# CiteSpace-Based Bibliometric Review of Pickup and Delivery Problem from 1995 to 2021
## 4 Visualization Results and Bibliometric Analysis Based on CiteSpace
### Reference Analysis
#### 4.5.2 Reference Co-Citation Clustering Analysis
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Title** & **Author** & **Freq.** & **Source** \\ \hline An adaptive large neighborhood search heuristic for the Pickup and Delivery Problem with Time Windows and Scheduled Lines [55] & [PERSON] et al. & 26 & Computers \& Operations Research \\ \hline Static pickup and delivery problems: a classification scheme and survey [5] & [PERSON] et al. & 24 & Top \\ \hline An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows [38] & [PERSON] and [PERSON] & 23 & Transportation Science \\ \hline Finding optimal solutions for vehicle routing problem with pickup and delivery services with time windows: A dynamic programming approach based on state–space–time network representations [57] & [PERSON] and [PERSON] & 23 & Transportation Research Part B: Methodological \\ \hline Adaptive large neighborhood search for the pickup and delivery problem with time windows, profits, and reserved requests [56] & [PERSON] et al. & 22 & European Journal of Operational Research \\ \hline A branch-and-cut algorithm for the pickup and delivery traveling salesman problem with LIFO loading [58] & [PERSON] et al. & 20 & Networks \\ \hline A hybrid discrete particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery [59] & [PERSON] et al. & 20 & Computers \& Industrial Engineering \\ \hline A tabu search heuristic for the static multi-vehicle dial-a-ride problem [26] & [PERSON] and [PERSON] & 20 & Transportation Research Part B: Methodological \\ \hline A parallel simulated annealing method for the vehicle routing problem with simultaneous pickup-delivery and time windows [52] & [PERSON] et al. & 19 & Computers \& Industrial Engineering \\ \hline Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries [42] & [PERSON] et al. & 19 & European Journal of Operational Research \\ \hline Dynamic pickup and delivery problems [6] & [PERSON] et al. & 19 & European Journal of Operational Research \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The top 10 high-cited references in the research on PDP. As shown in Table 10 and Figure 12, the largest Cluster #0 (column generation) has 152 members and a silhouette score of 0.873, which mainly focuses on handling large-scale linear programming and can be well combined with exact algorithms (e.g., branch-and-cut and branch-and-price) as part of the methodology in the research on PDP. Column generation initially solves the restricted master problem considering a subset of the entire decision space, and iteratively adds additional columns that have the potential to generate a negative reduced cost to the restricted master problem until no newer columns can be included [60]. [PERSON] et al. [61] first applied column generation to formulate a pricing subproblem (i.e., shortest path problem) for the PDPTW considering precedence, capacity, and pairing constraints, where each column represents an admissible route. In addition, a label elimination algorithm was proposed to accelerate the efficiency of dynamic programming for solving this subproblem. Inspired by their work, [PERSON] and [PERSON] [62] introduced a branch-and-cut-and-price algorithm to address PDPTW, where the lower bound defined as the set partitioning relaxation formulation of original mixed-integer program was computed through column generation. [PERSON] and [PERSON] [63] considered a kind of PDPTW in which a freight vehicle of heterogeneous fleet may need to visit a customer's location multiple times to satisfy his all demand. To avoid the proliferation of nodes in branch-and-bound tree caused by excessive suboptimal routes developed by standard column generation, they designed an improved column generation that inhibits from regenerating the routes with the same route vectors. Nowadays, the solution algorithms based on column generation have become predominant among several exact algorithms that were developed to collect the optimal vehicle routes of many variants of PDPs.