Analysis of distribution path optimization algorithm based on big data technology

3.1 Distribution path optimization problem study

The distribution path problem was first proposed by Dantzig and Ramser in 1959. Since its introduction, the problem has received a lot of attention from experts in operations research, computer science, and network optimization. Its research results are now widely used in many fields of logistics management. As the core optimization problem of the logistics distribution process, the vehicle path problem refers to the planning of vehicles' driving routes and service stations to achieve the established logistics distribution goals under the premise of satisfying certain constraints (Barenji et al., 2019). However, with the diversification of customer needs, the distribution path problem has developed to date with increasingly complex models and more and more optimization objectives and constraints. For example, while satisfying the amount of customer demand and the delivery time specified by the customer, considering the carrying capacity of the vehicle and the traffic road condition restrictions, etc., to achieve the shortest transportation distance, the least time, the lowest cost, and other distribution goals.

Long years later and decades of research development, a large number of research results have been achieved in the vehicle path problem. The existing vehicle path problems can be classified according to different classification criteria, as shown in Fig. 1.

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Fig. 1

Distribution path problem classification.

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Under the constraints of the farthest distribution distance and load capacity of the vehicle, the distribution center develops a reasonable vehicle distribution plan, and the distribution staff carries out the distribution in an orderly manner according to the distribution plan (Sun et al., 2019). The model of the standard vehicle path optimization problem is represented mathematically as follows.

In this case, when i = 0, it is the distribution center. When i = 1,2,…, N, it denotes the customer point. $C_{\mathit{ij}}$ denotes the transportation cost from customer i to customer j, and $Q_k$ denotes the maximum load capacity of vehicle k.

Objective equation (3) indicates the lowest total cost of the logistics system; equation (4) indicates that the weight of each vehicle loaded with materials cannot exceed the maximum vehicle capacity; equation (5) ensures that there is only one vehicle for distribution at each customer point, and a total of K vehicles complete the distribution task; equation (6) ensure that the vehicles finally return to the departure point and the customer's distribution requirements are satisfied.

3.2 Research on ant colony algorithm based on big data technology

The colony can always find the optimal path from the anthill to the food source, which is more intelligent than a single ant. For each ant in the whole colony when it starts to look for food, it randomly chooses the path and releases pheromones in the path to look for food, this pheromone will keep volatilizing over time, for the path closer to the food, more ants may pass through this path in a certain time, thus for the path closer to food, more ants may pass this path in a certain time, thus forming a positive feedback parallel mechanism. On this basis, the logistics distribution path is established and the multi-objective function is optimized, mainly including weight index, time efficiency index, customer importance index, time window index, and total path index. The artificial ants in the ant colony algorithm will add a heuristic factor to this path and bring in a “visual” effect. The path length is added as an influencing factor for the path selection so that the ants can find the optimal path faster, as shown in Fig. 2. Ant colony algorithm for e-commerce logistics distribution path optimization has the following advantages.

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Fig. 2

Schematic diagram of path optimization.

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4.1 Experimental design

First, the logistics end distribution vehicle path optimization problem is used as a model to build the urban spatial network. In the urban spatial network logistics center is represented by the primary city point, the distribution center is represented by the secondary city point, and the end-customer point is represented by the tertiary point. Then, the urban spatial network is used as the basis to build the operation network containing logistics transportation, warehousing, and distribution processes. Finally, the parameters are initialized according to the scale of the problem under study. The working principle of logistics simulation is as follows: first, the goods start from the starting point (logistics center), then, they are transported to the nearest secondary point (logistics distribution center), and finally, they are transported to each tertiary point (end-customer point), and the whole logistics system distribution ends. Among them, the specific end-customer point which is distributed by the logistics distribution center is assigned according to the clustering idea.

In the process of parameter configuration of the logistics system, different parameters can be set for the experimental simulation according to the different needs of the actual problem. In the logistics simulation, Fig. 3 shows the customer location distribution (Sulova, 2021). From them, “x” indicates the logistics center, “y” indicates the logistics distribution center, and the points with numbers indicate the customer points, with 1–100 to distinguish the different customer points. The solid blue line indicates the distribution service between the logistics center and the distribution center. The red solid line is the line from one logistics center to another logistics center, which means that the logistics center and the logistics center are operational. There is no line between the logistics center and the end-customer point, which means it is not operational. The order quantity of one, two, or three points is configured in pieces, and the mass of each piece is generated randomly from 1 kg to 10 kg. The order quantity is converted to mass for city capacity calculation, which indicates the capacity of transporting goods between cities. When the city capacity is not able to transport all the goods, some of the goods will be stored in the logistics warehouse at random from all the goods, waiting for the next transport. Some parameters of terminal distribution: the rated load of the vehicle, the farthest driving distance of the vehicle, the running speed of the vehicle, the service time of the vehicle, etc. are the constraints of vehicle scheduling, which are configured according to the actual needs in the process of system initialization. The geographic coordinates of the logistics center, logistics distribution center, and terminal customer points are randomly generated between 0 and 1, which is more general in the process of studying the actual problem. In the column of system, the operation is some functional buttons of the logistics simulation model, which can terminate the system operation in time when the logistics system is abnormal.

