Other Approaches The Current Bus Crew Scheduling Approaches

Abdul Samad Shibghatullah 27 30052008

2.3.4 Other Approaches

In this subsection we discuss approaches that do not belong to heuristics and mathematical programming. These approaches include genetic algorithms Wren and Wren, 1994; Clement and Wren, 1995; Kwan et al., 1999, tabu search Cavique et al., 1999; Shen and Kwan, 2001, ant system Forsyth and Wren, 1997, and constraint programming Layfield et al., 1999. Wren and Wren 1994 carried out a feasibility study to test whether or not genetic algorithms could be used to solve larger crew scheduling problems more robustly, more quickly, and more cost-effectively than other methods. The bus schedules are represented as chromosomes and the values of each gene identifies the duties that cover it. Then duties are discarded or chosen from the complete set until the bus work is covered and no duty is redundant Wren and Wren, 1994. Processes based upon genetic algorithm techniques of crossover forming a schedule from a combination of two or more others and mutation slightly altering a schedule in some small way can be applied to the schedule in the hope of producing better solutions and allowing a limited number of schedules to evolve. Results obtained using genetic algorithm approaches without the option of mutation, and with limited constraints on small test problems, produced very good solutions quickly, encouraging further investigation. Further work was carried out by Clement and Wren 1995, which depicted chromosomes as an unordered set of duties, each with a binary value dependent on whether or not the duty is present in schedule. Different methods of crossover and mutation techniques were experimented with and tested on three real world problems. Although the genetic algorithm was successfully applied to real world scheduling problems with relatively limited research, the results produced were generally poorer than those of more established techniques Clement and Wren, 1995. The method by Clement and Wren 1995 was subsequently modified by Li and Kwan 2003 by incorporating fuzzy set theory. Li and Kwan 2003 used a greedy heuristic method to collect sets of duties. These sets are then evaluated using fuzzy set theory. A genetic algorithm with fuzzy evaluation is processed repeatedly in a number of steps. The objective is to find a schedule cover with minimum cost using the minimum Abdul Samad Shibghatullah 28 30052008 number of duties. The genetic algorithms are used to fine-tune the objective by evaluating the structure using multi-starting points. This is done repeatedly in five steps. The main finding is that the approach produces a near-optimum weight distribution for large size real life problems. Tabu search is an iterative technique that moves step by step from an initial solution towards a solution close to the global optimum. Cavique et al. 1999 used tabu search to reduce the number of pre-generated shifts. The algorithm iteratively removes some inefficient shifts, and sometimes their adjacent shifts from the current solutions, and then applies the re-cutting algorithm to construct shifts to repair the broken schedule. The result was found very efficient at improving the initial solution after the first few iterations, but it was then found it difficult to make further improvements. Shen and Kwan 2001 developed HACS Heuristics for Automatic Crew Scheduling, which also used a tabu search to get rid of infeasibility shifts and fulfill the objectives. Four neighborhood structures were applied, namely: swapping two links, swapping two spells, inserting one spell, and recutting blocks. The first three concentrate on refinement of links with fixed relief opportunities, while the last one considers variable active relief opportunities while links are reconstructed. HACS starts from a rough initial solution, and can deal with complex problems by simply adjusting the cost function and the penalty function to the rules stipulated in specific problems. Ant colony optimization was developed by Dorigo et al. 1995 based on the behaviour of ants searching for food, which can be modelled into a search algorithm. The fundamental idea is that when ants move they leave pheromone trails that can be detected by other ants and which slowly evaporate over time. Forsyth and Wren 1997 used virtual ants to trace paths through a bus schedule with the paths representing crew duties to create crew schedules from pre-generated duties. Each ant will create a solution at each iteration. A heuristic approach is used to select relief points, and then the ant chooses a duty from the set that starts at that relief point. The process repeats until the entire bus works are covered. Good duties will be used more often by the ants and be more likely to be chosen for a crew schedule. Abdul Samad Shibghatullah 29 30052008 Constraint programming provides a powerful and easy system for modelling restrictions and using these restrictions to search for a solution Tsang, 1993. Layfield et al. 1999 used constraint programming to remove relief points that are unlikely to be used in good schedules, thus reducing the problem size. The program first produces the morning part of the schedule simulating the manual scheduling process. It puts a limit on the number of spells to prevent too short duties being produced. A morning schedule is constructed by using randomised heuristics to build the partial schedule one duty at a time. Several morning schedules are constructed, and the relief points not used in these schedules are removed. Then the algorithm performs iterative process to construct a feasible crew schedule that satisfies all the constraints. This program can also be used to produce the evening part of a schedule. The process has speeded up TRACS II in several cases, but its solution cost is mostly slightly higher Layfield et al., 1999.

2.3.4 Critiques of the Current Approaches