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We present a time complexity analysis of the Opt-IA artificial immune system(AIS). We first highlight the power and limitations of its distinguishingoperators (i.e., hypermutations with mutation potential and ageing) byanalysing them in isolation. Recent work has shown that ageing combined withlocal mutations can help escape local optima on a dynamic optimisationbenchmark function. We generalise this result by rigorously proving that,compared to evolutionary algorithms (EAs), ageing leads to impressive speed-upson the standard Cliff benchmark function both when using local and globalmutations. Unless the stop at first constructive mutation (FCM) mechanism isapplied, we show that hypermutations require exponential expected runtime tooptimise any function with a polynomial number of optima. If instead FCM isused, the expected runtime is at most a linear factor larger than the upperbound achieved for any random local search algorithm using the artificialfitness levels method. Nevertheless, we prove that algorithms usinghypermutations can be considerably faster than EAs at escaping local optima. Ananalysis of the complete Opt-IA reveals that it is efficient on the previouslyconsidered functions and highlights problems where the use of the fullalgorithm is crucial. We complete the picture by presenting a class offunctions for which Opt-IA fails with overwhelming probability while standardEAs are efficient.

When Hypermutations and Ageing Enable Artificial Immune Systems to Outperform Evolutionary Algorithms