Tabu search for bus and train driver scheduling with time windows

The bus and train driver scheduling problem involves assigning bus or train work to drivers in such a way that all the bus or train work is covered and the number of drivers and duty costs are minimised. This is complicated by the fact that there are many restrictions on the duty generation. 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 driver duties from which a minimal and most efficient subset is selected. Filtering rules are often applied so that the set of potential duties generated would not be prohibitively large. Moreover, windows of relief opportunities (WROs), which provide ranges of opportunities for relieving drivers, are beyond the capability of being handled by the existing systems. The usual practice is to consider one, sometimes two, discrete times within each time window. Optimality of solution is therefore compromised. The research presented in this thesis focuses on solving the driver scheduling problem with WROs using a constructive approach, which builds and refines a single schedule iteratively. Filtering rules are unnecessary under the approach. The 2-opt heuristic approach is first investigated, during which the potential of constructive heuristics is explored. Based on the experience, the Tabu Search meta-heuristic approach is then investigated. Multi-neighbourhoods and an appropriate memory scheme, which are essential elements of Tabu Search are designed and tailored for the driver scheduling problem with WROs. Alternative designs have been tested and compared with best known solutions drawn from real-life data sets. The tabu search approach is very fast, can handle WROs, and has achieved results comparable to those based on mathematical programming approaches. Taking advantage of WROs, it can improve best known solutions obtained by the existing systems. Consequently, it could be incorporated into existing systems to improve the solution by taking advantage of WROs.

[1]  Lawrence Bodin,et al.  ENHANCEMENTS TO THE RUCUS2 CREW SCHEDULING SYSTEM , 1983 .

[2]  Brian W. Kernighan,et al.  An efficient heuristic procedure for partitioning graphs , 1970, Bell Syst. Tech. J..

[3]  Barbara M. Smith,et al.  Impacs - A bus crew scheduling system using integer programming , 1988, Math. Program..

[4]  Suniel David Curtis.  Constraint satisfaction approaches to bus driver scheduling , 2000 .

[5]  ANTHONY WREN,et al.  A genetic algorithm for public transport driver scheduling , 1995, Comput. Oper. Res..

[6]  Anthony Wren,et al.  An Improved ILP System for Driver Scheduling , 1999 .

[7]  Anthony Wren,et al.  Experiences with a Flexible Driver Scheduler , 2001 .

[8]  Yajie Tian,et al.  A tabu search with a new neighborhood search technique applied to flow shop scheduling problems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[9]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[10]  M Barbara,et al.  Forming Bus Driver Schedules using Constraint Programming , 1999 .

[11]  Raymond S. K. Kwan,et al.  Tabu Search for Driver Scheduling , 2001 .

[12]  Lawrence Bodin,et al.  ENHANCEMENTS TO THE RUCUS-II CREW SCHEDULING SYSTEM. FROM THE BOOK COMPUTER SCHEDULING OF PUBLIC TRANSPORT 2 , 1985 .

[13]  Anthony Wren,et al.  Experiences with a Crew Scheduling System Based on Set Covering , 1988 .

[14]  Prithviraj Banerjee,et al.  ESP: A New Standard Cell Placement Package Using Simulated Evolution , 1987, 24th ACM/IEEE Design Automation Conference.

[15]  Paolo Brandimarte,et al.  Routing and scheduling in a flexible job shop by tabu search , 1993, Ann. Oper. Res..

[16]  Martin Desrochers,et al.  A Column Generation Approach to the Urban Transit Crew Scheduling Problem , 1987, Transp. Sci..

[17]  Yasuhiro Hayashi,et al.  Application of tabu search to optimal placement of distributed generators , 2001, 2001 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.01CH37194).

[18]  Masao Fukushima,et al.  Probabilistic analysis of 2-opt for travelling salesman problems , 1998, Int. J. Syst. Sci..

[19]  J M Rousseau,et al.  HASTUS I: A MATHEMATICAL PROGRAMMING APPROACH TO THE BUS DRIVER SCHEDULING PROBLEM. FROM THE BOOK COMPUTER SCHEDULING OF PUBLIC TRANSPORT , 1981 .

[20]  Victor J. Rayward-Smith,et al.  Modern Heuristic Search Methods , 1996 .

[21]  C. Reeves.  Modern heuristic techniques for combinatorial problems , 1993 .

[22]  PhD DEng D. T. Pham BE,et al.  Intelligent Optimisation Techniques , 2000, Springer London.

[23]  Shen Lin.  Computer solutions of the traveling salesman problem , 1965 .

[24]  D Dupuis.  HASTUS--AN INTERACTIVE SYSTEM FOR BUSES AND CREW SCHEDULING , 1986 .

[25]  S E Elias,et al.  THE USE OF DIGITAL COMPUTERS IN THE ECONOMIC SCHEDULING FOR BOTH MAN AND MACHINE IN PUBLIC TRANSPORTATION , 1964 .

[26]  Anthony Wren,et al.  A bus crew scheduling system using a set covering formulation , 1988 .

[27]  Jean-Marc Rousseau,et al.  Overview of HASTUS Current and Future Versions , 1988 .

[28]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[29]  Jean-Marc Rousseau,et al.  RELAXATION APPROACHES TO LARGE SCALE BUS DRIVER SCHEDULING PROBLEMS , 1982 .

