Real-space evolutionary annealing

Standard genetic algorithms can discover good fitness regions and later forget them due to their Markovian structure, resulting in suboptimal performance. Real-Space Evolutionary Annealing (REA) hybridizes simulated annealing and genetic algorithms into a provably convergent evolutionary algorithm for Euclidean space that relies on non-Markovian selection. REA selects any previously observed solution from an approximated Boltzmann distribution using a cooling schedule. This method enables REA to escape local optima while retaining information about prior generations. In parallel work, REA has been generalized to arbitrary measure spaces and shown to be asymptotically convergent to the global optima. This paper compares REA experimentally to six popular optimization algorithms, including Differential Evolution, Particle Swarm Optimization, Correlated Matrix Adaptation Evolution Strategies, the real-coded Bayesian Optimization Algorithm, a real-coded genetic algorithm, and simulated annealing. REA converges faster to the global optimum and succeeds more often on two out of three multimodal, non-separable benchmarks and performs strongly on all three. In particular, REA vastly outperforms the real-coded genetic algorithm and simulated annealing, proving that the hybridization is better than either algorithm alone. REA is therefore an interesting and effective algorithm for global optimization of difficult fitness functions.