## 8 Conclusions  
In this paper, we study the problems of smart grid applications, especially in HANs, which utilize a wide variety of sensor-based devices that operate using short-range communication technologies such as IEEE 802.15.4. In addition, these sensors operate using batteries. The misuse of these devices will decrease the lifetime of the network and lead to a rapid node death. For this reason, this paper uses a theoretical analysis to mitigate these problems using our proposed algorithm (MOSFP) along with three well-known algorithms in the multi-objective optimization field, namely OMOPSO, NSGA-II, and SPEA2. These algorithms have been used to optimize four network features that are used to evaluate the QoS of the network. These features consist of network end-to-end delay, end-to-end latency, network throughput, and energy efficiency. The parameter of a physical layer such as packet payload size is considered to maximize both network throughput and energy efficiency, and also to minimize both the network end-to-end delay and end-to-end latency. The results have been reported using two different ways. In a first way, the statistical analysis of one-way ANOVA (Tukey's test) between the algorithms is conducted for each objective function based on ten-time runs. In a second way, a sample of the Pareto-optimal set of each algorithm has been analyzed using the knee point and intersection point concepts.  
The mean difference from one-way ANOVA (Tukey's test) indicates that our algorithm (MOSFP) significantly outperformed SPEA2 in optimizing the proposed features while no significant mean difference is observed between MOSFP and, OMOPSO and NSGA-II. However, the overall performance of MOSFET outperformed OMOPSO, NSGA-II and SPEA2 by 3%, 6% and 51%, respectively. Furthermore, MOSFET found the best average value of energy efficiency feature compared with the other algorithms, which is very important to increase the lifetime of the network. In the second test, the Pareto front results illustrated that MOSFET algorithm, which has a good spread and approximation of the true Pareto front of the proposed network features, outperformed the other algorithms. This is very clear with the Pareto front of MOSFET in Figure 15, which obtained on 19 non-dominated solutions related to Pareto front rather than NSGA-II, and SPEA2. Furthermore, we can notice that MOSFET has the best spread and distribution of solutions related to the true Pareto front while the OMOPSO is in the second, followed by NSGA-II and SPEA2, as summarized in Figure 15. Overall, the knee point and the intersection point of all the Pareto-optimal sets for all the algorithms illustrated that the optimal value of packet payload size is equal to 45 bytes, a value which manages a trade-off between the maximization and minimization objective functions. This paper takes the smart grid as the case study as this network is affected by end-to-end delay, especially in dense cities.  
The objective functions in this paper may have their limitations. Other variables may exist in real implementation that may affect the outcome of the studies. Therefore, the value of the payload size resulting from the experiment should be tested in real environnenta in the future to ensure the reliability of the proposed method. Finally, one aspect that we would like to explore in the future is the hybridization between our algorithm (MOSFP) and other algorithms such as genetic algorithms to increase the algorithm convergence and we will use it to optimize some problems related to data aggregation [77; 78] in WSNs.  
The authors acknowledge University of Malaya for the financial support (University Malaya Research Grant (RP036 (A, B, C)-15 AET)) and facilitating in carrying out the work.  
The concept, design and evaluation of MOSFP is done by [PERSON], [PERSON] and [PERSON] structure the paper and device experiments with selected benchmarking; [PERSON] and [PERSON] contribute in the statistical evaluation.  
The authors declare no conflict of interest.