩. ⟨hal-04006938v2⟩
15 Consultations
48 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More