Automated Train Scheduling System using Genetic ...

2015 International Symposiwn on Advanced Computing and Communication (ISACC)

Automated Train Scheduling System using Genetic Algorithm Rahul Barman, Chandra Jyoti Baishya, Bandonlang Kharmalki, Aphibakordor Syiemlieh, Kriti Bikash Pegu, Tanuja Das, and Goutam Saha Department of Information Technology North-Eastern Hill University Shillong, India [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Abstractrail

activity

The increment of interest for transport service in stipulates

higher

proportion

of

consumed

infrastructure capacity. In this system of activity stream, even minor deviations from the arranged schedule can affect its stability, and this can bring about a noteworthy diminishment of the nature of transport service. Given the way that the railroad business is as of now running without much abundance limit, better arranging and planning instruments are expected to successfully deal with the rare assets, keeping in mind the ultimate goal to adapt to the quickly expanding interest for rail route transportation. The objective of operational scheduling of trains is to safely move about each train, as fast as possible, from its origin to its destination such that the total delay of all trains can be minimized. This paper presents a (Fixed Path

+

Genetic

Algorithm) heuristic model, an optimization-based approach for scheduling of trains. The Fixed Path model assumes that path of the trains is fixed for preparing the train schedule. The Genetic Algorithm is used for selecting the path for each train that takes minimum time to arrive at the destination. Together it presents a schedule

that

can

minimize

the

travel

maximizing capacity of the network.

time

of

each

train

This paper proves the fact

that applying the proposed model, rail traffic can be improved regarding the increase of the timetable stability and maximizing capacity subject to safety constraints.

Keywords-fixed path; genetic algorithm; heuristic model; rail traffic; train schedule.

I.

INTRODUCTION

The railroad in a few countries, involves an expansive system. The entire system is partitioned into zones and sections such that the operations become manageable. A section can be defined as a portion of the line, between two major stations of a railway network. The entire section is divided into either station section or block section. A section consists of many entities such as the station, main line, control towers, loop lines, electrical equipment, signals, etc. and operates many types of trains. As there is a substantial assortment of trains, like a passenger-freight service, long distance/suburban service, an optimal scheduling strategy should be framed for smooth operation of the section. Because of the expanded use of rail as a method of transportation, more and trains have to access the restricted track assets. In this way, a good schedule for the trains gets the chance to be fundamental with a particular deciding objective

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to keep the rail's crises framework. At the point when the systems are near saturation, a very much outlined schedule can have a noteworthy effect in minimizing the delay. In urban territories, the trackage arrangements are exceptionally complex, contrasted with rural zones where most trackage setups are entirely single tracks with sidings or twofold tracks. A common complex system contains different trackage designs and complex intersection convergences. The issue of discovering the ideal deadlock-free dispatch times that minimizes the delay for trains in such a general system is known to be NP-hard [1]. Huntley et al. [2] built up a framework called computer­ aided routing and scheduling system (CARS) for CSX transportation. The framework optimizes the routing and scheduling problem interactively. The CARS framework uses simulated annealing to perform a global search on the minimwn cost solution. There has been significant earlier works on train scheduling. Cordeau et al. [3] did a survey on both train routing and off-line scheduling. As of late, Caprara et al. [4] did a review on passenger railway optimization, focussing on the European environment more, where passenger trains dominate. Then again, Ahuja et al. [5] reviewed railroad planning and scheduling using network models. Kraay and Harker [6] proposed a model to provide a link between tactical and operational scheduling. They proposed a non-linear mixed integer programming model for the optimization the freight train schedules in real-time. Scheduling of railways is a noteworthy assignment that gives two prompt solutions. •

Allotment of assets to tasks, the assets in the connection of railroads can be classified into tracks, crew and locomotives. The task is the trip which basically includes usage of all the three assets for a solitary task or a trip.

•

Sequencing of the asset usage, this includes distinctive operational standards for the three classes of assets.

