## 5 Conclusions  
The present paper addresses the optimal scheduling and management of EHs in day-ahead energy markets for participation with EGHNs to maximize energy profit using the new IFLA algorithm and satisfying the operating and hub constraints. The research findings are listed below:  
* The results showed that the IFLA, FLA, PSO, and MRFO methods obtained energy profits of $472.13, $435.34, $442.17, and $467.62, respectively, in the day-ahead market, which indicates the better performance of the proposed framework based on IFLA in achieving more energy profit. * The system's profit is significantly affected by the price of electricity, natural gas, and heating energy. The profit of the heating market of the day-ahead is negative in the hours of electric energy storage and positive in the rest of the hours. Furthermore, the profit of the day-ahead gas market in the day-ahead heating market is negative compared to the day-ahead gas. * With a 20% increase in load demand compared to the base state, the profit decreases from $472.13 to $236.89, and with a 20% decrease in load demand, it increases to $763.46. Therefore, the increase (decrease) in load demand causes a decrease (increase) in the profitability of the EH.
* With the increase (decrease) in the FOR of renewable energy sources and CHP, the system profit decreases (increases). The system profit in the base state (FOR = 0%) decreases from $472.13 to $379.46 for FOR = 5%, and also declines to $297.09 for FOR = 10%. \begin{table}
\begin{tabular}{c c} \hline
**FOR** & **Profit (\$)** \\ \hline
0\% & 472.13 \\
1\% & 445.43 \\
2\% & 428.92 \\
3\% & 412.43 \\
4\% & 395.94 \\
5\% & 379.46 \\
6\% & 362.98 \\
7\% & 346.51 \\
8\% & 330.03 \\
9\% & 313.56 \\
10\% & 297.09 \\ \hline \end{tabular}
\end{table} 
Table 6: Energy profit considering the FOR changes. **Author Contributions:** Conceptualization, M.A., A.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A. ; methodology, M.A. and A.A.; software, M.A. and A.S.A. ; validation, M.A, Y.Q. and A.A.; formal analysis, M.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A. ; investigation, M.A., A.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A. ; resources, M.A., A.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A. ; data curation, M.A., A.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A. ; writing--original draft preparation, A.S.A. and A.A.; writing--review and editing, M.A., A.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A. ; visualization, M.A., A.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A. ; supervision, A.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A. ; project administration, M.A., A.A., Y.Q., A.S.A., M.Z., A.B.A. and M.G.B.A. ; All authors have read and agreed to the published version of the manuscript. **Funding:** This research supported by the deputyship for research and innovation, ministry of education in Saudi Arabia under project number (IFP-2022-35). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Data will be available on request. **Acknowledgments:** The authors extend their appreciation to the deputyship for research and innovation, ministry of education in Saudi Arabia for funding this research work through the project number (IFP-2022-35). **Conflicts of Interest:** The authors declare no conflict of interest. **Nomenclature**