5.2 Proposed MOACO Algorithms for the DM-RJRP
5.3.4 Algorithm Computation Times
The experiments were run on a 2.9GHz Intel Xeon E5-2666 v3 (Haswell) processor. Table 5.7 shows the average execution times for dynamic scenarios m = 2, f = 15 and m = 8, f = 5. The times are shorter than those in Chapter 4, Section 4.5.3 because the experiments were run on a faster processor. These two scenarios were chosen as they are the extremes of the delay scenarios. The timing results for all algorithms were similar, therefore only the results for DM-PACO-R are shown.
Over all changes, when two trains are added every 15 m (m = 2, f = 15), the average execution time is less than a minute. However, when eight trains are added every five minutes (m = 8, f = 5), the large number of trains in the problem increases the work of the simulator and results in an average execution time of 11.50 m for change 12. This large computation time is, of course, unacceptable in a real- world situation. However, it could be reduced by choosing a different termination condition, e.g., running the algorithm until there has been no improvement in the solutions for a predefined number of iterations. In addition, ACO is very amenable to being run in parallel [22], which would cut down the computation time considerably and make it feasible for real-time operation.
5.4
Summary
In this chapter, the dynamic Stenson junction simulator from the previous chapter has been extended to introduce a second objective, that of minimising additional energy consumption. This has enabled an investigation into the application of ACO algorithms to a dynamic multi-objective railway rescheduling problem. The investi- gation of DMOPs in the railway industry is a little explored area, as is the application of ACO algorithms to such problems.
An additional goal of this work was to attempt to identify the features of an ACO algorithm that make it suitable for coping with both the dynamic as well as
multi-objective nature of this problem. The study involved the use of several multi- objective ACO algorithms. Two of the algorithms were based on multi-objective P-ACO, the others were based on different variations of a multi-objective MMAS algorithm where the aim of the modifications was to improve the performance of the algorithm on the DM-RJRP.
It is apparent that all the ACO algorithms can find a POS of solutions for the DM-RJRP. However, the algorithm based on P-ACO performs better than the algorithms based on MMAS. The performance of multi-objective MMAS can be improved, on this problem, by retaining the non-dominated archive between changes. However, for a comparable performance with DM-PACO-R, on scenarios with large and frequent changes, multi-objective MMAS also benefits from retaining the pheromone trails between changes. The best performing algorithm DM-PACO-R also outperformed NSGA-II and FCFS.
An interesting observation in this work is that a scenario that was more difficult for the algorithm to solve in the dynamic single objective version of this problem was not necessarily the most difficult scenario to solve when the problem was made multi-objective. This suggests that the problem difficulty is not only influenced by the magnitude and frequency of dynamic change but also by the interaction between the objectives.
This work has concentrated on modifications to the algorithm after it encounters a dynamic change. It is feasible that the internal mechanisms of the algorithms may also have an effect on their ability to solve this DMOP. For example, DM- MMAS updates the pheromones with the best iteration ant in each objective while DM-PACO updates with the ants in a memory created from the non-dominated set. In addition, it is possible that NSGA-II’s performance could be improved by modifications to make it able to retain information between changes such as the introduction of elite immigrants. In future work, the aim is to investigate the effect of these internal mechanisms on the algorithms’ performance.
The fact that the model used to explore this problem simulates the physical movement of trains through the junctions, means that on the high magnitude, high frequency changes the time taken to produce a solution is unrealistically long. In addition, this work is focused on a small area of the railway network and does not take into account the effect that changes made in a local area will have on the global behaviour of the network. For this reason, the railway model created for the next chapter is an event-based, macroscopic model of the railway that takes into account the movements of the trains between timing points on a train’s journey. This new model allows the assessment of the impact local decisions, made at the station, have
Station Rescheduling in Dynamic
Environments
It is very apparent, when commuting from Leicester to Nottingham, that delays to trains arriving at Leicester station are a common occurrence. A delayed train will miss its scheduled time slot on the platform and will have to be reallocated to a new time slot either on its original platform or on a different platform. The reallocation may results in secondary delays to trains that may have to be delayed themselves to allow the delayed train to be accommodated. This raises the question of whether it is possible to use ACO to determine the best platform to allocate to a delayed train to minimise the overall delay in the system. However, it is not enough to make a local decision about the best platform to place the platform on as this does not take into account the ongoing journeys of the affected trains. Therefore, one of the aims of the work, in this chapter, is to not only investigate reallocating trains to new platforms but to take into account the effect the local reallocation decisions have on subsequent conflicts at the timing points on the remainder of each train’s route.
