A multi-objective optimization framework for online ridesharing systems* Hamed Javidi Dan Simon Ling Zhu Yan Wang Dept. of Electrical Engineering Dept. of Electrical Engineering Ford Motor Company Ford Motor Company and Computer Science and Computer Science Ann Arbor, USA Cleveland, USA Cleveland State University Cleveland State University Email: [email protected] Email: [email protected] Cleveland, USA Cleveland, USA Email: [email protected] Email: [email protected] Abstract—The ultimate goal of ridesharing systems is to match appear later. In dynamic ridesharing, however, they can appear travelers who do not have a vehicle with those travelers who after the beginning of the time period. In other words, in static want to share their vehicle. A good match can be found among ridesharing all drivers and all riders and all corresponding those who have similar itineraries and time schedules. In this way each rider can be served without any delay and also each data, including departure and arrival locations, and pickup and driver can earn as much as possible without having too much drop off times, are known at the beginning of the time period. deviation from their original route. We propose an algorithm In dynamic ridesharing new riders and drivers continuously that leverages biogeography-based optimization to solve a multi- appear to request rides and to provide transportation. objective optimization problem for online ridesharing. It is Static ridesharing is not realistic and cannot be used in a necessary to solve the ridesharing problem as a multi-objective problem since there are some important objectives that must be real-world application, so we focus on dynamic ridesharing. considered simultaneously. We test our algorithm by evaluating Due to the unpredictable nature of the problem, future driver performance on the Beijing ridesharing dataset. The simulation appearances and rider requests are unknown. results indicate that BBO provides competitive performance The ridesharing problem [1], [2] is related to the vehicle relative to state-of-the-art ridesharing optimization algorithms. routing [3] and multi-vehicle pickup and delivery problems Index Terms—Ridesharing, Carpooling, Multi-objective opti- [4], [5], in which customers request to be picked up from their mization, Trip matching, Real-time optimization, Biogeography- origins and dropped off at their destinations while satisfying based optimization vehicle capacity and time constraints. Effective and efficient optimization technology that matches drivers and riders is I. INTRODUCTION one of the necessary components for an optimized ridesharing system. There are some significant challenges in this problem, In recent years ridesharing systems have become extremely such as fast computation, scalability, seat utilization, and popular. They are becoming popular because commuters prefer quality of service (e.g., average trip delay). to find a more economical way to take their trips. Ridesharing There are multiple objectives in this problem. One objective provides an appropriate alternative for urban transportation is minimizing the distance traveled by each rider and each due to the potential benefits; e.g., decreased traffic congestion, driver. Another objective is minimizing the waiting time of the diminished fuel consumption, and reduced greenhouse gas riders before being picked up by a driver. Another objective emissions. Ridesharing could lead to more efficient use of is maximizing the total benefit obtained through successful empty car seats and could significantly alleviate some of the matches, which is defined based on the drivers’ preferred societal concerns about issues like traffic congestion and air mode of payment [6]. Another objective is matching rate, arXiv:2012.05046v1 [math.OC] 7 Dec 2020 pollution. i.e., maximizing the number of riders who can be picked up People who do not have a can be serviced by a vehicle that and delivered to their destination. In this paper, we mainly has a similar route and overlapping travel times, or by a vehicle focus on two important objectives that are well-known among that can reroute to match the passenger’s destination. There are researchers: matching rate and total travel distance. multiple types of ridesharing systems; e.g., taxi sharing, car There have been various approaches to solving the dy- sharing, courier services, scooter sharing, bike sharing. These namic ridesharing problem. In [7], a rolling horizon solution ridesharing and shuttle services reduce costs for the riders and is proposed. This approach periodically matches unmatched provides income for drivers. riders with drivers who have empty seats. At each iteration There are two categories of ridesharing: static and dynamic. of the rolling horizon, a matching problem is solved with In static ridesharing, all driver and rider requests are available an objective function aimed at minimizing the total travel at