Kaizen

The latest international conference on computer-aid scheduling of public transport was held in June 2000 in Berlin, Germany. During the conference, several transport scheduling packages were exhibited. The following are some examples:

• GIST

GIST (Dias et al., 2000; Lourenço et al., 2000) is a decision support system to assist the planning department of transportation companies or transit authorities in operations management. GIST is designed as a modular system, including the following processes:

network information management, route information management, timetabling management, vehicle scheduling, crew scheduling, and crew rostering. GIST gives special attention to interactive facilities and friendly interfaces, combined with optimisation tools.

GIST models the crew scheduling problem as a single objective linear programming problem to minimise the cost. Lourenço et al (2000) indicate that the bus companies involved in the GIST project have not been satisfied with the bus-driver module based on the single-objective LP,

even though the optimal solution could be obtained. Therefore, Lourenço et al (2000) present a multi-objective meta-heuristic approach for the bus-driver scheduling problem. Lourenço’s approach aims to solve the driver scheduling problem in a user-friendly environment. The approach has been incorporated in GIST and can obtain many alternative solutions in a short time, but the detail has not been published yet.

• Trapeze

Trapeze (see http://www.trapezesoftware.com/index.html) is a commercial package of Trapeze Software Group, Canada. It provides transport software for public transport, dial-a-ride, student transport, medical transport, and other community transport services. It includes a function for scheduling public transport drivers. In the exhibition, a demonstration of driver scheduling was given. Trapeze produced a solution very quickly but the quality of the solution was difficult to judge and no information on the technique used was made available.

• HASTUS

HASTUS (see http://www.giro.ca/) is the result of over 20 years of ongoing research and development at GIRO, in collaboration with the University of Montreal’s Centre for Research on Transportation. The latest version of HASTUS, called HASTUS 5, offers an integrated transit database and a set of application modules, e.g., HASTUS-Vehicle, which generates vehicle timetables and vehicle schedules; HASTUS-Crew, which produces crew schedules, and HASTUS-Roster, which automatically generates multi-day operator assignment. The approach used in the crew scheduling component is described in (Rousseau and Desrochers, 1995) (see Section 2.3.4).

2.7 Conclusions - generate-and-select approach vs. constructive approach

This chapter has reviewed the driver scheduling approaches, which can be roughly divided into two groups: generate-and-select approach and constructive approach.

The generate-and-select approach is at present the most successful for bus and train driver scheduling. It involves generating a set of legal potential duties from which a minimal and most efficient subset is selected. The generation process is problem-oriented while the selection process can be algorithm-oriented. After generating a set of duties, a solution may be found by a variety of selection methods, such as mathematical programming, evolutionary algorithms, constraint programming, etc. This makes the approach adaptable to different situations although the generation algorithm is likely to be adjusted depending on the situations. Most approaches used in present commercial systems such as TRACS II and HASTUS can be regarded or implicitly regarded as generate-and-select approaches. The recent researches of Kwan et al, Li and Kwan, and Curtis et al are also based on the generate-and-select approach (see Sections 2.4 and 2.5). Unfortunately, the number of potential duties is usually enormous, which precludes the selection methods from finding an optimal solution in practical time. It is therefore inevitable that some restrictions have to be imposed to limit the set of potential duties to within an acceptable size or search depth, etc. Optimality is therefore compromised. Moreover, manipulation of the parameterised restrictions is usually hard for non-experienced users.

In contrast, a constructive approach, which constructs an initial schedule and then refines it iteratively, has no need of artificial rules or explicit reduction in problem size. Obviously for constructive approaches, the fewer rules that are imposed on the validity of a driver duty, the easier it is to construct a solution. Moreover, the more relief opportunities that are provided in

the blocks, the more chance it has to refine the schedule. Windows of relief opportunities provide ranges of opportunities for drivers to change over. The constructive approach could take benefit of windows of relief opportunities to refine schedules with more flexibility in recutting blocks. This opens up the opportunity of building a realistic model with a chance of obtaining ‘good’ solutions.

The early heuristic systems (see Section 2.2) are based on the constructive approach.

Unfortunately, the refinement functions, where one was used, were very weak. They relied on good initial schedules constructed based on human schedulers’ knowledge, such as in TRACS and RUCUS, and hoped to get a good final solution by simple refinement. This is the reason that the early heuristics tended to require much effort to be adapted to new situations. Also, extensive final manual adjustments to the schedule were needed. Possibly none of the early heuristics are still in use. Cavique et al’s tabu search approach (see Section 2.4.1) is of a constructive type. The refining algorithms Cavique et al used are more powerful than those in the early heuristic systems because a tabu search technique is applied, which can help escape from local optima. However, Cavique et al’s algorithms only construct duties with up to two spells, aim to minimise only the number of duties but not the cost, and are only evaluated for Lisbon Underground. The algorithms may not be suitable for most other practical situations.

The early constructive approaches have been abandoned. Instead, the generate-and-select approach is at present the most successful for bus and train driver scheduling. However, the advantages of constructive approaches can overcome some limitations inherent in generate-and-select approaches. Furthermore, the modern computing power and modern searching methods make good refining algorithms possible. Unfortunately, the solution quality of a constructive heuristic approach is difficult to guarantee.

The research presented in this thesis will investigate a constructive approach to tackle the bus and train driver scheduling problem with windows of relief opportunities, which the generate-and-select approach cannot handle. The initial research is on 2-opt heuristics presented in Chapter 3, based on which further research into a tabu search meta-heuristic approach is presented from Chapter 4 onwards.