Cauchy annealing schedule: an annealing schedule for Boltzmann selection scheme in evolutionary algorithms

Boltzmann selection is an important selection mechanism in evolutionary algorithms as it has theoretical properties which help in theoretical analysis. However, Boltzmann selection is not used in practice because a good annealing schedule for the inverse temperature parameter is lacking. In this paper, we propose a Cauchy annealing schedule for Boltzmann selection scheme based on a hypothesis that selection-strength should increase as evolutionary process goes on and distance between two selection strengths should decrease for the process to converge. To formalize these aspects, we develop formalism for selection mechanisms using fitness distributions and give an appropriate measure for selection strength. In this paper, we prove an important result, by which we derive an annealing schedule called Cauchy annealing schedule. We demonstrate the novelty of proposed annealing schedule using simulations in the framework of genetic algorithms.