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Analysis of the (1+1) EA for a Dynamically Changing Objective Function

Evolutionary algorithms (EAs) are a class of randomized search heuristics, that are often successfully used for black-box optimization. Nevertheless, there are only few theoretical results about EAs, which are furthermore limited to static objective functions, i. e. functions that do not change over time, despite of the practical relevance of dynamic optimization. Here, the runtime of a simple EA, the (1+1) EA, is theoretically analyzed for a dynamically changing objective function. The main focus lies on determining the degree of change of the fitness funcion, where the expected runtime of the (1+1) EA changes from polynomially to super-polynomially. The proofs presented show methods how to analyze EAs with dynamically changing objective functions.