# Two-Stage Genetic Algorithm for Optimization Logistics Network for Groupage Delivery
## 3 Materials and Methods
### Vehicle Routing Problem
\begin{table}
\begin{tabular}{p{42.7 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Reference** & **Focus** & **Applied Approach** & **Results** & **Limitations** \\ \hline [PERSON] et al. [13] & Location–inventory routing model for perishable products. & GA with novel chromosome representation and local search heuristics. & Achieved high-quality solutions in reasonable time, validated through analysis. & Limited to perishable products; further scalability not discussed. \\ \hline [PERSON] et al. [14] & Transportation–location routing problem (TLRP) with environmental and social concerns. & Non-dominated Sorting GA (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO). & MOPSO outperformed NSGA-II in minimizing costs, fuel consumption, and emissions. & Focused on sustainability; computational time for large-scale networks not discussed. \\ \hline [PERSON] et al. [15] & Multinode facility location routing problem with hierarchical logistics. & GA optimizing facility location problem (FLP) and vehicle routing problem (VRP) with bidirectional routing. & Reduced costs by 6–8\% compared with traditional logistics systems, validated through a case study. & Limited dynamic considerations for real-time operations. \\ \hline [PERSON] et al. [16] & Two-stage location-routing model for cold-chain logistics. & Hybrid GA to minimize costs and accommodate varying vehicle capacities. & Confirmed feasibility and cost reduction compared with single-stage routing models. & Limited to cold-chain logistics; real-world application data not detailed. \\ \hline [PERSON] et al. [17] & Integrated location, routing, and inventory model for sustainable supply chains. & Two-phase approach using hybrid metaheuristics with sustainability considerations. & Parallel hybridization yielded superior performance; decentralization improved the sustainability. & Limited focus on perishables; broader applicability not addressed. \\ \hline [PERSON] et al. [18] & Optimization of mobile charging vehicles (MCVs) for battery electric vehicles (EVs). & Mixed-integer linear program using hybrid metaheuristics with sustainability considerations. & Demonstrated efficiency improvements with microsoft energy capacity or charging rates. & Applicability depends on technological advancements in BEVs and infrastructure. \\ \hline [PERSON] [19] & Location routing problem with simultaneous pickup and delivery (LRPSPD). & Hyper-heuristic approach (ILS-HH) with selection mechanisms and activation strategies. & Outperformed classical methods; FRRMAB-TS identified as the most effective method. & Limited evaluation on real-world data; focused primarily on computational efficiency. \\ \hline [PERSON] et al. [20] & Facility location and VRP for healthcare logistics in the Netherlands. & Branch-and-bound algorithm and fast hybrid heuristic. & Heuristic outperformed commercial solvers; robust performance validated on real-world data. & Limited to healthcare logistics; scalability for larger networks not discussed. \\ \hline [PERSON] et al. [21] & Multi-objective hazardous waste management with stochastic uncertainty. & Stochastic mixed-integer nonlinear programming (MINLP) with simheuristic (NSGA-II + Monte Carlo simulation). & Effectively solved stochastic combinatorial problems with high-quality solutions in reasonable time. & Limited application beyond hazardous waste; computational complexity for larger datasets. \\ \hline [PERSON] et al. [22] & Green routing problem with depots, time windows, and vehicle heterogeneity. & Combined GA and simulated annealing (SA) algorithm. & Efficient compared with exact solvers (GAMS software); validated algorithm performance. & Limited to green VRP; did not address large-scale industrial networks comprehensively. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of related work. focuses on finding a single optimal route [24], while the VRP involves planning several routes, each respecting vehicle capacity constraints.