# CiteSpace-Based Bibliometric Review of Pickup and Delivery Problem from 1995 to 2021
## 4 Visualization Results and Bibliometric Analysis Based on CiteSpace
### Reference Analysis
#### 4.5.1 Reference Co-Citation Network Analysis  
As shown in Figure 11, each node in references co-citation network denotes a reference, each link connecting two nodes denotes the co-citation relationship between two references. The larger the radius of the circle, the more frequently the reference is cited. Moreover, considering the overall density of co-citation network is only 0.0034, there may be few opportunities for co-citation between the core references because references contained in some academic documents might be from different disciplines.  
Table 9 lists the top 10 high-cited documents in the research on PDP, ranking by the frequency of citations. Among them, [PERSON] and [PERSON] [38] first applied ALNS method to address the PDPTW with capacity constraints, which greatly motivated scholars to adopt ALNS heuristic to discover the better solution for other PDPs with different topics. For example, the top-ranked article entitled \"An adaptive large neighborhood search heuristic for the Pickup and Delivery Problem with Time Windows and Scheduled Lines\" [55] analyzed the feasibility and flexibility of vehicles transport goods requested by customers in line with the predetermined routes and schedules, and an ALNS algorithm with ten removal operators and five insertion operators was proposed to generate good-quality route choice and time planning for pickup and delivery vehicles. The results of several computational experiments indicated that the implementation of scheduled line can reduce the operating costs and CO\({}_{2}\) emissions. [PERSON] et al. [56] studied the PDP involving time windows, profits, and reserved requests together, which can be solved through their creative technique that the destroy/repair operator and local search procedure of ALNS running in successive segments are modified to generate the near optimal solutions.  
Although the optimal solution is difficult to obtain, some researchers reformulated the PDP as a special optimization model and employed exact algorithm that matches the structure of proposed model to cope with the computational difficulties. [PERSON] and [PERSON] [57] formulated PDPTW on state-space-time transportation networks, which can be solved efficiently by utilizing Lagrangian relaxation algorithm to decompose the main problem to a sequence of time-dependent route choice problems that minimize the travel cost for each vehicle. In order to solve the PDP with LIFO loading optimally, [PERSON] et al. [58] attached valid inequalities to three correlative mathematical models, which not only increases the linear programming relaxation of these models but also integrates with branch and cut algorithm well in the calculation process.  
There is an interesting phenomenon that Table 9 lists two high-cited documents [52; 59] related to the topic of \"simultaneous pickup\" and three high-cited documents [38; 55; 56] related to the topic of \"LNS\". Meanwhile, both \"simultaneous pickup\" and \"LNS\" are the current hotspots in the field of PDP as aforementioned. Therefore, as critical topics in the research on PDP, \"simultaneous pickup\" and \"LNS\" have received extensive attention from scholars and are still worthy of future research. The rest of the high-cited references in Table 9 are mentioned in the previous section, to avoid repetition, it is not described again here.  
Figure 11: Co-citation network map of references in the research on PDP.