The potential usefulness of this forecasting approach was illustrated by a dis- cussion with the Station Master and his dispatch team at Birmingham New Street station. They revealed that often, when reallocating delayed trains to platforms, they will look ahead to the rest of the trains journey to see the impact the lo- cal rescheduling decision will have. If part of this process could be automated it would allow the dispatcher to consider the ongoing effect of many more rescheduling options in the short time they have available to reschedule delayed trains.
The motivation behind this work was the desire to demonstrate the applicability of ACO algorithms to a real-world problem and to provide a step forward in the development of a real-time dispatching system that could be used to help decide which platform to allocate to a delayed train to minimise delay. To make the problem
as realistic as possible a model of the station was created using Network Rail’s schedule data from the Integrated Train Planning System (ITPS) [30]. The model details both the movement of trains through the station and the movement of all trains at each of the timing points on the trains’ routes. This allows the long-term consequences of the reallocation decisions to be determined. The use of real schedule data makes the results applicable to a real-world dispatching system as the same data is available to the dispatchers when rescheduling trains.
Real world train delay data is not available for the British railway network at the current time. Network Rail produce a train movements data feed which could be used to monitor delay but as there is no information about the cause of the delay it would be unfair to compare the results of the real delay resolution with the solution found by the algorithm. For example, if the real delay was caused by a track block- age, the ACO algorithm would have no knowledge of this and may find an improved solution because it included the blocked track section in its rescheduling decisions. Therefore, in order to investigate the effect of the magnitude and frequency of the delay on the performance of the algorithms, different magnitudes and frequencies of delays were simulated in the model.
The problem of reallocating trains to platforms after a delay can be divided into two sub-problems. The first problem is to decide the platform to allocate to the delayed train (the reallocation sub-problem); the second is to decide the order that the trains should leave the station (the resequencing sub-problem). Solving these sub-problems can allow trains to overtake other trains at the station. This is important because often the limitations of the railway infrastructure means that overtaking is only possible at stations [21]. In this work two colonies of ants have been used to address each of these sub-problems. Investigations have been carried out to examine the effectiveness of using each colony separately and of combining them into a multi-colony algorithm.
The unique contributions of this chapter are:
• The creation of a dynamic benchmark problem for a dynamic station reschedul- ing problem based on Network Rail’s schedule feed.
• A contribution to the field of understanding of how ACO algorithms can be applied to the field of dynamic railway rescheduling, specifically dynamic plat- form reallocation and resequencing.
• The creation of a unique framework that combines two colonies of ants, one that reallocates trains to the platforms after a delay and the other that deter-
In addition a novel best-ant-replacement scheme has been introduced in this work that takes into account not only the delay that results from a particular set of platform reallocations but also the physical distance between the train’s original and its new platform. Results showed that this modification worked well to minimise platform displacement where platform displacement is a measure of the physical distance between a train’s original platform and its reallocated platform. The smaller the platform displacement the shorter the travel distance from the train’s original platform to the reallocated platform and the smaller the inconvenience to passengers and rail crew.
To evaluate the effectiveness of using ACO algorithms for this problem, their performance is compared with those obtained using TS, VNS and running with no platform reallocation or resequencing (NO-ALG). TS has previously been used by Corman et al. [54] for railway rescheduling while VNS has been applied by Sam`a et al. [10]. In both cases, the algorithms were used within the AGLIBRARY optimisation solver of ROMA and were found to improve performance.
Part of this work was previously published in [123].