Past work has shown that a genetic algorithm with crossover performs better than a genetic algorithm with mutation alone (Grefenstette et al., 1990; Wilson, 1987). This section attempts to test the hypothesis that crossover improves the performance of ICET. To test this hypothesis, it is not sufficient to merely set the crossover rate to zero. Since crossover has a randomizing effect, similar to mutation, we must also increase the mutation rate, to compensate for the loss of crossover (Wilson, 1987; Spears, 1992).
It is very difficult to analytically calculate the increase in mutation rate that is required to compensate for the loss of crossover (Spears, 1992). Therefore we experimentally tested three different mutation settings. The results are summarized in Table 12. When the crossover rate was set to zero, the best mutation rate was 0.10. For misclassification error costs from $10 to $10,000, the performance of ICET without crossover was not as good as the performance of ICET with crossover, but the difference is not statistically significant. However, this comparison is not entirely fair to crossover, since we made no attempt to optimize the crossover rate (we simply used the default value). The results suggest that crossover is mildly beneficial, but do not prove that pure mutation is inferior.