  Artificial Immune Systems (AIS) employing hypermutations with linear static
mutation potential have recently been shown to be very effective at escaping
local optima of combinatorial optimisation problems at the expense of being
slower during the exploitation phase compared to standard evolutionary
algorithms. In this paper we prove that considerable speed-ups in the
exploitation phase may be achieved with dynamic inversely proportional mutation
potentials (IPM) and argue that the potential should decrease inversely to the
distance to the optimum rather than to the difference in fitness. Afterwards we
define a simple (1+1)~Opt-IA, that uses IPM hypermutations and ageing, for
realistic applications where optimal solutions are unknown. The aim of the AIS
is to approximate the ideal behaviour of the inversely proportional
hypermutations better and better as the search space is explored. We prove that
such desired behaviour, and related speed-ups, occur for a well-studied bimodal
benchmark function called \textsc{TwoMax}. Furthermore, we prove that the
(1+1)~Opt-IA with IPM efficiently optimises a third bimodal function,
\textsc{Cliff}, by escaping its local optima while Opt-IA with static potential
cannot, thus requires exponential expected runtime in the distance between the
cliff and the optimum.
