An evolutionary strategy for global minimization and its Markov chain analysis

The mutation-or-selection evolutionary strategy (MOSES) is presented. The goal of this strategy is to solve complex discrete optimization problems. MOSES evolves a constant sized population of labeled solutions. The dynamics employ mechanisms of mutation and selection. At each generation, the best solution is selected from the current population. A random binomial variable N which represents the number of offspring by mutation is sampled. Therefore the N first solutions are replaced by the offspring, and the other solutions are replaced by replicas of the best solution. The relationships between convergence, the parameters of the strategy, and the geometry of the optimization problem are theoretically studied. As a result, explicit parametrizations of MOSES are proposed.