Optimizing travel routes using temporal networks constructed from GPS data Tatsuro Mukai, Yuichi Ikeda Graduate School of Advanced Integrated Studies in Human Survivability Kyoto University Kyoto, Japan [email protected], [email protected] Abstract—Because of the complexity of urban transportation mation terminals, such as smartphones, are now widely used networks and the temporal changes in traffic conditions, it and carried by most individuals at all times. Therefore, it is difficult to assess real-time traffic situations. However, the has become possible to compose big data from the global development of information terminals has made it easier to obtain personal mobility information. In this study, we propose positioning system (GPS) measured using these devices and methods for evaluating the mobility of people in a city using use the data to analyze movement [6]. global positioning system data. There are two main methods for To analyze human mobility, network science is useful [7][8]. evaluating movement. One is to create a temporal network from Networks whose connection status changes with time are real data and check the change in travel time according to time called temporal networks [9]. They are more difficult to eval- zones or seasons. Temporal networks are difficult to evaluate because of their time complexity, and in this study, we proposed uate than static networks because of their time-varying nature, an evaluation method using the probability density function of but since they represent real-world problems well, they have travel time. The other method is to define a time-dependent been used in various fields such as interpersonal communica- traveling salesman problem and find an efficient traveling route tion [10][11][12][13], transmission to an unspecified number by finding the shortest path. By creating a time-dependent of people using SNS and the web [14][15][16][17], physi- traveling salesman problem in an existing city and solving it, a traveler can choose an efficient route by considering traffic cal contact [18][19][20][21], and cytology [22][23][24][25]. conditions at different times of the day. We used 2 months of Temporal networks are also preferred to represent movement data from Kyoto City to conduct a traffic evaluation as a case as a network, to capture changes in traffic conditions over study. time. Kujala et al. used temporal networks to evaluate the Index Terms—Temporal network, Dynamic network, Route public transportation system in Helsinki [26]. They constructed recommendation the networks from timetables and open map information and evaluated public transportation by focusing on travel time and I. INTRODUCTION the number of transfers. One of the major issues confronting urban areas is trans- Besides, the shortest path problem can be used to find portation planning [1]. Smooth transportation contributes sig- an efficient travel route. In recent years, the shortest path nificantly to residents’ life satisfaction, but transportation problem is as a real-world problem with a time component planning is becoming more difficult because of the global [27]. Heuristic solutions to such a problem, such as the time- population growth in urban areas. In addition, the development dependent traveling salesman problem (TDTSP), have been of tourism has increased the number of visitors to these areas, devised [28][29][30][31]. and a known tourism problem has emerged [2]. This negatively In this study, we propose two methods: one is to evaluate affects both visitors and residents [2][3][4]. human mobility using temporal networks constructed from arXiv:2106.00328v1 [cs.SI] 1 Jun 2021 Three reasons make road traffic in urban areas difficult GPS data, and the other is to search for the shortest path by [5]. First, the urban road networks are typically compli- constructing and solving the TDTSP. In both methods, location cated. Cities are often densely populated with tunnels and information measured from smartphones is converted into a elevated structures that, with numerous roads, form a complex timetable of location transitions called ”transfer connections”, transportation network. Second, travelers may be heading for from which an optimal set of paths to the destination is different destinations. This creates a great deal of uncertainty obtained to construct mobility networks. In the evaluation of in transportation planning as the number of travelers increases. movement using temporal networks, networks are visualized Third, the road traffic situation changes over time. Depending and compared according to seasons, time zones, and whether on traffic congestion, travelers may change their transportation the moving person is a resident or a visitor. In a methodology and traveling route choices, and travel times for the same of finding the shortest path, the time weights of the TDTSP are traveling route can often vary significantly. determined from the set of optimal paths, and the