## 5 Conclusions  
With the deepening of the research on resource reuse, product recycling has attracted the attention of enterprises and academic researchers. In the research on product recycling, the research on reverse logistics networks, especially the location of reverse logistics facilities, has always been the focus. In this paper, energy consumption was taken as a starting point, the carbon emissions and benefits in the reverse logistics network were taken as the functional objectives for modeling and optimization, and an improved gravity \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Facilities Capacity**} & **Carbon Emission** & **Benefit** & **Multi-Target Carbon** & **Multi-Objective Benefit** \\  & **Target (kg)** & **Target (CNY)** & **Emissions (Average/kg)** & **(Average/Yuan)** \\ \hline
60\% & 1,292,562,212.6 & 203,526,880.0 & 1,978,225,539 & 202,127,278.6 \\
80\% & 1,637,062,212.6 & 205,222,804.0 & 2,505,471,881 & 203,811,540.2 \\
100\% & 2,814,143,312.6 & 206,683,179.8 & 4,306,957,233 & 205,261,872.6 \\
120\% & 2,242,048,412.6 & 206,799,041.6 & 3,431,384,103 & 205,376,938.4 \\
140\% & 2,274,738,212.6 & 20,703,8051.8 & 3,481,414,807 & 205,614,305 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Results of different facility capacities. optimization algorithm was used to solve the reverse logistics facility location model, arriving at an excellent set of location schemes. Considering the influencing factors of network facilities construction, this paper evaluated the alternatives with multiple indexes, and made the final choice of facilities location. The main conclusions can be summarized as follows:  
(1) A double objective function optimization model of reverse logistics facility location was constructed. The three-level recycling facilities of recycling center, classification center and processing center were combined with the original logistics system of manufacturers, suppliers and consumers to form a closed-loop logistics system. In order to study the facility location problem of three-level reverse logistics, the capacity of recycling center, classification center, processing center and the transportation volume between different recycling facilities were taken as constraints, and the two objective functions of low-carbon and maximum revenue were used to optimize the location scheme of logistics facilities. The carbon emission target was divided into two parts: transportation carbon emission and treatment carbon emission. According to the different stages of transportation and treatment, the carbon emission in the process of product recovery was quantified, and the income was divided into four parts according to the different stages of recovery, and the total recovery income was calculated, respectively. (2) The improved universal gravitation algorithm was used to solve the location model of reverse logistics facilities, and the Pareto set of location scheme was obtained. By combining the optimization characteristics of classical particle swarm optimization algorithm and universal gravitation algorithm, the two algorithms complemented each other, and a hybrid particle swarm optimization algorithm with better optimization performance was obtained. Taking the mobile phone recycling in Jilin Province as an example, it was proved that the hybrid algorithm has excellent convergence performance, meets the needs of solving the facility location model, and obtains the optimal solution set satisfying the double objectives. In addition, the accuracy and stability of the algorithm were verified by different recovery rate and facility capacity. In future research, our work will focus on the following: (1) applying additional effort to real-time advanced methods for selecting Pareto solutions [42; 43; 44] and (2) after noting that the raw data have uncertain and imprecise features, integrating an advanced optimization method in the model [45; 46]. Conceptualization, L.C. and H.Z. ; methodology, M.Z. and Z.Y. ; validation, G.X., G.T. and T.L. ; investigation, D.Y.