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While the theoretical analysis of evolutionary algorithms (EAs) has madesignificant progress for pseudo-Boolean optimization problems in the last 25years, only sporadic theoretical results exist on how EAs solvepermutation-based problems.  To overcome the lack of permutation-based benchmark problems, we propose ageneral way to transfer the classic pseudo-Boolean benchmarks into benchmarksdefined on sets of permutations. We then conduct a rigorous runtime analysis ofthe permutation-based $(1+1)$ EA proposed by Scharnow, Tinnefeld, and Wegener(2004) on the analogues of the \textsc{LeadingOnes} and \textsc{Jump}benchmarks. The latter shows that, different from bit-strings, it is not onlythe Hamming distance that determines how difficult it is to mutate apermutation $\sigma$ into another one $\tau$, but also the precise cyclestructure of $\sigma \tau^{-1}$. For this reason, we also regard the moresymmetric scramble mutation operator. We observe that it not only leads tosimpler proofs, but also reduces the runtime on jump functions with odd jumpsize by a factor of $\Theta(n)$. Finally, we show that a heavy-tailed versionof the scramble operator, as in the bit-string case, leads to a speed-up oforder $m^{\Theta(m)}$ on jump functions with jump size~$m$.%

Towards a Stronger Theory for Permutation-based Evolutionary Algorithms