Distance Measures in Genetic Algorithms

Metric is one of the fundamental tools for understanding space. It gives induced topology to the space and it is the most basic way to provide the space with topology. Different metrics make different topologies. The shape of the space largely depends on its metric. In understanding genetic algorithms, metric is also basic and important. In genetic algorithms, a good distance measure not only helps to analyze their search spaces, but can also improve their search capability. Hamming distance has been popular in most researches for genetic algorithms that deal with discrete spaces. It has also been widely adopted in studies about the analysis of the problem space. In this paper, we propose more reasonable distance measures depending on situations in the process of genetic algorithms and show that they are actually metrics. We propose three distance measures: one for the population-based search, another for the solution space based on K-ary encoding, and the third as an approximate measure of performance improvement of linkage-based genetic algorithms. Since the genetic algorithm is a population-based search, the distance measure between populations is useful for understanding the behavior of genetic algorithms. We propose an intuitive and reasonable metric.