Since the tasks require three distinct assets at the same time and under differing allotment standards, the assignment is exceedingly mind boggling. Different arrangements are created for railroad planning with distinctive targets like minimizing tardiness, minimizing aggregate delay and maximizing asset use. The standard methodologies are to get global or local solutions for the above goals under different blends of

framework limitations. The framework limitations are further delegated hard/soft or operational/desirability constraints. To model a real world framework, a substantial number of constraints are required; the issues' intricacy increments with the quantity of constraints considered. Most researchers attempt to provide a planning support for the railways while some desirability constraints are relaxed. Our research is to schedule a close-to-real world passenger railway service. This paper reports a mathematical model of the system and implemented results of our heuristic scheduling procedure. II. A.

B.

Fixed Path Formulation

This is the mixed integer programming model introduced by [10]. The authors in[9] develop a similar model which focuses on passenger railways that we use for benchmarking purpose. We refer the model formulated by [10] as Fixed Path, as the exact path of each train is to be specified prior to solving the model. The Fixed Path model is introduced below: Notations: Set of all the trains to be scheduled Set of all rail track nodes

Length of train q, q E

PROBLEM FORMULATION

Network Construction

The fundamental aim of operational scheduling for trains is to move every train securely from its initial station (origin) to its last station(destination) as fast as would be prudent so that the aggregate delay of all the trains are reduced. The inputs to the scheduling problem are the network trackage configuration and the features of each train (e.g. train speed, length, origin station, destination station, etc.). The output of the train scheduling problem is a detailed set of instructions of train movements (e.g. the tracks each train travels on and when and where to stop for meet/pass) [7]. Deadlocks should not occur in the network this is one of the constraints of the scheduling problem and the minimum headway distance should be obtained between the two trains. For formulating the problem mathematically, the railway network has been translated into nodes and arcs [5], [8] - [9]. Each node represents a train track segment, a station or a junction. Each individual node could have different speed limits imposed on it compared to other nodes. An arc represents the linkage between two nodes. Normally, the length of a junction node and arc element is zero. Each track node has a capacity of one; this means that the track node can be occupied by only one train at any time. And due to this capacity rule, the length of a track node should not be too long; otherwise the track resources cannot be fully utilized. A network construction of a portion of a typical complex railway is shown in Fig. 1 [10]. The length of the train may be greater than the length of a node. Thus, a single train can occupy more than one node simultaneously. As a general rule, a train can go at different speeds. However, we assume trains travel at their maximum speed in order to make the mathematical model simpler. In the following models, speed limits are not imposed on the nodes. Trains pass each node at its maximum speed. Also, the train tracks are divided into nodes with a length that is greater than the maximum length of all the trains. This ensures a single train can occupy at most two nodes at a time while maintaining minimum headway clearance. The schedule specifies the path each train takes and the arrival and departure times of each train on every node of the specified path. The sequence of nodes to be traversed by a train, starting from its origin till it reaches its destination is called the path. Next, we are going to introduce a mathematical formulation of the scheduling problem. This formulation assumes the path for each train is given.

Q, q

=

1,2, ... , IQI

Path train qtakes. Starts with train q's origin

�

�

n

node,

to train q's destination node,n . All the nodes

train qwill be traversing are: {nq.b nq.z, ..., nq Ipq I },

� andnqlpql

wherenq.1 =n

J

�

=n .

The minimal travel time between train q's head

B ,g

entering into node nq.gand train q's tail leaving node nq•g•

t .g

The time train q's head arrives at node q, 9 n

t .g

The time train q's tail leaves fTom node q,g n

� �

/1

Minimal safety headway between two consecutive trains. The binary variable indicates which train gets to pass

Xq1.qZ.k

node kfirst.

1:

train q1passes node kbefore train qz.

