A dynamic day-ahead paratransit planning problem

Abstract We consider a dynamic planning problem for the transport of elderly and disabled people. The focus is on a decision to make one day ahead: which requests to serve with own vehicles, and which ones to assign to subcontractors, under uncertainty of late requests which are gradually revealed during the day of operation. We call this problem the Dynamic Day-ahead Paratransit Planning problem. The developed model is a nonstandard two-stage recourse model in which ideas from stochastic programming and online optimization are combined: in the first stage clustered requests are assigned to vehicles, and in the dynamic second-stage problem an event-driven approach is used to cluster the late requests once they are revealed and subsequently assign them to vehicles. A genetic algorithm is used to solve the model. Computational results are presented for randomly generated data sets. Furthermore, a comparison is made to a similar problem we studied earlier in which the simplifying but unrealistic assumption has been made that all late requests are revealed at the beginning of the day of operation.

Column generation approaches to ship scheduling with flexible cargo sizes

We present a Dantzig-Wolfe procedure for the ship scheduling problem with flexible cargo sizes. This problem is similar to the well-known pickup and delivery problem with time windows, but the cargo sizes are defined by an interval instead of a fixed value. We show that the introduction of flexible cargo sizes to the column generation framework is not straightforward, and we handle the flexible cargo sizes heuristically when solving the subproblems. This leads to convergence issues in the branch-and-price search tree, and the optimal solution cannot be guaranteed. Hence we have introduced a method that generates an upper bound on the optimal objective. We have compared our method with an a priori column generation approach, and our computational experiments on real world cases show that the Dantzig-Wolfe approach is faster than the a priori generation of columns, and we are able to deal with larger or more loosely constrained instances. By using the techniques introduced in this paper, a more extensive set of real world cases can be solved either to optimality or within a small deviation from optimalityTransportation; integer programming; dynamic programming

Enhancement on the modified artificial bee colony algorithm to optimize the vehicle routing problem with time windows

The vehicle routing problem with time windows (VRPTW) is a non-deterministictime hard (NP-hard) with combinatorial optimization problem (COP). The Artificial Bee Colony (ABC) is a popular swarm intelligence algorithm for COP. In this study, existing Modified ABC (MABC) algorithm is revised to solve the VRPTW. While MABC has been reported to be successful, it does have some drawbacks, including a lack of neighbourhood structure selection during the intensification process, a lack of knowledge in population initialization, and occasional stops proceeding the global optimum. This study proposes an enhanced Modified ABC (E-MABC) algorithm which includes (i) N-MABC that overcomes the shortage of neighborhood selection by exchanging the neighborhood structure between two different routes in the solution; (ii) MABC-ACS that solves the issues of knowledge absence in MABC population initialization by incorporating ant colony system heuristics, and (iii) PMABC which addresses the occasional stops proceeding to the global optimum by introducing perturbation that accepts an abandoned solution and jumps out of a local optimum. The proposed algorithm was evaluated using benchmark datasets comprising 56 VRPTW instances and 56 Pickup and Delivery Problems with Time Windows (PDPTW). The performance has been measured using the travelled distance (TD) and the number of deployed vehicles (NV). The results showed that the proposed E-MABC has lower TD and NV than the benchmarked MABC and other algorithms. The E-MABC algorithm is better than the MABC by 96.62%, MOLNS by 87.5%, GAPSO by 53.57%, MODLEM by 76.78%, and RRGA by 42.85% in terms of TD. Additionally, the E-MABC algorithm is better than the MABC by 42.85%, MOLNS by 17.85%, GA-PSO and RRGA by 28.57%, and MODLEN by 46.42% in terms of NV. This indicates that the proposed E-MABC algorithm is promising and effective for the VRPTW and PDPTW, and thus can compete in other routing problems and COPs

A two-stage model for a day-ahead paratransit planning problem

We consider a dynamic planning problem for paratransit transportation. The focus is on a decision to take one day ahead: which requests to serve with own vehicles, and which requests to subcontract to taxis? We call this problem the day-ahead paratransit planning problem. The developed model is a non-standard two-stage integer recourse model. Both stages consist of two consecutive optimization problems: the clustering of requests into routes, and the assignment of these routes to vehicles. To solve this model, a genetic algorithm approach is used. Computational results are presented for randomly generated data sets

Data-Driven Optimization Models for Feeder Bus Network Design

Urbanization is not a modern phenomenon. However, it is worthwhile to note that the world urban population growth curve has up till recently followed a quadratic-hyperbolic pattern (Korotayey and Khaltourina, 2006). As cities become larger and their population expand, large and growing metropolises have to face the enormous traffic demand. To alleviate the increasing traffic congestion, public transit has been considered as the ideal solution to such troubles and problems restricting urban development. The metro is a type of efficient, dependable and high-capacity public transport adapted in metropolises worldwide. At the same time, the residents from crowded cities migrated to the suburban since 1950s. Such sub-urbanization brings more decentralized travel demands and has challenged to the public transit system. Even the metro lines are extended from inner city to outer city, the commuters living in suburban still have difficulty to get to the rail station due to the limited transportation resources. It is becoming inevitable to develop the regional transit network such as feeder bus that picks up the passengers from various locations and transfer them to the metro stations or transportation hubs. The feeder bus will greatly improve the efficiency of metro stations whose service area in the suburban area is usually limited. Therefore, how to develop a well-integrated feeder system is becoming an important task to planners and engineers. Realizing the above critical issues, the dissertation focus on the feeder bus network design problem (FBNDP) and contributes to three main parts: 1. Develop a data-mining strategy to retrieve OD pair from the large scale of the cellphone data. The OD pairs are able to present the users’ daily behaver including the location of residence, workplace with the timestamp of each trip. The spatial distribution of urban rail transit user demand from the OD pair will help to support the establishment and optimization of the feeder bus network. The dissertation details the procedure of data acquisition and utilization. The machine leaning is applied to predict the travel demand in the future. 2. Present a mathematical model to design the appropriate service area and routing plans for a flexible feeder transit. The proposed model features in utilizing the real-world data input and simultaneously selecting bus stops and designing the route from those targeted stops to urban rail stops. 3. Propose an improved feeder bus network design model to provide precise service to the commuters. Considering the commuters are time-sensitive during the peak hours, the time-windows of each demand is taken in to account when generating the routes and the schedule of feeder bus system. The model aims to pick up the demand within the time-windows of the commuters’ departure time and drop off them within the reasonable time. The commuters will benefit from the shorter waiting time, shorter walking distance and efficient transfer timetable