# Niching-Driven Divide-and-Conquer Hill Exploration
## 4 Experiments
### Effect of NDDCHE in Heuristic Mode  
The above experiment shows the ideal effect of the proposed hierarchical divide-and-conquer framework. However, although the hill regions are gradually learned from scratch in NDDCHE in omniscient mode, the locations of the optima and the boundaries of BoAs are utilized to ensure the accuracy of learning, which is far beyond the practical cases. So, in the following experiments, the parts of NDDCHE in omniscient mode are replaced with their heuristic versions to demonstrate the feasibility of the proposed framework.  
An ablation study on the effect of each of the two major parts of NDDCHE is also conducted during this process. Firstly, the methods for updating seed solutions in omniscient mode are replaced with their heuristic versions, while that for updating hill regions remain the omniscient versions. The framework in this mode is named NDDCHE in the half-heuristic mode for ease of description. A comparison between NDDCHE in omniscient mode and that in half-heuristic mode can show the effect of updating seed solutions in practical cases. Next, a comparison between NDDCHE in half-heuristic mode and that in heuristic mode, where all methods in NDDCHE are in their heuristic forms, can show the effect of updating hill regions.  
For LRDE, 100 independent runs of LRDE with NDDCHE in half-heuristic mode and LRDE with NDDCHE in heuristic mode are conducted on the test problem. The results are shown in Figure 10b,c. For ease of comparison, the result of LRDE with NDDCHE in omniscient mode is shown in Figure 10a. It can be observed that the errors of LRDE  
Figure 8: Variation of the average error of 100 runs of different niching methods with different restart strategies for each optimum of the test function with the evolution. (**a,d,g,j**) Niching methods with constant population size. (**b,e,h,k**) Niching methods with increasing population size. (**c,f,i,l**) Niching methods with NDDCHE and constant population size. (**a–c**) kNPSO. (**d–f**) NSDE. (**g–i**) NEA2. (**j–l**) HillVallEA.  
integrated with NDDCHE in half-heuristic mode are a bit larger than those in omniscient mode, and there is no significant difference between the effects of NDDCHE in half-heuristic mode and NDDCHE in heuristic mode.  
As for the four remaining niching methods, 100 independent runs with NDDCHE in half-heuristic mode and them with NDDCHE in heuristic mode are conducted on the test problem. The results are shown in Figure 11e-l. Like LRDE, the result of the four remaining niching methods with NDDCHE in omniscient mode is shown in Figure 11a-d for ease of comparison. The results demonstrate that the decrease in the error in heuristic mode is a bit slower than that in half-heuristic mode, which is also a bit slower than that in half-heuristic mode.  
Figure 10: Heat maps of the average error of 100 runs of LRDE integrated with NDDCHE in different modes with different radii of repulsion for each optimum of the test problem. (**a**) Omniscient mode. (**b**) Half-heuristic mode. (**c**) Heuristic mode.  
Figure 9: Variation of the ratio of evaluations spent by different niching methods with different restart strategies in each BoA to the total evaluations with the evolution. (**a,d,g,i**) Niching methods with constant population size. (**b,e,h,k**) Niching methods with increasing population size. (**c,f,i,l**) Niching methods with NDDCHE and constant population size. (**a–c**) kNPSO. (**d–f**) NSDE. (**g–i**) NEA2. (**j–l**) HillVallEA.  
in omniscient mode. However, compared with the difference between whether the EC method uses NDDCHE or not, the difference between niching methods using different modes of NDDCHE is almost negligible.  
Above all, the methods in heuristic mode or half-heuristic mode basically achieve the same effect as the methods in omniscient mode on the test problem, which indicates that the effectiveness of NDDCHE can be guaranteed without prior knowledge about optima or BoAs.