# An Analysis of Differential Evolution Population Size
## 8 Summary Discussion and Implications
### Implications for Practitioners  
Based on the results and discussions presented above, the following recommendations are provided for practitioners to consider:  
1. **Focus on moderate population sizes and avoid excessively large ones:** Choose moderate population sizes. The results indicate that excessively large population sizes do not necessarily enhance performance and can even hamper it. Practitioners should be mindful of the potential drawbacks of significant increments in population size, and avoid unnecessary wastage of computational costs. Large population sizes should only be considered for highly complex problems in high-dimensional spaces, where they may be specifically required. 2. **Population size limit**: The results indicate the existence of a population size threshold beyond which performance starts to deteriorate. Practitioners are advised to pay close attention to this threshold by fine-tuning the population size and making careful, incremental adjustments. 3. **Avoid tuning parameters in isolation and recognize the impact of parameters interactions**: Based on the findings from fANOVA, practitioners should recognize the significant interactions between DE control parameters. Tuning control parameters individually can fail to capture the interactions between them, leading to a misinterpretation of performance variations that arise from these interactions. Specifically, the crossover rate plays a pivotal role affecting DE performance, especially when using small population sizes. 4. **Consider problem-specific population size adaptations**: The findings in this study indicate that different problems require different population size settings. Practitioners working with complex, multimodal, or composition problems should experiment using population sizes beyond typical recommendations to achieve optimized performance. This is specifically advisable for extremely complex problems in high-dimensional spaces. 5. **Avoid relying on rule-of-thumb guidelines for setting the population size**: The results challenge the commonly used guidelines for setting the population size in the DE algorithm. Practitioners should avoid relying solely on these rules and instead determine the most suitable parameters for their specific problem by conducting on-the-run analysis during the optimization process. It is essential to consider the unique characteristics of the problem at hand. 6. **Consider the priority of the control parameters**: The results indicate that, for certain problems, the population size holds the highest importance and thus critically affects the DE performance compared to other parameters, such as with the Weierstrass function (F6). Practitioners dealing with similarly complex landscapes should prioritize fine-tuning the population size compared to other DE parameters. 7. **Apply proper statistical testing for robust population size evaluations**: Practitioners are advised to use appropriate statistical validation techniques to ensure the accurate evaluation of an optimal population size. This is particularly crucial when testing and comparing different population sizes, where a two-step statistical analysis is necessary (such as the Friedman-Shaffer test). 8. **Leverage fANOVA to provide insights into DE control parameters**: The fANOVA approach utilized in this study offers a robust method for assessing the importance of control parameters and provides insights into their interrelationships. Practitioners working with DE can adopt similar statistical techniques to gain a deeper understanding of which parameters to prioritize and identify critical relationships between control parameters that require special attention for the specific problem at hand. 9. **Consider complementary approaches**: In related studies, different approaches have been explored to optimize DE control parameters including the population size.