# Two-Stage Genetic Algorithm for Optimization Logistics Network for Groupage Delivery
## 4 Results  
The efficacy of the developed algorithm was assessed by applying it to a real-world logistics scenario that involved the delivery of goods to different cities. This evaluation was facilitated by utilizing a tariff matrix that outlined the delivery costs. This analysis focused on a selected group of cities and the corresponding volumes of cargo transported (measured in tons) from a central warehouse. To assess the performance of the algorithm, the following criteria was considered:  
1. Total delivery cost: the sum of the costs for delivering cargo across all routes (linehaul and last mile). 2. Utilization efficiency: the ratio of delivered cargo volume to the nominal capacity of the truck body. The optimization process was conducted in two stages. First, the algorithm determined the optimal locations for regional hubs for cross-docking. Then, it optimized the delivery route to the final destinations. This approach ensured that both the total route distance and the costs of last-mile delivery were minimized. A comparative analysis was performed between the algorithmic solution and the expert-proposed solutions provided by the logistics company NOYTECH using several criteria to guide the expert's decisions. The expert prioritized minimizing the total delivery cost while ensuring the optimal delivery flow between cities. Additionally, the efficient use of terminals was a key focus, with two target utilization rates considered (90% and 95%) to balance the cost and terminal capacity. The expert solution involved selecting terminal locations in eight cities: Tyumen, Nizhny Novgorod, Kazan, Ufa, Chelyabinsk, Omsk, Novosibirsk, and Krasnoyarsk. These selections were based on geographic and logistical considerations to minimize the transportation costs. Additionally, an expert provided estimated linehaul utilization rates for the delivery routes:  
Figure 7: Mechanisms of categorical mutations. * Moscow-Nizhny Novgorod-Kazan: 74%. * Moscow-Ufa-Chelyabinsk: 75%. * Moscow-Omsk-Novosibirsk-Krasnoyarsk: 98%. The solution's total budget was calculated to be RUB 601,516, which factored in all operational costs. The GA used in the optimization was configured with several critical parameters. The population size was set to 100 individuals, with a mutation rate of 0.02 and a crossover rate of 0.8. The number of generations was fixed at 200. These parameters were chosen to balance the exploration and exploitation in the solution space, ensuring efficient convergence to an optimal solution. The case study addressed the logistics problem of group cargo delivery. Each value in Table 2 represents the tonnage of delivered cargo between the corresponding pairs of cities. This cargo distribution and the corresponding optimized delivery routes were used to compare the performance of the algorithm against the expert solution, with a focus on cost minimization and terminal utilization. The first GA-based solution utilized terminals in six cities (Figure 8a): Kemerovo, Kirov, Krasnoyarsk, Nizhny Novgorod, Perm, and Chelyabinsk. The linehaul routes and their respective utilization rates were as follows:  
* Moscow-Kirov-Perm-Kemerovo-Krasnoyarsk: 90%. * Moscow-Chelyabinsk: 62%. * Moscow-Nizhny Novgorod: 73%. The total budget for this solution was RUB 577,331, which resulted in savings of RUB 24,185, or 4.02%. The second GA-based solution used terminals in seven cities (Figure 8b): Kazan, Kemerovo, Krasnoyarsk, Nizhny Novgorod, Perm, Tyumen, and Ufa. The linehaul routes and utilization rates for this solution were as follows:  
* Moscow-Kazan-Ufa: 95%. * Moscow-Perm-Kemerovo-Krasnoyarsk: 88%. * Moscow-Nizhny Novgorod: 37%. * Moscow-Tyumen: 94%. The total budget was RUB 553,206, which yielded the highest savings of RUB 48,310, or 8.03%.