ant colony However, thanks to the development of information termi- optimization (ACO) method is used to solve the problem. nals in recent years, it has become easier to obtain mobility In the application of the ACO method, a congestion level is data and provide mobility information to individuals. Infor- obtained from GPS and used in the calculation. The main contributions of this study include the following: destination, update the label. Repeat until you have scanned • By applying existing methods for constructing temporal all of C. networks and evaluating public transportation, we con- 2) pCSA: An extension of the CSA for more complex struct temporal networks from the GPS of smartphones. scenarios is the profile CSA (pCSA). This algorithm returns a With the GPS, it is possible to take into account other set of Pareto-optimal (departure time, arrival time) paths from means of transportation other than public transportation, each stop to a certain destination. Pareto-optimal here means and it is expected that the evaluation will be realistic, that the departure time is optimized to be slower and the arrival including delays in transportation because of congestion. time is optimized to be faster. With the development of information terminals in recent This algorithm uses an array C of timetable connections years, GPS has been commonly used, so it can be easily sorted in descending order of departure time. Whengiven a extended to other cities. Temporal networks can describe destination pt as input, it creates the empty set of Pareto- real-world problems more precisely than can static net- optimal paths for each stop, c 2 C is scanned in turn, and works, but evaluating temporal networks is difficult. In check if pt is reachable. If it is reachable and (τdep(c); τ∗) is this study, we proposed a new evaluation method for Pareto-optimal compared to the set of paths held by the starting mobile networks using probability density functions. point of c, it is added to the set. Here τdep(c) represents the • In this study, we determined the time weights of edges departure time of c and τ∗ represents the arrival time to pt. in the TDTSP from GPS data based on the method used Do this until you have scanned all of C. to create temporal networks. Although existing studies 3) mcpCSA: The mcpCSA is an extension of the pCSA. have created the TDTSP from GPS data, the weights The mcpCSA extends the Pareto-optimal (departure time, were determined originally. In addition, to apply ACO arrival time) treated in the pCSA to the multi-criteria Pareto- the TDTSP, we decide a congestion level from the GPS optimal like (departure time, arrival time, number of transfers). and calculate the transition probability using this level. B. Time Dependent Traveling Salesman Problem Selecting a route is difficult if the destination is crowded at certain times of the day. To reduce traffic congestion, it is important to recommend efficient travel routes to facilitate movement. To determine the The rest of the paper is organized as follows. In Section II, travel route, we formulate and solve the TDTSP. we introduce the basic methodology. In Section III, we discuss 1) Problem Formulation: The TDTSP is a shortest path improvements to the basic methodology. In Section. IV, we problem on a time-dependent network represented by the describe the proposed method. Following that we discuss the directed graph G = (V; E; W; T ). Here V represents the set of experimental results in Section V. Finally, we conclude our nodes, E represents the set of edges, W represents the set of study in Section VI. time weights, and the time interval T is the set of time-varying II. BASIC METHODOLOGY periods. The weight w(vi; vj; τ) 2 W depends on the starting point A. Temporal network configuration method vi 2 V , the ending point vj 2 V , and the time τ 2 T . Although networks are used in various fields, several real- P ath(v1; vn) = [v1; v2:; vn] represents the transition per- world networks change over time. Networks, those in which mutation of nodes from v1 2 V to vn 2 V . the edge connections change with time are called temporal When the time starting from v1 is τ0 2 T , the sum networks [9]. Temporal networks are often more realistic than of the time weights of P ath(v1; vn), fτ0 (P ath(v1; vn)), is static networks and have been used in road traffic analysis. calculated recursively as follows, Kujala et al. [26] constructed a temporal network from pub- lic transport timetables to model the movement of people. f (v ; v ) = w(v ; v ; τ ) ; (1) They used a multi-criteria profile connection scan algorithm τ0 1 2 1 2 0 f (v ; v ) = w(v ; v ; τ + f (v ; v )) (mcpCSA) to construct the network. This algorithm is used τ0 1 i i−1 i 0 τ0 1 i−1 (2) to compute optimal travels in a dynamic public transportation +fτ0 (v1; vi−1): network, which can represent many events occurring between The TDTSP is a combinatorial optimization problem to find nodes as a temporal network.