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Typical artificial immune system (AIS) operators such as hypermutations withmutation potential and ageing allow to efficiently overcome local optima fromwhich evolutionary algorithms (EAs) struggle to escape. Such behaviour has beenshown for artificial example functions constructed especially to showdifficulties that EAs may encounter during the optimisation process.{\color{black}However, no evidence is available indicating that these twooperators have similar behaviour also in more realistic problems.} In thispaper we perform an analysis for the standard NP-hard \partition problem fromcombinatorial optimisation and rigorously show that hypermutations and ageingallow AISs to efficiently escape from local optima where standard EAs requireexponential time. As a result we prove that while EAs and random local search(RLS) may get trapped on 4/3 approximations, AISs find arbitrarily goodapproximate solutions of ratio (1+$\epsilon$) {\color{black}within $n(\epsilon^{-(2/\epsilon)-1})(1-\epsilon)^{-2} e^{3} 2^{2/\epsilon} + 2n^3 2^{2/\epsilon}+ 2n^3$ function evaluations in expectation. This expectation is polynomial inthe problem size and exponential only in $1/\epsilon$}.

Artificial Immune Systems Can Find Arbitrarily Good Approximations for the NP-Hard Number Partitioning Problem