7 A Genetic Algorithm on a Scale-Free Network

This paper describes the application of the Barabasi-Albert model of a small-world network to genetic algorithms. These networks have two types of connections. Most connections are “local”, connecting only to immediate neighbors. The other type is “long-range”, connecting randomly to distant individuals. For the genetic algorithm, we place a population of chromosomes in such a network. Crossover (mating) only occurs between connected individuals. The locality encourages diversity similar to that seen by other authors using spatially restricted mating. On the other hand, the long-range connections allow superior characteristics to spread relatively rapidly through the entire population. We control the rapidity of this spread by the frequency of long-range connections. We have implemented this technique using the Barabasi-Albert model for small-world networks. The most important characteristic of this model is that it generates scale-free graphs. We have evaluated this technique on some engineering design problems which are typical of those encountered at General Dynamics — NN Shipbuilding, the largest shipbuilder in the US. We compare the Barabasi-Albert model with a different small-world model (Watts-Strogatz) that does not have the scale-free characteristic. We also compare it with the conventional genetic algorithm and we show its superiority under many conditions.