0: train qzpasses node kbefore train q1' An arbitrarily large number

M Figure 2 shows the relationship between variables, t�.g, t�.g+b t�,g, B�,g, and BJ,g, Since the length of the train is taken into account, the variable t�,g+l is always smaller than the variable, t�,g. The 0-1 mixed integer programming formulation of Fixed Path is described as follows: (1) such that, t ,g+1 - t ,g �

�

�

J

B ,g'

for all q E

Q and 1

� 9 � Pq 1-

1

for all q E

Q and 1

� 9 � Pq 1-

1

I

t ,g - t ,g+1 � B .g - B ,g'

�

�

J

I

J

B:,IPq I' for all q E Q Xq"q2 kM + t� "g � t�2 h + 111, , ,

tg,IPq 1 - t:,IPq 1 for all q1, qz E

�

(2) (3) (4)

(5) Q and node k = nq"g = nq2,h (1 - Xq"q2,k)M + t�2,h � t�"g + 111, (6) for all qlo qz E Q and node k =nq"g = nq2,h Xq"q2 k = {0,1}, for all q1,qZ E Q and 1 � k � NI (7) , The objective function (1) it minimizes the sum of the arrival times of all trains at their destinations which is equal to the total delay of all the trains. Constraint (2) ensures the minimum travelling time of the train on each track. The equal or greater sign makes it possible for a train to wait for its next required resource to be cleared. Constraint (3) ensures the minimum time a train needs to completely clear its previous occupied resource after its head enters the next node. The deadlock avoidance mechanism is realized by constraints (5) and (6). These constraints together make sure that no more than one train can occupy the same node simultaneously. If train

ql,gets to pass node k before train qz the arrival time of qz at node k has to be equal to or greater than the departure time of ql from node k plus the safety headway of /l, and vice versa.

train if it follows a slower train, from overtaking the slower train.

The Fixed Path model can be utilized to tackle the scheduling issue for any general system, until the length of each node is not shorter than the maximum length of each train. One of the significant drawbacks of the Fixed Path algorithm is, as its name recommends, the exact path of every train should be fixed and serves as the input to the system. Then again, the sequence of nodes a train ventures is a pivotal variable that can influence the trains' delay. Along these lines, the outcomes acquired from this model are sUb-optimal. To make this point clearer, assume we have a single track system with one siding as appeared in Fig. 3.

FIXED PATH FORMULATION

Suppose trains are bi-directional i.e. travels in both directions, from STl to ST2 and from ST2 to STl. Specifying for each train, if it uses siding C' or not is a must if we want use Fixed Path. There may be additional delays to change from the main track to siding C. Accordingly, if there are no trains going the other way in the system, it is not required to dispatch the train to siding C. Else, if two trains are going on the system in inverse headings, one of them needs to go to the siding C to let the other train pass. Subsequently, the ideal way a train ought to take relies on upon the travelling direction and location of alternate trains. Settling the path before taking care of the scheduling issue can prompt an answer a long way from the global optimal solution. And if there are both slow and fast trains on the network, fixing the path might prevent the fast

H

. .I

I

J

I.

III.

PROPOSED ALGORITHM: GENETIC ALGORITHM

The heuristic, called GA + Fixed Path, uses a genetic algorithm to evolve the population of the candidate paths. The Fixed Path model is used to calculate the fitness values for each set of paths. The first step in solving a genetic algorithm problem is to defme the genetic representation of the population and the chromosomes. In GA+ Fixed Path, the set of paths used by trains in GA is termed as chromosomes [11] - [12]. All the possible paths are first numbered accordingly. For the example problem, there is a total of 16 possible paths in each direction. They are numbered from 1 to 16 (see Fig. 4 for the numbering of the paths). Instead of using Os and 1s to represent the chromosome, the chromosome of the GA + Fixed Path model is formed by the numbers that represent the selected path for each train. For the case of six trains, a chromosome might look like: (2, 3, 2, 1, 10, 1). The meaning of this chromosome is that: train 1 takes path number 2; train 2 takes path number 3; train 3 takes path number 2 and so on. With a given a chromosome, the Fixed Path formulation can be used to solve the scheduling problem. The returned delay is treated as the fitness value of this chromosome. Let P denote a single chromosome. The GA + Fixed Path algorithm is described in the flowchart in Figure 5.

r>.,·1

Fig. 1.

Network Construction.

taq , g''') ,

...

i

1 I I

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