Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

This paper considers the design and analysis of algorithms for vehicle routing and scheduling problems with time window constraints. Given the intrinsic difficulty of this problem class, approximation methods seem to offer the most promise for practical size problems. After describing a variety of heuristics, we conduct an extensive computational study of their performance. The problem set includes routing and scheduling environments that differ in terms of the type of data used to generate the problems, the percentage of customers with time windows, their tightness and positioning, and the scheduling horizon. We found that several heuristics performed well in different problem environments; in particular an insertion-type heuristic consistently gave very good results.

https://www.jstor.org/stable/pdfplus/170697.pdf

Algorithms for the vehicle routing and scheduling problems with time window constraints

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A User’s Guide

This paper is devoted to bilevel optimization, a branch of mathematical programming of both practical and theoretical interest. Starting with a simple example, we proceed towards a general formulation. We then present fields of application, focus on solution approaches, and make the connection with MPECs (Mathematical Programs with Equilibrium Constraints).

/pdf/an-overview-of-bilevel-optimization-4x7xo28qzy.pdf

An overview of bilevel optimization

In pickup and delivery problems vehicles have to transport loads from origins to destinations without transshipment at intermediate locations. In this paper, we discuss several characteristics that distinguish them from standard vehicle routing problems and present a survey of the problem types and solution methods found in the literature.

/pdf/the-general-pickup-and-delivery-problem-20022i8cyz.pdf

The General Pickup and Delivery Problem

This paper describes the bus network design problem, summarizes the different approaches that have been proposed for its solution and proposes a new approach incorporating some of the positive aspects of prior work. The proposed approach is intended to be easier to implement and less demanding in terms of both data requirements and analytical sophistication than previous methods. An algorithm is presented that can be used to design new bus routes taking account of both passenger and operator interests; however, this algorithm focuses on only a single component of the overall bus operations planning process described in this paper.

Bus network design

In this paper we describe a heuristic algorithm, Advanced Dial-A-Ride with Time Windows (ADARTW), for the advance-request version of the multi-vehicle, many-to-many Dial-A-Ride Problem (DARP) with service quality constraints. DARP is concerned with developing a set of routes for a fleet of vehicles carrying customers between specified origins and destinations. “Many-to-many” means that each customer can have a distinct origin and destination, while “advance-request” means that all the requests are received well before the time of vehicle dispatching. Finally, “service quality constraints” guarantee that (1) customers’ ride times will not exceed a prespecified maximum and (2) the time of pick-up or delivery of customers will not deviate from the most-desired pick-up or delivery time of these customers by more than pre-specified amounts (“the time windows”). The algorithmic approach to be described is interesting for two reasons. First, it addresses what is probably the most applicable and realistic version of the real-world problem in a way that avoids excessive abstraction and simplification and emphasizes flexibility and convenience to the algorithm’s user. Second, it can generate at low computation cost what are apparently high-quality solutions to much larger problems (e.g. 2500 customers and 30 simultaneously active vehicles) than have hitherto been attempted. Many North American systems serving elderly and handicapped passengers require reservations a day in advance, while in other cases return trips may be scheduled as immediate requests. This second scenario can also be handled with an extension of the algorithm presented in this paper. The DARP was first examined by Wilson et al. (1971, 1976, 1977) in connection with the development of real-time algorithms for the Dial-A-Ride systems of Haddonfield, NJ, and Rochester, NY. ADARTW derives some of its fundamental concepts (building tours through sequential insertion of customers, general form of the objective function) from that work. A paper by Roy et al. (1983) which appeared as this paper was being completed also uses similar concepts and solves essentially the same version of DARP. Hung et al. (1982) have been tackling the same problem but have adopted an entirely different approach involving processing (scheduling and routing) one vehicle at a time rather than all vehicles simultaneously, as is done by ADARTW. Psaraftis (1983a) has developed a dynamic programming algorithm for solving the single-vehicle DARP optimally for a small number of customers in the presence of time windows, and Solomon (1983) has recently published an excellent review of the vehicle routing problem (not DARP) with time-window constraints. Descriptions of several versions of DARP without time-window constraints can be found

A heuristic algorithm for the multi-vehicle advance request dial-a-ride problem with time windows

Holding is one of the most commonly used real-time control strategies in transit operations. Given a transit network and its operations plan, the holding problem is to decide at a given time at a control station, which vehicle is to be held and for how long, such that the total passenger cost along the route is minimized over a time period. Previous research on the holding problem has always assumed no real-time information available. Such an assumption not only poses great difficulties in solving the problem, but also limits practical applications in a real-time, dynamic operations environment. In this paper we formulate the holding problem as a deterministic quadratic program in a rolling horizon scheme, and develop an efficient solution algorithm to solve it. Using headway data collected by an automated system, we tested the algorithm and evaluated the impact of the resulting holding policies. Important and interesting properties of the holding solution, obtained from both theoretical and computational analyses, are presented.

The Holding Problem with Real-Time Information Available

Automatic data collection (ADC) systems are becoming increasingly common in transit systems throughout the world. Although these ADC systems are often designed to support specific fairly narrow functions, the resulting data can have wide-ranging applications, well beyond their design purpose. This paper illustrates the potential that ADC systems can provide transit agencies with new rich data sources at low marginal cost, as well as the critical gap between what ADC systems directly offer and what is needed in practice in transit agencies. To close this gap requires data processing/analysis methods with support of technologies such as database management systems and geographic information systems. This work presents a case study of the automatic fare collection (AFC) system of the Chicago Transit Authority (CTA) rail system and develops a method for inferring rail passenger trip origin-destination (OD) matrices from an origin-only AFC system to replace expensive passenger OD surveys. A software tool is created to facilitate the method implementation. Results of the application in CTA are given.

Estimating a Rail Passenger Trip Origin-Destination Matrix Using Automatic Data Collection Systems

Few studies have adequately assessed the cost of transfers 2 in public transport systems, or provided useful guidance on transfer improvements, such as where to invest (which facility), how to invest (which aspect), and how much to invest (quantitative justification of the investment). This paper proposes a new method based on path choice, 3 taking into account both the operator’s service supply and the customers’ subjective perceptions to assess transfer cost and to identify ways to reduce it. This method evaluates different transfer components (e.g., transfer walking, waiting, and penalty) with distinct policy solutions and differentiates between transfer stations and movements. The method is applied to one of the largest and most complex public transport systems in the world, the London Underground (LUL), with a focus on 17 major transfer stations and 303 transfer movements. This study confirms that transfers pose a significant cost to LUL, and that cost is distributed unevenly across stations and across platforms at a station. Transfer stations are perceived very differently by passengers in terms of their overall cost and composition. The case study suggests that a better understanding of transfer behavior and improvements to the transfer experience could significantly benefit public transport systems.

/pdf/assessing-the-cost-of-transfer-inconvenience-in-public-573ru2i9a2.pdf

Nigel H. M. Wilson

Papers

Bus network design

A heuristic algorithm for the multi-vehicle advance request dial-a-ride problem with time windows

The Holding Problem with Real-Time Information Available

Estimating a Rail Passenger Trip Origin-Destination Matrix Using Automatic Data Collection Systems

Assessing the cost of transfer inconvenience in public transport systems: A case study of the London Underground