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Fig. 3

Customer location distribution map.

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In the process of e-commerce logistics distribution path optimization, the path (time) optimization principle is upheld, and the slope and congestion factors in the distribution path are taken into consideration because they will affect the progress of the whole distribution process, this paper mainly adopts the way of turning flat road to consider all kinds of influencing factors, to improve the fineness of the model calculation process and improve the path optimization effect, so that the whole logistics end distribution can deliver the goods in the consumer's expected or the courier company's expected time to deliver, and improve the user's satisfaction. In the travel business problem, the distance between distribution nodes is expressed using the Euclidean distance. Since the route of logistics end distribution is not simply a line between two points, but winding, the distance between two distribution points cannot be calculated simply by the absolute distance between coordinate points, and in the study of e-commerce, logistics end distribution, the coordinates of each distribution point in the two-dimensional plane only indicate the position between each distribution point The distance between distribution nodes in the process of logistics end distribution path optimization is expressed by the length of the route between distribution points(Mohammed et al., 2020). Because of the consideration of the influence factors in the distribution process, in the process of path optimization, the specific influence factors to flat road formula can be used to achieve the distribution process of the slope length to flat road length. And the transformed flat road length is added to the expectation factor in the ant colony optimized path process. Fig. 4 shows the optimal path analysis after optimization roar.

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Fig. 4

Algorithm optimization path.

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The scheduling arrangement module is to make reasonable arrangements for the implementation of specific distribution tasks based on the route planning results generated by the route planning module and consists of two functions: route arrangement and vehicle arrangement (Zhang et al., 2021). The route arrangement function generates a route list and identifies the sub route information formed after the route optimization with the route list number for the vehicle arrangement function to match the information of drivers and vehicles responsible for the implementation of logistics distribution tasks. The relationship between route arrangement and other module interfaces is: route arrangement realizes the data acquisition of path optimization results through the interface, completes the identification of the route and the route order, loading volume and distance display of a single-vehicle at a time, generates the route list information for vehicle arrangement class operation, and the status of customer orders involved in planning the formation of distribution routes is changed from pending to pending distribution (Kuo and Chen, 2020). Vehicle arrangement function generates dispatching order, implements the distribution tasks associated with the route list to specific distribution vehicles and personnel, generates dispatching plan, and can provide logistics distribution/pickup service to customer orders that have formed route list through route planning. The vehicle arrangement function calls customer orders, route orders, and vehicle information to carry out the arrangement of vehicle personnel, the association of orders and distribution orders, the results of vehicle arrangement are used to update the location of customer orders, generate dispatching tables for vehicle departure arrangements, and associate route tables with dispatching tables.

4.2 Analysis of results

To verify the feasibility of the algorithm and the validity of the model, the proposed model is solved using the ant colony algorithm and compared using the NSGA-II, and MOEA/D algorithms. To understand the distribution of the solution sets in the target space by NSGA-II, and MOEA/D, the Pareto fronts of the four algorithms on the VRPTW multi-objective model are shown in Fig. 5. From the Pareto frontier comparison, it can be seen that the solution set obtained by the MOEA/D-IRG algorithm is the closest to the Pareto frontier, followed by the ant colony algorithm and MOEA/D, while NSGA-II is the worst. In terms of the solution set distributivity, the solution sets obtained by the MOEA/D-IRG algorithm are more uniform compared to the three compared algorithms. The simulation experimental results show that the solution set obtained by the MOEA/D-IRG algorithm is better in terms of convergence and diversity when considering the shortest distribution distance and the least distribution time as the objectives, indicating that the decision variable interaction identification strategy can effectively identify the potential structures among decision variables and form subcomponents, reduce the consumption of the number of fitness evaluations in the grouping process of decision variables, and improve the convergence efficiency of the algorithm. S3-CMA-ES searches for solutions through a group of sub-populations and uses CMA-ES to optimize each sub-population to promote population convergence, but sacrifices the diversity of the algorithm to some extent. the decomposition strategy of MOEA/D transforms the multi-objective problem into a set of single-objective problems to solve, and the decomposition strategy can effectively maintain the diversity of the population, but with the expansion of the problem size, the convergence of the algorithm The worst quality of the solution set is obtained by NSGA-II because the adaptation of the search space becomes more complex as the problem size increases, and the search for non-dominated solutions becomes more difficult, and the use of non-dominated ranking strategy to select the population makes the algorithm easily fall into local optimum.

