Los determinantes institucionales

Rescheduling Problems

As with single objective rescheduling problems, EC techniques are less commonly employed than non-EC techniques. Very few produce a POS of trade-off solu- tions. Table 3.3 gives a summary of current research using EC techniques for multi-objective railway rescheduling problems. In nearly all cases the researchers choose to combine the objectives into a single, often weighted, objective to produce a single solution.

Wegele and Schnieder [12] considered two objectives, minimising total delay penalty and minimising the use of a different gate to that published in the time table. They combined both objectives into a single objective and solved it with a three-part system consisting of a BB method to find the starting solution; a GA to improve the starting solution; and a conflict tree, based on a Unified Modelling Language (UML) sequence diagram, to analyse the trains interactions and to check for conflicts. They evaluated their system on a Petri net model of 1% of the German railways network in Northern Germany which incorporated both single and double track railway lines and included 104 stations with over 1000 passenger and freight trains in a 24 hour period. They found that the algorithm could find a solution very quickly, in around 3 min, and that this solution was only 11.2% worse than an optimal solution created by assuming none of the trains conflicted with each other. Chang and Chung [13] considered the multiple objectives of minimising train

running time, dwell time, minimum headway, average travel time, timetable devi- ation and maximising train load. They based their work on a homogeneous Mass Rapid Transit (MRT) system in Taipei. To solve the problem they combined the objectives into a single objective and solved it with a GA where the chromosome encoded the timetable in the form of chains of trains at the switches and signals. To examine how their system could handle rescheduling they considered two scenarios: the first involved a surge in the passenger flow at one station, the second involved delaying the 23rd train in the schedule by 300 s. Their results showed that the algorithm responded to a surge in passengers by increasing the average number of trains that passed by the affected station from 4 to 6. It achieved this by reducing the dispatching headway of the trains and decreasing the running time and dwell time. Their algorithm also responded well to a delay in one of the trains. After 10 minutes, it had produced a new schedule close to the original timetable and reduced the total delay. To make the rescheduling process faster, they employed a chromo- some mask which limited the activity of the algorithm to only the trains affected by the disruption. In addition they seeded the rescheduling population with the existing schedule.

This work is limited by the fact that it has been applied only to a fairly simple train scenario, that of homogeneous trains all travelling in the same direction. A further problem with the system is that it relies on knowing exactly where each train is at any particular moment in time. This requires an expensive and reliable infrastructure that allows the precise position of each train to be pinpointed. This is not available in many countries, particularly the UK, at this present time. Further, the stopping condition for the algorithm is that of finding a feasible solution that does not violate running time, headway or dwell time constraints. There is no way of knowing if this is the optimal solution.

Zhao et al.’s [14] considered the two objectives of minimising total delay penalty and minimising energy usage. Their aim was to discover an optimal speed profile for each train that followed a delayed train where the speed profile describes the speed that each train should travel between each station. They combined the objectives into a single weighted fitness function with different weights to represent different driving styles, for example weights of 6:4 placed a stronger emphasis on minimising delay and resulted in an objective that gave a priority to reducing journey time whereas weights of 4:6 placed the emphasis on reducing energy usage. They de- veloped a multi-train simulator to test their approach involving four trains along a 27.5 km single track with three stations. They compared the performance of three algorithms, an enhanced brute force (EBF) method, an ACO algorithm and a GA.

The EBF method was enhanced by only considering trains with a speed greater than plus or minus 10 km from the estimated speed to constrain the size of the problem and to reduce the computation time. In the ACO algorithm, each node to be chosen by an ant consists of a train and a speed between two stations. In this way the ants chose speed profiles for each train in turn. For the GA, each chromosome encodes a set of target speeds for the trains. The GA and ACO algorithms were run until a target number of iterations had been reached or there had been no change in the best solution for a set number of iterations. To create the delay scenario, the first train was delayed by 120 s. Only the speed profiles of the trains that followed the delayed train were optimised, the delayed train itself was run as quickly as possible, within the line speed limits, to catch up with the timetable.

They found that both the GA and ACO were able to find solutions close to the optimal found by the EBF algorithm, but with significantly lower computation times. The ACO and GA algorithms took from 7.5 to 10.5 min to find a solution while the EBF took over 29 hours. All algorithms produced solutions better than running without any optimisation, for example the GA produced solutions with a 17.9% reduction in total cost compared to running without any optimisation algo- rithm. This work is interesting in that it considers both accumulated delay penalty and energy usage. However, using a single weighted fitness function means that to find the results for different driving styles the algorithm had to be run several times with different weightings. In a real-world delay scenario, there may not be enough time to do this.

Pochet et al. [15] considered the bi-objective problem of minimising deviation from the target headway and minimising delay at critical points. This allowed them to simultaneously attempt to maintain both regularity and punctuality. Although they had multiple objectives they returned a single solution for each scenario. They were concerned with the problem of managing delay when there are two types of trains in the network; those that use communication based train control (CBTC) and those that do not. In a CBTC system the position of trains can be accurately determined and maintained by controlling the train’s speed and acceleration while it is running. Such trains use a moving block signalling system, as opposed to the fixed- block signalling system of non-CBTC trains. This allows CBTC trains to operate with shorter headways and increases the capacity of the railway line. However, mixing the two types of trains together on one line increases the complexity of the rescheduling process. They considered trains travelling in one direction on the East/West line in the region of Paris taking in 14 single track segments, six stations and five trains.

To tackle the problem they developed a GA that encodes the percentage increase or decrease in running or dwell time of each train at each of the stops on its route. The non-CBTC trains were not considered in the chromosome but were incorporated as constraints. They compared the results of the GA with a basic regulation method which consisted of reducing the running time of delayed trains as much as possible until the delay was recovered. They found that the GA improved punctuality and regularity when the objectives were conflicting and when disturbances were large (over 260 s). This is an interesting approach to the problem of dealing with delay scenarios involving a mixture of CBTC and non-CBTC trains. However, it does not change the running times of the non-CBTC trains, which means that there may be a possibility for further improvement if the non-CBTC trains were also allowed some flexibility. In addition, although they used two objectives they returned only a single solution, which implies that the objectives have been combined in some way. In all of the above work the objectives are combined into a single weighted objective to produce a single solution. Although, in a way, this appears to be an easy and more straightforward approach, it raises questions about how to combine the objectives. The decision about the relative importance of each objective requires domain knowledge and can never be adjusted to reflect a dispatcher’s priorities at a particular moment in time. Using a multi-objective algorithm (MOA) instead would enable a set of trade-off solutions to be given to the dispatcher to allow the dispatcher to make an informed decision based on the circumstances at that point in time. In effect a MOA removes the guesswork when setting up the algorithm. This can only be a good thing in terms of giving dispatchers all the information they need to make informed decisions.