## 5 Conclusions  
A Novel metaheuristic algorithm inspired by Egyptian stray dogs' behaviors is introduced in this paper to solve the OPF problem. Four cases are studied including minimizing each fuel cost, power loss and voltage drop as a single objective function and minimizing all of them as a multi-objective function.  
ESDO demonstrates faster convergence, and a superior exploration-exploitation balance compared to the other algorithms, making it highly effective in dynamic and complex environments. Four objective functions are evaluated in this paper to show the performance of the ESDO technique in solving different OPF functions, summarized as follows:  
* Case 1: From the point of view of fuel cost minimization, the lowest fuel cost corresponds to the ESDO in comparison with PSO, MVO, and GOA. That is why ESDO is more efficient than other algorithms in the context of operating cost reduction.
* Case 2: ESDO's Alpha Dog and Beta Dog strategy shows a minimum power loss in comparison with the other algorithms, which significantly outperforms other algorithms on this point and confirms ESDO's capability to maintain low power loss for system stability.
* Case 3: In voltage drop minimization, ESDO gave excellent voltage stability, presenting the lowest voltage drop compared to all the algorithms tested, proving its strength in dealing with voltage-related constraints.
* Case 4: Convergence analysis shows that ESDO reduced the multi-objective function values to their minimum possible values more consistently than others and outperformed its competitors with reference to speed and final solution quality.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **Inspiration** & **Convergence** & **Exploration–Exploitation Balance** & **Computational Complexity** & **Susceptibility to Local Optima** \\ \hline
**PSO** & Bird flocking/Fish schooling & Fast, but may stagnate & Good, but weak in later stages & Low & High \\ \hline
**MVO** & Multiverse theory & Moderate & Strong balance & Medium & Low \\ \hline
**GOA** & Grasshopper swarming behavior & Moderate, but slow & Strong global exploration & Medium & Moderate \\ \hline
**HHO** & Harris hawks hunting strategy & Fast & Adaptive and dynamic & Medium & Low \\ \hline
**HO** & Hippopotamus water–land & Good & Strong adaptability & Medium & Moderate \\ \hline
**ESDO** & Egyptian stray dogs’ behavior & Fast & Excellent dynamic balance & Medium & Low \\ \hline \hline \end{tabular}
\end{table}
Table 12: Algorithms key characteristics comparison.  
To summarize, these results clearly indicate that ESDO is a highly effective optimization technique for OPF, outperforming both classical and modern algorithms in terms of efficiency, accuracy, and robustness across various operational scenarios.  
Conceptualization, M.A. and H.Y.D.; methodology, M.A. and M.H.E.; software, M.A. and M.H.E.; validation, M.A., H.Y.D., M.F.M. and M.H.E.; formal analysis, H.Y.D. and M.H.E.; investigation, M.H.E. and H.Y.D.; resources, M.H.E., M.A., M.F.M. and H.Y.D.; writing--original draft preparation, M.H.E., M.A. and H.Y.D.; writing--review and editing, M.A., M.F.M. and H.Y.D.; supervision, M.A., H.Y.D. and M.F.M. All authors have read and agreed to the published version of the manuscript.  
This research did not receive any external funding.  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The authors declare no conflicts of interest.