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Fig. 5

Comparison of Pareto fronts of the three optimization algorithms.

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From the distributivity of the solution sets in Fig. 5, the solution sets obtained by the MOEA/D-IRG algorithm are more uniform compared to the three compared algorithms. After obtaining the customer information, the proposed ant colony optimization algorithm and three comparison algorithms are used to calculate the urban logistics vehicle path planning model, and the calculation results are shown in Fig. 6.

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Fig. 6

Comparison of the path lengths of the three algorithms.

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We can see from Fig. 6 that the path calculated by the ant colony algorithm has the lowest cost and shortest time in the whole distribution process considering the slope and congestion, and Case 3 saves 34 m of dynamic path length than Case 2, indicating that we can save 34 m of dynamic length cost by considering the slope and congestion under the condition of path optimization with the ant colony algorithm, while Case 3 saves 5269–4923 = 346 m of dynamic path length compared with Case 1, indicating that the route optimized by the ACO algorithm can save 346 m of dynamic path length cost compared with the empirical path, which is a cost-saving ratio of 6.6%. The results show that the time required to find the optimal path by the designed optimization algorithm is less than 2 min, while the time required to find the optimal path by the traditional algorithm is more than 3 min, up to 4.6 min. The comparison shows that the time required by the traditional algorithm to find the optimal path 10 times is higher than that of the designed algorithm. Therefore, considering the waiting time, slope, and congestion, the path optimization process of e-commerce logistics end distribution process by ant colony algorithm can save more cost and improve the efficiency of distribution, and then we can use the ant colony algorithm for the informationization process of e-commerce logistics end distribution path optimization, and use informationization to serve the logistics end distribution, provide more high-quality and efficient distribution services for e-commerce customers, and increase customer satisfaction.

As can be seen from Fig. 7, the minimum total cost of convergence of the improved ACO is $3217.2, and the total cost obtained by MOEA/D optimization is $3490.6, with the former saving $273.4 over the latter. The quality of the solution obtained by the improved ant colony algorithm is better than the solution obtained by the other algorithms. In addition, the improved ant colony algorithm finds the global optimal solution faster than the traditional ant colony algorithm, and the convergence speed is better than that of the basic ant colony algorithm. The comparative analysis of the total cost convergence graphs of the four algorithms shows that the improved ant colony algorithm has improved the accuracy and convergence speed, expanded the search range of the solution space, avoided the shortcomings of other algorithms that are easy to fall into local optimum, optimized the cold chain logistics distribution path effectively, saved the logistics cost for the enterprise, and improved the logistics efficiency of the enterprise.

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Fig. 7

Total cost convergence of the ant colony algorithms and improved ant colony algorithms.

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From Fig. 7, it can be seen that the improved ant colony algorithm has improved the accuracy and convergence speed, expanded the search range of the solution space, and avoided the disadvantages of other algorithms that tend to fall into local optimum. The ant colony optimization algorithm can only have one population for optimizing two objectives in each independent experiment, and therefore its position update follows the integrated learning strategy commonly employed for the single population case to assist its update phase, rather than learning from an archive containing a large number of historical optimal solutions. As can be seen in Fig. 8, the non-dominated solution frontier derived from ant colony optimization shows a uniform distribution in the target space, while the non-dominated solution frontier derived from ant colony optimization is relatively trapped in a local optimum. Meanwhile, the size of each realistic dataset significantly affects the distribution of the frontier, i.e., narrower frontier distributions are easily found in large-scale realistic datasets. From this analysis, it can be concluded that the advantage of the archiving mechanism is that it can search for more new non-dominated solutions based on the historical optimal solutions retained by previous generations, which means that it is more capable of finding high-quality solutions in a wider search space than traditional methods.

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Fig. 8

Ant colony optimization results for different target points.

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This design of big data context of e-commerce logistics distribution path optimization algorithm compared with the traditional algorithm can save a lot of logistics distribution costs, which is in line with the e-commerce logistics distribution path optimization The economic utility of the optimization.