the beginning of the time period and no new riders or drivers distance and maximizing the matching rate. There are several This document is the results of the research project funded by Ford Motor approaches to determine the frequency of the iterations in a company. rolling horizon framework.The main two approaches include periodic optimization with a fixed time step, and event-driven (B) Proposing an efficient matching algorithm. We propose optimization, where an event can include the appearance of a quick and efficient matching algorithm based on an one or more new riders. Event-driven approaches are usually evolutionary algorithm that can be used for dynamic used when systems are expected to respond quickly to an event ridesharing. in the environment while periodic optimization may imply (C) Implementing state-of-the-art papers. In order to longer response delay [8]. compare the performance of our algorithm with other The ridesharing problem is known to be a non-deterministic research, we implemented state-of-the-art optimization polynomial time (NP-hard) problem [9], [10]. That is, to find methods for the dynamic ridesharing problem. the optimal solution of the problem may require an enormous II. PROBLEM STATEMENT AND FORMULATION amount of computation time, depending on the problem size. Because of the nature of this problem, optimal solutions are In this section, we first define terms, including parameters unattainable in large-scale problems in a reasonable amount and variables, then we present the mathematical formulation of of time. There is a trade-off in this type of problem: optimal the proposed ride-sharing system and introduce the objective solution, or fast computation with near-optimal solution. A functions. near-optimal solution can be found with an online algorithm A. Definitions whose computation time is fairly low. Research has been done on both approaches to this problem. In some cases, it is im- Definition 1 (Route) Let G = (V; E) be a a graph of a road practical to generate optimal solutions within a given (usually network system, where V is the set of vertices representing small) time bound [10], [11]. Furthermore, for some cases, intersections and E is the set of edges representing streets. achieving a good feasible solution in a short time is more Each edge (u; v) 2 E has a weight wuv indicating travel desirable than finding the optimal solution. Consequently, a distance along the street. A route is a set of connected edges, trade-off between optimality and computation time must be and its cost is the sum of the weights of all the edges in the considered. route. Early work on this problem focused on traditional integer Definition 2 (Rider) A rider wants to be matched with a programming approaches, which are limited to small scale driver who can meet the rider’s constraints. Each rider r begins problems; e.g., 8 drivers and 96 riders [12]–[14]. This method at origin ro and requests to be transported to destination rd by returns the optimal solution for the problem by searching all a driver. Each rider is associated with a time window (re; rl). possible states of the problem. However, the computation time The early time re is the earliest possible time the rider r can of such methods is too high so this method can be applied only be picked up, and the late time rl is the latest time that the to small problems. rider can be dropped off. Riders requests will appear in the ride-sharing system in real time. Heuristic approaches [7], [11], [21] have been proposed to Definition 3 (Driver) A driver can be assigned to riders solve the real-time taxi ridesharing problem. One approach is whose constraints match the driver’s constraints. D is a set to find a greedy solution, which assigns one rider request at a of drivers. Each driver d 2 D begins its trip at its origin d time to the best available vehicle. Although these approaches o and ends at its destination d . Each driver has its own time are fast, the solution is not good enough. One of the most d constraint (d ; d ): d ≤ d , where d is the earliest possible well-known algorithms that uses an approximation method e l e l e departure time from d and d is the latest possible arrival time to approach this problem is T-share [11]. They partitioned o l at d . Each d 2 D has properties d , d , d , d , the Beijing road network using a grid and define a road d loc cap load speed d . Here, d 2 V is the driver’s current location, which network node as an anchor point of each cell and then used sch loc is the current vertex of driver d; d is the maximum seat precomputed travel distances and travel times of the shortest cap capacity; d is the number of riders; d is the driver’s paths between each pair of cells. The strategy is greedy so load speed speed, which is assumed to be constant; and d is the trip it tries to find the best vehicle match in terms of minimized sch schedule of the driver d, which is defined below.