Raymond S. K. Kwan

A fuzzy genetic algorithm for driver scheduling

Abstract This paper presents a hybrid genetic algorithm (GA) for the bi-objective public transport driver scheduling problem. A greedy heuristic is used, which constructs a schedule by sequentially selecting shifts, from a very large set of pre-generated legal potential shifts, to cover the remaining work. Individual shifts and the schedule as a whole have to be evaluated in the process. Fuzzy set theory is applied on such evaluations. For individual shifts, their structural efficiency is assessed by fuzzified criteria identified from practical knowledge of the problem domain. A GA is used to derive a near-optimal weight distribution amongst the fuzzified criteria, so that a single-valued weighted evaluation can be computed for each shift. The corresponding schedule constructed utilising the weight distribution is evaluated by the GA’s fitness function, in which the two objectives of minimising the number of shifts and minimising the total cost are formulated as a fuzzy goal. Comparative results on real-world problems are presented.

Distributed choice function hyper-heuristics for timetabling and scheduling

This paper investigates an emerging class of search algorithms, in which high-level domain independent heuristics, called hyper-heuristics, iteratively select and execute a set of application specific but simple search moves, called low-level heuristics, working toward achieving improved or even optimal solutions. Parallel architectures have been designed and evaluated. Results based on a university timetabling problem show an important relationship between performance, algorithm software and hardware implementation.

Tabu Search for Driver Scheduling

This paper presents a Tabu Search heuristic for driver scheduling problems, which are known to be NP-hard. Multi-neighbourhoods and an appropriate memory scheme, which are essential elements of Tabu Search, have been designed and tailored for the driver scheduling problem. Alternative designs have been tested and compared with best known solutions drawn from real-life data sets. The algorithm is very fast, has achieved results comparable to those based on mathematical programming approaches, and has many potentials for future developments.

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.

A co-evolutionary algorithm for train timetabling

With many train operating companies sharing limited capacity on the UK rail network, the train timetabling problem is complex and difficult to solve. This paper reports on a cooperative coevolutionary approach for the automatic generation of planning train timetables at the early stages of the timetabling process, when the main objective is to try to accommodate the bids as much as possible and to identify the major conflicts that need resolving by negotiations with the train operating companies. Some test experiments based on artificial problem instances as well as a real network are discussed.

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.

A fuzzy simulated evolution algorithm for the driver scheduling problem

The paper presents a fuzzy simulated evolution algorithm for the public transport driver scheduling problem, which involves solving a set covering model. The novel scheduling algorithm incorporates the idea of fuzzy evaluation into simulated evolution, combining the features of iterative improvement and constructive perturbation, to explore solution space effectively and obtain superior schedules. Experiments with benchmark tests using data from the transportation industry demonstrate the strengths of the proposed algorithm in solving large size real-world driver scheduling problems. It is suggested that this approach might be suitable for other large-scale set covering problems.