Cristián E. Cortés

The pickup and delivery problem with transfers: Formulation and a branch-and-cut solution method

In this paper, a strict formulation of a generalization of the classical pickup and delivery problem is presented. Here, we add the flexibility of providing the option for passengers to transfer from one vehicle to another at specific locations. As part of the mathematical formulation, we include transfer nodes where vehicles may interact interchanging passengers. Additional variables to keep track of customers along their route are considered. The formulation has been proven to work correctly, and by means of a simple example instance, we conclude that there exist some configurations in which a scheme allowing transfers results in better quality optimal solutions. Finally, a solution method based on Benders decomposition is addressed. We compare the computational effort of this application with a straight branch and bound strategy; we also provide insights to develop more efficient set partitioning formulations and associated algorithms for solving real-size problems.

Hybrid adaptive predictive control for the multi-vehicle dynamic pick-up and delivery problem based on genetic algorithms and fuzzy clustering

In this paper, we develop a family of solution algorithms based upon computational intelligence for solving the dynamic multi-vehicle pick-up and delivery problem formulated under a hybrid predictive adaptive control scheme. The scheme considers future demand and prediction of expected waiting and travel times experienced by customers. In addition, this work includes an analytical formulation of the proposed prediction models that allow us to search over a reduced feasible space. Predictive models consider relevant state space variables as vehicle load and departure time at stops. A generic expression of the system cost function is used to measure the benefits in dispatching decisions of the proposed scheme when solving for more than two-step ahead under unknown demand. The demand prediction is based on a systematic fuzzy clustering methodology, resulting in appropriate call probabilities for uncertain future. As the dynamic multi-vehicle routing problem considered is NP-hard, we propose the use of genetic algorithms (GA) that provide near-optimal solutions for the three, two and one-step ahead problems. Promising results in terms of computation time and accuracy are presented through a simulated numerical example that includes the analysis of the proposed fuzzy clustering, and the comparison of myopic and new predictive approaches solved with GA.

DESIGN AND OPERATIONAL CONCEPTS OF HIGH-COVERAGE POINT-TO-POINT TRANSIT SYSTEM

Conceptual design and preliminary feasibility simulation results are presented for a flexible transit system for travel from any point to any point based on real-time personalized travel desires, which is now possible because of advances in communications and computing technologies. Although it is demand-responsive, the concept is significantly different from older demand-responsive transit systems, which were often failures. The proposed system requires high coverage, referring to the availability of a large number of transit vehicles (often minibuses or vans), which could also operate in conjunction with private transit and paratransit systems. The design strictly eliminates more than one transfer for any passenger. The system could potentially provide a transit alternative that is much more competitive with personal automobile travel than are conventional transit systems because of significantly lower waiting times. The passenger demand for such a system is uncertain, but preliminary simulations show that under a variety of acceptable demand levels, the system can operate with high cost-effectiveness. The focus is on describing the details of the concept and providing arguments in favor of the system based on simulations. The system essentially attempts to solve a stochastic real-time passenger pickup-and-delivery problem with a large number of vehicles. A strict optimization formulation and solution for such a problem are computationally prohibitive in real time. The design proposed is effectively geared toward a decomposed solution using detailed rules that achieve vehicle selection and route planning. If real-time update of probabilities is included, this scheme could be considered as a form of quasi-optimal stochastic control.

GENERAL-PURPOSE METHODOLOGY FOR ESTIMATING LINK TRAVEL TIME WITH MULTIPLE-POINT DETECTION OF TRAFFIC

A methodology was developed to find appropriate travel times for highway links using data from point detectors that could be at various points within the link or could even be outside the link. The travel times were found using a definition that the appropriate value is the one experienced by a virtual vehicle reaching the midpoint of the link at the midpoint of the time step. A simple iterative scheme was proposed to find the travel time profiles. The accuracy of the scheme depends on whether aggregated detector data or individual vehicle spot speeds are used. Comparison of estimated travel times with actual experienced travel times of all vehicles in a microscopic simulation showed the technique to give very good results, comparable with having a high number of probe vehicles reporting travel times.

Hybrid predictive control strategy for a public transport system with uncertain demand

In this article, a hybrid predictive control (HPC) strategy is formulated for the real-time optimisation of a public transport system operation run using buses. For this problem, the hybrid predictive controller corresponds to the bus dispatcher, who dynamically provides the optimal control actions to the bus system to minimise users’ total travel time (on-vehicle ride time plus waiting time at stops). The HPC framework includes a dynamic objective function and a predictive model of the bus system, written in discrete time, where events are triggered when a bus arrives at a bus stop. Upon these events, the HPC controller makes decisions based on two well-known real-time transit control actions, holding and expressing. Additionally, the uncertain passenger demand is included in the model as a disturbance and then predicted based on both offline and online information of passenger behaviour. The resulting optimisation problem of the HPC strategy at every event is Np-hard and needs an efficient algorithm to solve it in terms of computation time and accuracy. We chose an ad hoc implementation of a Genetic Algorithm that permits the proper management of the trade-off between these two aspects. For real-time implementation, the design of this HPC strategy considers newly available transport technology such as the availability of automatic passenger counters (APCs) and automatic vehicle location (AVL) devices. Illustrative simulations at 2, 5 and 10 steps ahead are conducted, and promising results showing the advantages of the real-time control schemes are reported and discussed.

