Optimal Type of Evolutionary Algorithm
The choice of the type of EA determines the properties of global exploration in MAs. In order to determine which EA produces better results in the investigated problem domains, a series of design experiments was performed. Figure 13 shows a comparison of the behavior of two algorithms, i. e., MA-ES and MA-GA, for Problem Ia. Two average best-so-far curves in the upper part of Figure 13 correspond to the best results obtained with MA-GAs with two combinations of parents and offspring population sizes, i. e. MA-GA(5,25) and MA-GA(50,50). In both cases the mutation rate was equal to 0.3 and crossover rate was equal to 0.5. The results produced by MA-GAs are compared to the average best-so-far performance produced by MA-ES with the overlapping (MA-ES(5+25)) and nonoverlapping (MA-ES(5,25)) generational models. In this case, the rates of mutation and crossover were equal to 0.025 and 0.2, respectively
Figure 13 clearly shows that MA-ES outperformed MA-GA in this problem domain. The average fitness value produced by MA-GA(5,25) after 1,000 evaluations was equal to 569,056 lbs. compared to 542,029 lbs. achieved by MA-ES(5+25). This corresponds to almost 5% better results, on average, produced by MA-ES. The performance improvement between an average design produced after 1,000 fitness evaluations and an average design in the initial population was equal to 19,434 lbs., or 3.3%, for MA-GA(5,25). On the other hand, for MA-ES(5+25) these values were equal to 46,461 lbs. and 7.9%, respectively.
Concluding, the results of the design experiments revealed that MA-ES performed better than MAGAs in these problem domains. Hence, they were employed in the long-term design experiments reported in the next section.