Ring-Based Crossovers in Genetic Algorithms: Characteristic Decomposition and Their Generalization

Abstract

Effective crossover methods are essential for genetic algorithms because they enhance population diversity, resulting in an increase in the search space to be explored and the mitigation of trapping at local optima. Ring-based crossover methods are designed to address the shortcomings of traditional crossover techniques; for example, the ends of binary-encoded chromosomes tend to remain unaltered, even when their fitness values are low. By conjoining the leftmost and rightmost parts of a chromosome to form a ring, the ring-based crossovers allow offspring bits to be inherited from parent bits at the front and rear positions. Such a ring-based technique helps increase population diversity while requiring a relatively low number of fitness evaluations. To the best of our knowledge, there has been no comparative study or comprehensive analysis of ring-based crossover techniques. In this paper, we study and compare the characteristics of various existing ring-based crossover techniques (i.e., circle-ring (CRC), annular (AC), ring (RC) and front-rear crossover (FRC)). Although they each have distinct characteristics, they share a common crossover concept: bits at different positions can be swapped. We propose a generalized ring-based crossover (GRC) as an umbrella of the ring-based crossovers, embodying all of their beneficial characteristics. Chromosome shifting, ring forming, chromosome exchange and offspring creation are integrated into the proposed model. The experimental results show that GRC outperforms the other ring-based crossover methods in all experiments, and these results are consistent with the results of behavioral analysis. In a trap problem, GRC outperformed the state-of-the-art BOA method and require 40-times fewer fitness evaluations. GRC tends to maintain a variety of candidates in populations and to preserve the building blocks of solution, and it requires 93% and 57% fewer fitness evaluations (on average) compared to traditional crossover and other ring-based crossover methods.