Hybrid Adaptive Predictive Control for a Dynamic Pickup and Delivery Problem

This paper presents a hybrid adaptive predictive control approach that includes future information in real-time routing decisions in the context of a dynamic pickup and delivery problem (DPDP). We recognize in this research that when the problem is dynamic, an additional stochastic effect has to be considered within the analytical expression of the objective function for vehicle scheduling and routing, which is the extra cost associated with potential rerouting arising from unknown requests in the future. The major contributions of this paper are: first, the development of a formal adaptive predictive control framework to model the DPDP, and second, the development and coding of an ad hoc particle swarm optimization (PSO) algorithm to efficiently solve it. Predictive state-space formulations are written on the relevant variables (vehicle load and departure time at stops) for the DPDP. Next, an objective function is stated to solve the real-time system when predicting one and two steps ahead in time. A problem-specific PSO algorithm is proposed and coded according to the dynamic formulation. Then, the PSO method is used to validate this approach through a simulated numerical example.

Real-Time Mass Passenger Transport Network Optimization Problems

The aim of Real-Time Mass Transport Vehicle Routing Problem (MTVRP) is to find a solution to route n vehicles in real time to pick up and deliver m passengers. This problem is described in the context of flexible large-scale mass transportation options that use new technologies for communication among passengers and vehicles. The solution of such a problem is relevant to future transportation options involving large scale real-time routing of shared-ride fleet transit vehicles. However, the global optimization of a complex system involving routing and scheduling multiple vehicles and passengers as well as design issues has not been strictly studied in the past. This research proposes a methodology to solve it by using a three level hierarchical optimization approach. Within the optimization process, a Mass Transport Network Design Problem (MTNDP) is solved. This paper introduces MTVRP and presents a scheme to solve it. Then, the associated algorithm to perform the MTNDP optimization is described in detail. An instance for the city of Barcelona, Spain is solved, showing promising results with regard to the applicability of the methodology for large scale transit problems.

A robust optimization approach to dispatching technicians under stochastic service times

We consider the problem of dispatching technicians to service/repair geographically distributed equipment. This problem can be cast as a vehicle routing problem with time windows, where customers expect fast response and small delays. Estimates of the service time, however, can be subject to a significant amount of uncertainty due to misdiagnosis of the reason for failure or surprises during repair. It is therefore crucial to develop routes for the technicians that would be less sensitive to substantial deviations from estimated service times. In this paper we propose a robust optimization model for the vehicle routing problem with soft time windows and service time uncertainty and solve real-world instances with a branch and price method. We evaluate the efficiency of the approach through computational experiments on real industry routing data.

Bus-Stop Control Strategies Based on Fuzzy Rules for the Operation of a Public Transport System

In the daily operation of a bus system, the movement of vehicles is affected by uncertain conditions as the day progresses, such as traffic congestion, unexpected delays, randomness in passenger demand, irregular vehicle dispatching times, and incidents. In a real-time setting, researchers have devoted significant effort to developing flexible control strategies, depending on the specific features of public transport systems. In this paper, we propose a control scheme for the operation of a bus system running along a linear corridor, based on expert rules and fuzzy logic. The parameters of the fuzzy controllers were tuned through a particle swarm optimization (PSO) algorithm. That is, the control strategies aim at keeping regular headways between consecutive buses, with the objective of reducing the total waiting time of passengers. The proposed control systems rely on measures of the position of each bus, which are easy to obtain and implement by means of emerging automatic vehicle location devices through Global Positioning System (GPS) technology. The utilized strategies are holding, stop-skipping, and the integration of both. After tuning the controller parameters, we conducted several simulation tests, obtaining promising results in terms of savings in waiting times with the implementation of the proposed rules, noting that the best performance occurred when fuzzy rules are included. The methodology has great impact, and it is easy to implement due to its simplicity.

Branch-and-price and constraint programming for solving a real-life technician dispatching problem

We consider a real problem faced by a large company providing repair services of office machines in Santiago, Chile. In a typical day about twenty technicians visit seventy customers in a predefined service area in Santiago. We design optimal routes for technicians by considering travel times, soft time windows for technician arrival times at client locations, and fixed repair times. A branch-and-price algorithm was developed, using a constraint branching strategy proposed by Ryan and Foster along with constraint programming in the column generation phase. The column generation takes advantage of the fact that each technician can satisfy no more than five to six service requests per day. Different instances of the problem were solved to optimality in a reasonable computational time, and the results obtained compare favorably with the current practice.