A selection method for evolutionary algorithms based on the Golden Section

During millions of years, nature has developed patterns and processes with interesting characteristics. They have been used as inspiration for a significant number of innovative models that can be extended to solve complex engineering and mathematical problems. One of the most famous patterns present in nature is the Golden Section (GS). It defines an especial proportion that allows the adequate formation, selection, partition, and replication in several natural phenomena. On the other hand, Evolutionary algorithms (EAs) are stochastic optimization methods based on the model of natural evolution. One important process in these schemes is the operation of selection which exerts a strong influence on the performance of their search strategy. Different selection methods have been reported in the literature. However, all of them present an unsatisfactory performance as a consequence of the deficient relations between elitism and diversity of their selection procedures. In this paper, a new selection method for evolutionary computation algorithms is introduced. In the proposed approach, the population is segmented into several groups. Each group involves a certain number of individuals and a probability to be selected, which are determined according to the GS proportion. Therefore, the individuals are divided into categories where each group contains individual with similar quality regarding their fitness values. Since the possibility to choose an element inside the group is the same, the probability of selecting an individual depends exclusively on the group from which it belongs. Under these conditions, the proposed approach defines a better balance between elitism and diversity of the selection strategy. Numerical simulations show that the proposed method achieves the best performance over other selection algorithms, in terms of its solution quality and convergence speed.