Ann S. K. Kwan

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.

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.

Evolutionary Driver Scheduling with Relief Chains

Public transport driver scheduling problems are well known to be NP-hard. Although some mathematically based methods are being used in the transport industry, there is room for improvement. A hybrid approach incorporating a genetic algorithm (GA) is presented. The role of the GA is to derive a small selection of good shifts to seed a greedy schedule construction heuristic. A group of shifts called a relief chain is identi-fied and recorded. The relief chain is then inherited by the offspring and used by the GA for schedule construction. The new approach has been tested using real-life data sets, some of which represent very large problem instances. The results are generally better than those compiled by experienced schedulers and are comparable to solutions found by integer linear programming (ILP). In some cases, solutions were obtained when the ILP failed within practical computational limits.

Hybrid genetic algorithms for scheduling bus and train drivers

Introduces the subject of bus- and train-driver scheduling, and outlines a standard successful approach (TRACS II) using a blend of heuristics and integer linear programming. We discuss a few limitations of this system; in order to overcome these, we have investigated a range of metaheuristics and constraint programming approaches, and some of these are outlined. Finally, we present a hybrid genetic algorithm which is successfully used to overcome the above limitations. In this approach, all probable potential shifts are generated according to well-developed heuristics that are already used in TRACS II. The selection of such shifts to form a schedule is modeled as a set-covering problem, and the relaxation of this problem, ignoring integer conditions, is solved to optimality. A genetic algorithm then develops a solution schedule based on some of the characteristics of the relaxed solution. It is suggested that this approach might be suitable for other set-covering problems.

Effective search space control for large and/or complex driver scheduling problems

Abstract For real life bus and train driver scheduling instances, the number of columns in terms of the set covering/partitioning ILP model could run into billions making the problem very difficult. Column generation approaches have the drawback that the sub-problems for generating the columns would be computationally expensive in such situations. This paper proposes a hybrid solution method, called PowerSolver, of using an iterative heuristic to derive a series of small refined sub-problem instances fed into an existing efficient set covering ILP based solver. In each iteration, the minimum set of relief opportunities that guarantees a solution no worse than the current best is retained. Controlled by a user-defined strategy, a small number of the banned relief opportunities would be reactivated and some soft constraints may be relaxed before the new sub-problem instance is solved. PowerSolver is proving successful by many transport operators who are now routinely using it. Test results from some large scale real-life exercises will be reported.

Producing train driver shifts by computer

The privatisation of British Rail into twenty-five train operating companies and three freight companies has highlighted the need for each company to have efficient operating schedules. Manpower costs are a significant element in any transport organisation and the ability to minimise these costs is seen as crucial to the well running of these companies. In addition the need to try out different operating strategies is gaining importance as the search for cost cutting measures progresses. Building on previous experience, a new rail driver scheduling system, TRACS II, has been developed and used for a number of operating companies. Schedules comparable to, or better than, existing ones have been produced, and the system has been used to test several strategies.

Producing Train Driver Schedules Under Differing Operating Strategies

The privatization of British Rail into twenty five train operating companies and three freight companies has highlighted the need for each company to have efficient operating schedules. Manpower costs are a significant element in any transport organization, and the ability to minimize these is seen as crucial to the effective running of these companies. In addition, the need to try out different operating strategies is gaining in importance as the search for cost cutting progresses.

A hybridised integer programming and local search method for robust train driver schedules planning

When a train arrives at a station, it often stops for some time before continuing, giving rise to a window of relief opportunities (WRO), during which the train may be handed over between drivers. Incorporating these windows into the scheduling model may help improve the robustness and efficiency of driver schedules. However, if it is formulated as a set covering problem, the incorporation of WROs would cause the resulting model to be too big to be solved in realistic times with current technology. In this paper, we propose a combined integer programming and local search approach. In the first step, WROs are approximated, and the problem is solved using integer programming. Using the solution thus obtained as a starting point, WROs are restored and a multi-neighbourhood local search algorithm takes over. We also investigate the possibility of deriving a new set of approximations from the local search solution, and loop back to the integer programming phase. The algorithm is tested using real-life data from a large rail network in Scotland, producing improved, operational schedules for this network.

Critical time windowed train driver relief opportunities

Train driver scheduling is the problem of constructing an efficient schedule of driver shifts, each of which contains a sequence of work on one or more trains separated by breaks. Relief opportunities (ROs) occur when trains stop at a station. While relieving on arrival at a train station is the preferred practice in the UK rail industry, considering relieving at other times within the full window of relief opportunities (WRO) at a stop might allow for a schedule optimization algorithm to build better schedules. However, simply expanding each WRO into ROs at individual minutes within the WRO would exponentially increase the complexity of the combinatorial optimization problem. A rational approach would be to be selective in considering the WROs when applying Generate-and-Select (GaS); this could either take the form of a pre-processing stage to GaS, or that of augmenting (or even replacing) the generation phase of GaS.In this paper we first show a simple example where approximating WROs by a single relief point results in inefficient schedules, and hints at the complexity of exploiting WROs. We then study the potential of WROs in terms of the new spells and/or shifts they may allow to be created. We propose a heuristic extension to the GaS generation phase, where WROs are analysed in relation to individual scheduling constraints; ROs within WROs that are deemed useful are added to the set of arrival-time ROs. Results show an improvement over the traditional approach in a number of real-life instances from UK operations.We also present a constructive method to analyse a combination of scheduling constraints. Results show that the method is effective in exploiting constraints that may be skipped or difficult to consider by non-constructive approaches.