## 5 Current Trends  
### Descriptive Analysis  
This subsection addressed the third research question highlighted in Section 3.1. Table S1 in the Supplementary File of this paper tabulates the summary of papers based on the Types of SMP. A chart with the number of papers according to the Types of SMP is presented in Figure 3. Out of 103 selected papers, there are 56 papers categorised under ridesharing which is the greatest number among the literature. This is followed by carpooling (22), taxisharing (13), multi-modal (10), busyooling (2) and vanpooling (1). Meanwhile, Table S2 (see Supplementary File) presents the summary of papers based on the problem variants of the SMP. There are two different categories in terms of the problem variants. The first category is based on the number of drivers and riders (D-R) which has four different sub-categories. They are One-to-One (1-1), One-to-Many (1-M), Many-to-One (M-1), and Many-to-Many (M-M). They represent a single driver-single rider, single driver-multiple riders, multiple driver-single rider, and multiple driver-multiple riders, respectively. The second category of the problem variants is based on the number of origins and destinations (O-D) which can also be divided into four sub-categories. They are One Origin-One Destination (IO1D), One Origin-Multiple Destinations (IOMD), Multiple Origins-One Destination (MO1D), and Multiple Origins-Multiple Destinations (MOMD). In Figure 4, from the 56 papers reviewed in ridesharing, 24 of the papers are categorised under the 1-M problem. There are 18 of the 1-1 ridesharing papers which comes in second in rank. The third is the M-M ridesharing problems which covers 10 papers. There are three papers categorised under M-1 problem. There is only one paper under the MOMD ridesharing problem. From the 13 papers reviewed in taxisharing, 6 of the papers are categorised as the 1-M problem (see Figure 5). The 1-1, M-M, and MOMD problems are covered in two papers, which sees them ranked second. Lastly, there is one study categorised as taxisharing under 1 OMD problem. Figure 4: Distribution of Papers based on the Problem Variants: Ridesharing. Figure 3: Number of Papers based on the Types of SMP. In Figure 6, from the 21 papers reviewed in carpooling, the 1-M problem is in 9 of the studies, which makes it the highest percentage among all other problem variants for carpooling. The MOMD and 1-1 carpooling problems are covered in 4, which sees them ranked the second highest. The MO1D problem is covered in 2 which sees it come in at the third position. The M-1 and 1 OMD carpooling problems rank last, being in one study. Of the two papers of the busyooling problem, one is categorised under the 1-1 problem and another is the 1-M problem. For the vanpooling problem, only one paper is found in the review and this is categorised under the 1-M problem. Both problems are relatively new in the literature as compared to other problems in SMP. Table S3 (see Supplementary File) shows the summary of papers based on the problem characteristics of the SMP. The problem characteristics are Decentralised (DC), Multi-Objective (MO), Multi-Hop (MH), Ride-Back (RB), Transfer Point (TP), Time Window (TW), Meeting Point (MP), Role Flexibility (ROF), Route Flexibility (ROUF), Arrival Time Flexibility (ATF), Time Flexibility (TF), Driver Detour Flexibility (DDF), Pickup and Delivery Flexibility (PDF), Stable Matching (SB), Static (STA), Stochastic (STO), and lastly, Dynamic (Dy). The descriptions of the characteristics are stated below. A large-scale optimisation problem with many participants can be hard to solve using a centralised approach. In a DC approach, large-scale optimisation problems can be decomposed or clustered into smaller sub-problems in a short time [41]. Figure 5: Distribution of Papers based on the Problem Variants: Taxisharing. Figure 6: Distribution of Papers based on the Problem Variants: Carpooling. In a single-objective optimisation problem, only one optimisation goal or aim is focused on in the study.