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Mutation has traditionally been regarded as an important operator inevolutionary algorithms. In particular, there have been many experimentalstudies which showed the effectiveness of adapting mutation rates for variousstatic optimization problems. Given the perceived effectiveness of adaptive andself-adaptive mutation for static optimization problems, there have beenspeculations that adaptive and self-adaptive mutation can benefit dynamicoptimization problems even more since adaptation and self-adaptation arecapable of following a dynamic environment. However, few theoretical resultsare available in analyzing rigorously evolutionary algorithms for dynamicoptimization problems. It is unclear when adaptive and self-adaptive mutationrates are likely to be useful for evolutionary algorithms in solving dynamicoptimization problems. This paper provides the first rigorous analysis ofadaptive mutation and its impact on the computation times of evolutionaryalgorithms in solving certain dynamic optimization problems. More specifically,for both individual-based and population-based EAs, we have shown that anytime-variable mutation rate scheme will not significantly outperform a fixedmutation rate on some dynamic optimization problem instances. The proofs alsooffer some insights into conditions under which any time-variable mutationscheme is unlikely to be useful and into the relationships between the problemcharacteristics and algorithmic features (e.g., different mutation schemes).

The Impact of Mutation Rate on the Computation Time of Evolutionary Dynamic Optimization