Crossover Rate

Crossover is by far the most important evolution operation. I tested single-point and uniform crossover with a crossover probability of 0.6. The population size was chosen to be 200 and the algorithm was run for 250 generations. The jump mutation was set at 0.005 and the creep mutation at 0.05. Elitism of the best individual as well as niching was allowed. The top panels in Figure  show the convergence rate of the two cases, whereas the bottom panels show the corresponding traces. In this case uniform crossover (right panel) performs a little better since it reaches a lower cost-value after the allowed number of cost-function evaluations. Using uniform crossover, I tried six different values of crossover probability: 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0. I tried this large range of values because crossover rate is a particularly important evolution parameter. The top panels of Figure  show the comparison of the convergence rates for crossover rates of 0.5, 0.6 and 0.7 whereas the bottom panels show the same curves for crossover rates of 0.8, 0.9 and 1.0. The results are surprisingly similar, although it appears that the smaller crossover rates produce faster initial convergence, and so I chose a crossover rate of 0.6 for the remaining tests.

 

SG_compare_crossover1
Figure 5 Comparison of convergence rates for two types of crossover: single-point (left) and uniform (right). Top panels are convergence rates whereas bottom panels are trace match with continuous line representing the reference trace and dotted line the inverted trace.

 

SG_compare_crossover2
Figure 6 Comparison of convergence rates for different crossover rates. Top panels correspond to crossover rates of 0.5, 0.6 and 0.7 whereas bottom panels correspond to crossover rates of 0.8, 0.9 and 1.0.