Migration Rates and Optimal Topologies

Abstract

This chapter extended the previous deme-sizing equations to consider configurations that are likely to be used by practitioners. The first part of the chapter described the relation between the deme size, the migration rate, and the topology’s degree with the probability of success after two epochs. It showed how to find the configuration that optimizes the execution time while reaching a predetermined target quality. These calculations were also used to find an alternate expression for the optimal number of fully-connected demes (which was calculated initially in Chapter 4). Although this topology cannot integrate many demes, it can reduce the execution time substantially, and it may be competitive with other optimally-configured topologies.

The second part of the chapter generalized the results to multiple epochs. After multiple epochs, the topology is important because a deme receives indirect contributions from varying number of demes. Section 2 showed that different topologies with the same degree reach almost identical solutions after any number of epochs. A simple approximate model was derived to explain the small differences, but most importantly, the equivalence of topologies with the same degree facilitated the derivation of a model of solution quality. The quality model was transformed into an accurate deme-sizing equation, which in turn was used to minimize the execution time.

When the topology is fixed and the algorithm is executed until all the populations converge to the same solution, the optimal number of populations was found to be, which is asymptotically the same as parallel versions of GAs with a single population. This result suggests that, regardless of their type, parallel GAs can integrate large numbers of processors and reduce significantly the execution time of many practical applications.