# Neuroevolution for Parameter Adaptation in Differential Evolution
## 3 Results  
The computational experiments were performed to evaluate the ability of the proposed HA-NEAT-DBM to design parameter adaptation heuristics. For this purpose, the algorithm was trained on CEC 2022 benchmark functions and then evaluated. Such an approach implements offline parameter adaptation [19; 62], as opposed to online adaptation [63], where parameters are tuned during the optimization process. Training a single ANN with NEAT requires significant computational effort, and in the case of the current study, it is multiplied by the goal function complexity, which requires 10 runs of the NL-SHADE-RSP\({}_{s}\) algorithm on 12 test functions from the CEC 2022 competition [20]. Therefore, to reduce calculation time, HA-NEAT-DBM and NL-SHADE-RSP\({}_{s}\) were both implemented in C++11, compiled with GCC and ran on the OpenMPI-powered cluster of seven AMD Ryzen 1700 processors with eight cores each. There were 50 independent runs of HA-NEAT-DBM performed, each on a separate core, the computational resource was set to 10000 HA-NEAT-DBM evaluations and the time required to perform the training was around 16 days running 24/7. Testing the algorithms, however, required much less computation, as only the best solutions of each run were analyzed. The best solution was determined by the [PERSON] ranking of the results at the last generation, as described in the previous section. The post-processing of results, statistical tests and graphs were performed with Python 3.8 and matplotlib. The main parameters of NL-SHADE-RSP\({}_{s}\) are given in Algorithm 2. The first set of efficiency comparison experiments was performed on the CEC 2022 benchmark functions. The designed parameter adaptation heuristics, presented in the form of networks, were compared with the baseline NL-SHADE-RSP\({}_{s}\) and the original NL-SHADE-RSP, which is the winner of the previous year's competition CEC 2021 for biased, shifted and rotated functions. To compare the efficiency, all the ANNs were tested on all 12 functions, 30 independent runs and 10\(D\) and 20\(D\) cases. For every function, the Mann-Whitney statistical test was performed, with significance level \(p=0.01\), normal approximation and tie-breaking, i.e., runs with equal results were assigned averaged ranks, and the standard score \(Z\) value was calculated. In Table 2, the aggregated results are shown, i.e., the number of wins (+), ties (=) and losses (\(-\)) of one of the 50 heuristic compared to NL-SHADE-RSP\({}_{s}\) or NL-SHADE-RSP. The comparison of statistical tests results in Table 2 demonstrates that the neuroevolutionary parameter adaptation performs better than the standard SHADE parameter adaptation of the simplified NL-SHADE-RSP\({}_{s}\) algorithm in both 10\(D\) and 20\(D\) scenarios. It should be mentioned, however, that the heuristics are usually better on the same functions: For example, in the 20\(D\) case, almost all automatically designed parameter adaptation techniques are better on 3 functions and comparable on 9. These significant improvements were observed for F1 (Shifted and full Rotated Zakharov Function), F3 (Shifted and full Rotated Expanded Schaffer's 6 Function) and F5 (Shifted and full Rotated Levy Function), and the improvements were in terms of the number of function evaluations required to reach the optimum. On all other functions, the results were equal or comparable. As for the 10\(D\) scenario, the designed heuristics were better for most of the functions, except F4 (Shifted and full Rotated Non-Continuous Rastrigin's Function) and F8 (Hybrid Function 3, including Katsuura, HappyCat, Griewank's plus Rosenbrock's, Modified Schwefel's and Ackley's). The comparison with the original NL-SHADE-RSP, which uses specific crossover rate adaptation, adaptive archive probabilities and exponential crossover, shows that the designed heuristics for parameter adaptation are still capable of competing with this approach, but the results are worse in general.