Measure-theoretic evolutionary annealing

There is a deep connection between simulated annealing and genetic algorithms with proportional selection. Evolutionary annealing is a novel evolutionary algorithm that makes this connection explicit, resulting in an evolutionary optimization method that can be viewed either as simulated annealing with improved sampling or as a non-Markovian selection mechanism for genetic algorithms with selection over all prior populations. A martingale-based analysis shows that evolutionary annealing is asymptotically convergent and this analysis leads to heuristics for setting learning parameters to optimize the convergence rate. In this work and in parallel work evolutionary annealing is shown to converge faster than other evolutionary algorithms on several benchmark problems, establishing a promising foundation for future theoretical and experimental research into algorithms based on evolutionary annealing.