In this work, we introduce analytical replay experiments to the evolutionary computing community. Replay experiments originated in the context of laboratory experimental evolution as an empirical approach to identifying potentiating events that increased the likelihood of an observed evolutionary outcome. By restarting a population's evolution from different historical time points, replay experiments sample the distribution of what could have evolved from different points in time, which allows us to quantify how a population's potential for different evolutionary outcomes changed as a result of that population's history. In this work, we give a step-by-step guide to designing replay experiments for evolutionary computing systems. We then provide a demonstrative example replay experiment that measures how potentiation for problem-solving success changed in an evolved genetic programming population, showing that increases in potential for success do not necessarily correspond with increases in a population's fitness. Broadly, we argue that analytical replay experiments can be a powerful tool for expanding the theoretical foundations of evolutionary computing, and we offer suggestions for promising future research directions enabled by replay experiments.

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