## 5 Discussion and Conclusions  
This research employed metaheuristic algorithms, namely the PSO and DE algorithms, to solve the single-objective VRP for optimized routing solutions. The objective was to determine a solution with the lowest travel distance. The study used actual operational data from two delivery vehicles of the Chiang Rai post office over a period of 50 days. The data included geographic coordinates of the customer locations where those vehicles delivered parcels, which were then transformed into distance matrices for use by the optimization algorithms. For each delivery day, the algorithms tried to search and assign new routes to those two vehicles such that the total travel distance was minimized. The routing performances from the PSO and DE algorithms, as well as those from actual operations, were compared. The experimental results showed that both metaheuristic algorithms were far superior to the real delivery operations of the post office in all 50 days of the experiment. However, DE clearly outperformed PSO by providing outstanding solution quality for all instances. This result was mainly due to the different evolution mechanisms of DE and PSO. A PSO swarm has a high tendency to cluster rapidly and becomes stagnant, since the movement of a swarm is highly influenced by the global best solution. In addition, the diversification of DE is better than PSO, because the best solution in the population does not exert any influence on other solutions in the population. A new solution in DE would be selected only if it had better fitness, and thus the average fitness of the population would be equal or better from iteration to iteration. It is important to note that the results obtained from this study were based on the delivery constraints of the Chiang Rai post office. However, for the operations of other post offices, other constraints such as vehicle capacity, a customer's time window and the delivery time horizon could be taken into consideration. In such cases, the problem must be remodeled, and new solutions will be obtained under those circumstances. Another essential factor was the duration for running one optimization cycle in order to obtain the optimized solution. For both the DE and PSO algorithms, the average duration was approximately six minutes. Combining the decent results and acceptable runtime duration, the methods used in this study have the potential to be employed in real post office operations. Additionally, even though there were two vehicles in this study, the proposed algorithms can also be applied to large cities in which the post office operates several delivery vehicles. In essence, the methods proposed in this study could drastically help reduce the delivery cost and time for postman delivery operations. Additionally, the vehicle routing optimization process (with about 100 customer locations) only takes minutes rather than hours, which is practical in the actual post office work environment where all parcels have to be processed and dispatched quickly. There are some challenges to be considered if these methods are to be used in actual delivery operations. First, the post office operators need to determine a quick approach to convert customer addresses into geographic coordinates, which should be done systematically and automatically. Second, the duration to run an optimization cycle is proportional to the number of addresses and delivery vehicles. Therefore, the optimization parameters such as the population sizes and iterations should be well adjusted according to those numbers. Thus, the operators could utilize machine learning, artificial intelligence and image processing methods to quickly transform those customer addresses into definite GPS locations. They should also give enough lead time to account for the unexpected increase in processing time before all deliveries can start. In addition, the proposed PSO and DE use deterministic data, in which the customers and distance matrices are known in advance, and the routing is determined using these data.