Understanding how the time-complexity of evolutionary algorithms (EAs) depend on their parameter settings and characteristics of fitness landscapes is a fundamental problem in evolutionary computation. Most rigorous results were derived using a handful of key analytic techniques, including drift analysis. However, since few of these techniques apply effortlessly to population-based EAs, most time-complexity results concern simplified EAs, such as the (1+1) EA.This paper describes the level-based theorem, a new technique tailored to population-based processes. It applies to any non-elitist process where offspring are sampled independently from a distribution depending only on the current population. Given conditions on this distribution, our technique provides upper bounds on the expected time until the process reaches a target state.We demonstrate the technique on several pseudo-Boolean functions, the sorting problem, and approximation of optimal solutions in combinatorial optimisation. The conditions of the theorem are often straightforward to verify, even for Genetic Algorithms and Estimation of Distribution Algorithms which were considered highly non-trivial to analyse. Finally, we prove that the theorem is nearly optimal for the processes considered. Given the information the theorem requires about the process, a much tighter bound cannot be proved.

This paper introduces an easy to use technique for deriving upper bounds on the expected runtime of non-elitist population-based evolutionary algorithms (EAs). Applications of the technique show how the efficiency of EAs is critically dependant on having a sufficiently strong selective pressure. Parameter settings that ensure sufficient selective pressure on commonly considered benchmark functions are derived for the most popular selection mechanisms. Together with a recent technique for deriving lower bounds, this paper contributes to a much-needed analytical tool-box for the analysis of evolutionary algorithms with populations.

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Estimation of distribution algorithms (EDA) are stochastic search methods that look for optimal solutions by learning and sampling from probabilistic models. Despite their popularity, there are only few rigorous theoretical analyses of their performance. Even for the simplest EDAs, such as the Univariate Marginal Distribution Algorithm (UMDA) which assumes independence between decision variables, there are only a handful of results about its runtime, and results for simple functions such as OneMax are still missing.In this paper, we show that the recently developed levelbased theorem for non-elitist populations is directly applicable to runtime analysis of EDAs. To demonstrate this approach, we derive easily upper bounds on the expected runtime of the UMDA.