Anthony Wren

Bus Driver Scheduling — An Overview

In this paper, presented at the sixth International Workshop on Computer-Aided Transit Scheduling, the problem of bus driver scheduling is introduced, and some of the constraints and conditions existing in different user environments are presented. The way in which such conditions may affect solution methods is discussed.

A genetic algorithm for public transport driver scheduling

Abstract The problem of constructing daily shifts for public transport (generally bus) drivers is explained, and some of the currently available computer based solution methods are introduced. The need for improved methods is set out, and one of the more widely applied current methods is outlined in sufficient detail to show where new approaches may profitably be introduced. A feasibility study is described in which a simple genetic algorithm has been developed in order to examine the suitability of such an approach. This has required the development of a new crossover operator. Such an algorithm could ultimately replace part of the presented existing method, making it more efficient in terms of both of quality of result and of time taken to produce a good schedule. The simple algorithm has been shown to produce comparable results to the existing method on a test problem. The results encourage further investigation, but some complexities which can exist in real problems require further study. The results of the present experiments are presented, and the further complexities are discussed in the context of the genetic approach.

A BUS CREW SCHEDULING SYSTEM USING A SET COVERING FORMULATION

Abstract A bus crew scheduling system which uses mathematical programming is described. The system is based on a set covering formulation, and includes a number of heuristics to keep the problem to a manageable size. It has been in regular use by London Buses Ltd. since the beginning of 1985 and has been adopted by other bus companies. The crew scheduling problem is described, the solution process is presented and results are discussed briefly.

An improved ILP system for driver scheduling

Mathematical programming approaches to driver scheduling have been reported at many previous workshops and have become the dominant approach to the problem. However the problem frequently is too large for mathematical programming to be able to guarantee an optimal schedule. TRACS II, developed at the University of Leeds, is one such mathematical programming-based scheduling system. Several improvements and alternative solution methods have now been incorporated into the mathematical programming component of the TRACS II system, including a column generation technique which implicitly considers many more valid shifts than standard linear programming approaches. All improvements and alternative strategies have been implemented into the mathematical programming component of TRACS II to allow different solution methods to be used where necessary, and to solve larger problems in a single pass, as well as to produce better solutions. Comparative results on real-world problems are presented.

Scheduling, Timetabling and Rostering - A Special Relationship?

Computer solution of timetabling, scheduling and rostering problems has been addressed in the literature since the 1950s. Early mathematical formulations proved impossible to solve given the limited computer power of the era. However, heuristics, often very specialised, were used for certain problems from a very early date, although the term heuristic was not generally recognised until later; a few guaranteed optimality, some consistently produced good solutions, but most became unwieldy when adjusted to deal with practical situations. In some cases, weaknesses in the heuristics were overcome by appeal to manual intervention. Mathematical approaches to some problems returned to favour, successfully, around 1980. Some of the subsequent developments of these are very powerful in practical situations, but they are no panacea, and metaheuristics are the flavour of the nineties.

DRIVER SCHEDULING USING GENETIC ALGORITHMS WITH EMBEDDED COMBINATORIAL TRAITS.

The integer linear programming (ILP) based optimization approaches to driver scheduling have had most success. However there is scope for a Genetic Algorithm (GA) approach, which is described in this paper, to make improvements in terms of computational efficiency, robustness, and capability to tackle large data sets. The question “What makes a good fit amongst potential shifts in forming a schedule?” is pursued to identify combinatorial traits associated with the data set. Such combinatorial traits are embedded into the genetic structure, so that they would play some role in the evolutionary process. They could be effective in narrowing down the solution space and they could assist in evaluating the fitness of individuals in the population.

TRACS II: a hybrid IP/heuristic driver scheduling system for public transport

We discuss the driver scheduling problem in public transport and describe a combined integer linear programming/heuristic approach to its solution. The approach has been applied successfully in many operational and planning scenarios. Recent developments in the algorithms used allow the solution of very large bus and rail problems.

Experiences with a Flexible Driver Scheduler

We present a flexible user-driven ILP tool for the optimisation component of the TRACS II driver scheduling system. The system allows the user to select from a number of objective functions and to drive the LP relaxation through one of a range of optimisation processes. As a default we provide a Sherali objective which minimises the number of shifts, and within that yields the least cost. The default method of solving the LP relaxation is by specialised primal column generation for larger problems, and by dual steepest edge for smaller ones. The LP is capable of working with over 200, 000 previously generated shifts. Once the relaxed LP has been solved, we reduce the size of the problem, and enter a specialised branch and bound procedure. Using real data we show how, by being able to handle larger problems, our system reduces the need for problem decomposition and can produce better schedules.

Experiences with a Crew Scheduling System Based on Set Covering

The embryonic IMPACS crew scheduling system was introduced by Parker and Smith (1), and presented in a prototype form by Wren, Smith and Miller (6) at the 1983 Workshop. The basic form is still broadly similar to that given in (6), but several enhancements have been made, and a decomposition process has been introduced to deal with large problems. The current system is described, apart from the decomposition process, by Smith and Wren (2).

A flexible system for scheduling drivers

A substantial part of the operating costs of public transport is attributable to drivers, whose efficient use therefore is important. The compilation of optimal work packages is difficult, being NP-hard. In practice, algorithmic advances and enhanced computing power have led to significant progress in achieving better schedules. However, differences in labor practices among modes of transport and operating companies make production of a truly general system with acceptable performance a difficult proposition. TRACS II has overcome these difficulties, being used with success by a substantial number of bus and train operators. Many theoretical aspects of the system have been published previously. This paper shows for the first time how theory and practice have been brought together, explaining the many features which have been added to the algorithmic kernel to provide a user-friendly and adaptable system designed to provide maximum flexibility in practice. We discuss the extent to which users have been involved in system development, leading to many practical successes, and we summarize some recent achievements.