## 5 Computational Experiments and Discussion  
In this section, computational experiments are performed to illustrate the performance of the proposed hybrid HS-SA compared with other approaches in the literature. The proposed algorithm is coded in MATLAB software R2017b on a laptop computer with 1.60 GHz Intel(r) Core(tm) i5-4200U CPU with 8 GB of RAM. The parameters configuration of the proposed algorithm is provided in Table 1. The test problem instances are three popular benchmark datasets of Perl, Gaskell, and Christofides with additional simulated data of returned products and production rate. The additional data were generated randomly by using a uniform distribution. The production rate is set to be greater than the total demand and returns, \(P>\sum\limits_{j\in J}D_{j}+r_{j}+s_{j}\) while the returned products, \(R_{j}\) are generated by the uniform distribution of \(R_{j}\sim U\big{(}0,D_{j}\big{)}\). We set 70% of the returned products as the non-defects (\(r_{j}\)) items while the remaining are the defect items (\(s_{j}\)). The characteristics of the dataset are given in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **SHS** & **PHS** & **HS-SA** \\ \hline HMS & 300 & 300 & 300 \\ HMCR & 0.85 & \([0.7,0.95]\) & \([0.7,0.95]\) \\ PAR & 0.55 & \([0.3,0.9]\) & \([0.3,0.9]\) \\ _Maxlt_ & 10,000 & 5000 & 5000 \\ \(t\) & 500 & 100 & 100 \\ \(T_{0}\) & – & – & 30 \\ \(\alpha\) & – & – & 0.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters Setting for SHS, PHS, and HS-SA. To solve the LIRP problem, the location and allocation of the depots and customers are solved first. In the location-allocation problem, each of the customers is initially assigned to the nearest depots based on the Euclidean distance formulation. The customers will be moved around to the possible depots during the process of improvisation. The vehicle capacity limit constraint has been relaxed to minimize the number of open depots and it is assumed that only one vehicle is being used at each depot. However, the depot capacity limit should not be violated during the process. Then, the allocation of customers at each depot needs to be sequenced and divided into vehicles according to the vehicle capacity limit. This process is performed among the open depots only. The process of local optimization is performed within the open depots. Both depot capacity limits and vehicle capacity limits should not be violated. Finally, the inventory part is included during the process of minimizing the cost. Since there is no study on the LIRP that utilizes the EPQ model for defect and non-defect items in reverse logistics from the literature, in order to validate the performance of the proposed hybrid HS-SA algorithm, the LRP will be solved first and compared with other heuristics and metaheuristics found in the literature that used the same benchmark datasets. Tables 3-5 present the comparative results of the three benchmark datasets on the proposed hybrid HS-SA with the heuristic method (HR) of [8], simulated annealing in [9] (SA-W) and [10] (SA-Z), hybrid tabu search and ant colony (TACO) from [11], particle swarm optimization (PSO) with different variants of particle swarm optimization which are: standard PSO, PSO with MPNS-GRASP (PMG), PSO with MPNS-GRASP and ENS (PMGE) and hybrid PSO (HLRP) in [12] and honey bee mating optimization (HBMO) in [13]. A standard HS (SHS) and the proposed HS (PHS) from [7] are also included for comparison in all experiments. For each problem instances, the proposed algorithm as well as SHS and PHS are performed for 10 independent runs. In each table, note that the numerical results of the selected algorithms are extracted from the original papers found in the literature and the best result of each problem instances is highlighted in bold. Figures 3-5 illustrate the results of Tables 3-5 in a bar chart respectively.