On the Scalability of Parallel Genetic Algorithms

This paper examines the scalability of several types of parallel genetic algorithms (GAs). The objective is to determine the optimal number of processors that can be used by each type to minimize the execution time. The first part of the paper considers algorithms with a single population. The investigation focuses on an implementation where the population is distributed to several processors, but the results are applicable to more common master-slave implementations, where the population is entirely stored in a master processor and multiple slaves are used to evaluate the fitness. The second part of the paper deals with parallel GAs with multiple populations. It first considers a bounding case where the connectivity, the migration rate, and the frequency of migrations are set to their maximal values. Then, arbitrary regular topologies with lower migration rates are considered and the frequency of migrations is set to its lowest value. The investigation is mainly theoretical, but experimental evidence with an additively-decomposable function is included to illustrate the accuracy of the theory. In all cases, the calculations show that the optimal number of processors that minimizes the execution time is directly proportional to the square root of the population size and the fitness evaluation time. Since these two factors usually increase as the domain becomes more difficult, the results of the paper suggest that parallel GAs can integrate large numbers of processors and significantly reduce the execution time of many practical applications.