3. Analysis of scheduling evolution

Figure 5 shows the relationship between fitness value and training iterations of schemes 5–8. As can be seen, the BA and WOA converged quickly at the initial stage of the evolution. This is mainly due to the fact that the initial numbers of population of the BA and WOAs (*NP* = 30) were much larger than that of the CGA and ICGAs (*NP* = 4). This means a relatively strong ability for searching the solution space. However, with the increase in evolutional iterations, the search ability of the BA and the WOA gradually deterioratesdand they fell into the local extremum in the 135th and 139th generations, respectively. Although the CGA should be good at fast search, the distribution of probability values in the probabilistic model all decreased with evolution, and thus and the search performance on the solution space decreased. The algorithm stopped evolving at the 87th generation, falling into the local extremum. On the other hand, the ICGA had the similar fast search performance as the CGA during the initial stage and encountered evolutionary stagnation at the 94th generation. But as evolution continues, the ICGA started the mapping operation to reactivate the algorithm's evolutionary ability and found for the optimal solution in the 263th generation.

**Figure 5.** Relationship between fitness value and training iterations of schemes 5–8.

Figure 6 shows the relationship between fitness value and running time of schemes 5–8. As can be seen from the figure, the running speed of CGA and ICGA was very fast, but the CGA fell into the local extremum at 4 s. The optimization speed of the BA was the slowest among the four algorithms, and its optimal solution was 299 during the 35 s running time. From the figure, we can also see that the fitness value of the ICGA was the best among the four algorithms at the same CPU time. And the time used by the ICGA to get the same fitness value was the least among the four algorithms. The ICGA maintained the advantage that the CGA can converge quickly in the early stage of evolution. In the later stage of evolution, when falling into the local extremum, the ICGA improved the diversity of individuals in the population by mapping the original probabilistic model to a new probabilistic model, so that the algorithm could jump out of the local extremum and continue to evolve.

**Figure 6.** Relationship between fitness value and Running time of schemes 5–8.