[30]  Hanif D. Sherali,et al.  Equivalent weights for lexicographic multi-objective programs: Characterizations and computations , 1982 .

[31]  Yindong Shen,et al.  Tabu Search for Time Windowed Public Transport Driver Scheduling , 2002 .

[32]  Graham K. Rand,et al.  Computer Scheduling of Public Transport , 1982 .

[33]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[34]  Ann S. K. Kwan,et al.  Hybrid genetic algorithms for scheduling bus and train drivers , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[35]  Sam R. Thangiah,et al.  Computer-aided Scheduling of Public Transport , 2003, J. Sched..

[36]  G. Mitra,et al.  Computer Scheduling of Public Transport , 1982 .

[37]  L K Luedtke.  RUCUS II: A REVIEW OF SYSTEM CAPABILITIES. FROM THE BOOK COMPUTER SCHEDULING OF PUBLIC TRANSPORT 2 , 1985 .

[38]  Helena R. Lourenço,et al.  Multiobjective Metaheuristics for the Bus Driver Scheduling Problem , 2001, Transp. Sci..

[39]  Sarah Fores,et al.  Column generation approaches to bus driver scheduling , 1996 .

[40]  Anthony Wren,et al.  Bus Driver Scheduling — An Overview , 1995 .

[41]  Ana Madureira.  Meta-heuristics for the single-machine scheduling total weighted tardiness problem , 1999, Proceedings of the 1999 IEEE International Symposium on Assembly and Task Planning (ISATP'99) (Cat. No.99TH8470).

[42]  Yves Crama,et al.  Local Search in Combinatorial Optimization , 2018, Artificial Neural Networks.

[43]  Ulrich Faigle,et al.  Some Convergence Results for Probabilistic Tabu Search , 1992, INFORMS J. Comput..

[44]  D. Werra,et al.  Tabu search: a tutorial and an application to neural networks , 1989 .

[45]  Anthony Wren.  Bus scheduling: an interactive computer method , 1972 .

[46]  Martin Desrochers,et al.  CREW-OPT: Subproblem Modeling in a Column Generation Approach to Urban Crew Scheduling , 1992 .

[47]  J W Schmidt,et al.  THE STATUS OF COMPUTER-AIDED SCHEDULING IN NORTH AMERICA , 1980 .

[48]  Jinpeng Li,et al.  A Genetic Algorithm with Fuzzy Comprehensive Evaluation for Driver Scheduling , 2000 .

[49]  Barbara M. Smith.  Bus crew scheduling using mathematical programming , 1986 .

[50]  G. Reinelt.  The traveling salesman: computational solutions for TSP applications , 1994 .

[51]  D. I. Calvert,et al.  Computer Scheduling of Public Transport 2 , 1986 .

[52]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[53]  Raymond S. K. Kwan,et al.  INSTALLING AN URBAN TRANSPORT SCHEDULING SYSTEM , 1999 .

[54]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[55]  C. K. Mohan,et al.  Evolving schedule graphs for the vehicle routing problem with time windows , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[56]  Anthony Wren,et al.  Developments and Recent Experience with the BUSMAN and BUSMAN II Systems , 1992 .

[57]  Raymond S. K. Kwan,et al.  Object Oriented Bus Vehicle Scheduling — the BOOST System , 1999 .

[58]  Jean-Marc Rousseau,et al.  Results Obtained with Crew-Opt: A Column Generation Method for Transit Crew Scheduling , 1995 .

[59]  S Fores,et al.  Driver scheduling by integer linear programming: the TRACS II approach , 1998 .

[60]  Anthony Wren,et al.  VAMPIRES and TASC: two successfully applied bus scheduling programs , 1981 .

[61]  César Rego,et al.  Subgraph ejection chains and tabu search for the crew scheduling problem , 1999, J. Oper. Res. Soc..

[62]  Fred W. Glover,et al.  Ejection Chains, Reference Structures and Alternating Path Methods for Traveling Salesman Problems , 1996, Discret. Appl. Math..

[63]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[64]  Ann S. K. Kwan,et al.  Driver Scheduling Using Genetic Algorithms with Embedded Combinatorial Traits , 1999 .

[65]  Ann S. K. Kwan,et al.  Producing Train Driver Schedules Under Differing Operating Strategies , 1999 .

[66]  Nigel H. Wilson,et al.  Computer-Aided Transit Scheduling , 1999, Lecture Notes in Economics and Mathematical Systems.

[67]  José Vasconcelos Ferreira,et al.  Evaluating a DSS for Operational Planning in Public Transport Systems: Ten Years of Experience with the GIST System , 2001 .

[68]  P M Hildyard,et al.  ADVANCES IN COMPUTER-ASSISTED RUNCUTTING IN NORTH AMERICA. FROM THE BOOK COMPUTER SCHEDULING OF PUBLIC TRANSPORT , 1981 .

[69]  Jean-Marc Rousseau,et al.  ENHANCEMENTS TO THE HASTUS CREW SCHEDULING ALGORITHM. FROM THE BOOK COMPUTER SCHEDULING OF PUBLIC TRANSPORT 2 , 1985 .

[70]  José M. P. Paixão,et al.  COMPUTER-AIDED TRANSIT SCHEDULING: PROCEEDINGS OF THE SIXTH INTERNATIONAL WORKSHOP ON COMPUTER-AIDED SCHEDULING OF PUBLIC TRANSPORT , 1995 .