# Neuroevolution for Parameter Adaptation in Differential Evolution
## 3 Results
In the 10\(D\) case, there are from 2 to 4 losses, although the number of wins is larger, and in the 20\(D\) case, there are almost always 3 wins and 1 loss. This means that these algorithms behave differently on different functions, and the designed parameter adaptation techniques have other principles compared to successively adaptation. In particular, losses on 10\(D\) functions were observed on F6 (Hybrid Function 1, including Bent Cigar, HGBat and Rastrigin's functions), F8, F10 (Composition Function 2, including Rotated Schwefel's, Rotated Rastrigin's and HGBat functions) and F12 (Composition Function 4, including HGBat, Rastrigin's, Modified Schwefel's, Bent Cigar, High Conditioned Elliptic and Expanded Schaffer's functions). Here, the best parameter adaptation technique was designed at run 29: It performs well against both NL-SHADE-RSP\({}_{s}\) and NL-SHADE-RSP. The results in Table 2 seem promising, but it should be taken into account that the HA-NEAT-DBM algorithm used these functions to train and select best solutions here. Thus, a certain overfitting may have occurred here. The results in the 20\(D\) case could be considered as testing, but even though the dimension of the problems is different, the functions have the same structure and similar landscape. To test the efficiency of parameter adaptation the previous year's benchmark set, CEC 2021 was considered. In CEC 2021, there are eight different benchmarks, which combine different function alternations, such as bias, shift and rotation [21]. Table 3 contains the aggregated comparison on all eight benchmarks. Note that in the case of CEC 2021, the statistical tests did not use information about convergence speed, according to the competition rules. The numbers in Table 3 are the number of wins, ties and losses over all 8 benchmarks, each containing 10 test functions. Analyzing the results of CEC 2021, the difference between different automatically discovered heuristics could be clearly seen. For example, in some cases, the heuristics are always equal or worse than the NL-SHADE-RSP\({}_{s}\) parameter adaptation, and in other cases, the heuristics are usually better. For example, runs 2, 22, 28, 36, 42 and 49 could be considered as relatively successful as they have comparable or better performance on both 10\(D\) and 20\(D\). However, when compared to the original NL-SHADE-RSP, the results of the ANNs designed by HA-NEAT-DBM are relatively poor: Even run 49, which is one of the most successful, has only 13 wins on 10\(D\) and 43 losses. Such a difference in performance is probably due to the fact that NL-SHADE-RSP was specifically designed for the CEC 2021 benchmark, and has special parameter adaptation mechanisms that allow it to reach high a performance level. The experiments on the CEC 2021 benchmark also allow the efficiency of the designed heuristics to be determined in solving biased, shifted and rotated problems. To perform the comparison, the baseline NL-SHADE-RSP\({}_{s}\) was compared to the heuristic from run 49 on different benchmarks, and the results are shown in Table 4.  
The results of statistical tests in Table 4 show that in the basic scenario, without bias, shift and rotation of functions, the heuristic from run 49 performs quite well in the 10\(D\) and 20\(D\) cases; however, if the functions are shifted, the results are worse. The rotation procedure, which significantly changes the landscape, does not influence the performance of the heuristic compared to NL-SHADE-RSP\({}_{s}\). Moreover, in the 20\(D\) case, it appears to be better for the Rotation and Bias benchmarks on 4 functions out of 10. In particular, here the improvements were achieved on F2 (Shifted and Rotated Schwefel's function), F3 (Shifted and Rotated Lunacek bi-Rastrigin function), F6 (Hybrid Function 2, including Expanded Schaffer, HGBat, Rosenbrock's and Modified Schwefel's functions) and F7 (Hybrid Function 3, including Expanded Schaffer, HGBat, Rosenbrock's, Modified Schwefel's and High Conditioned Elliptic functions).