1
USE OF A HYBRID ALGORITHM FOR MODELLING
COORDINATED FEEDER BUS ROUTE NETWORK AT SUBURBAN RAILWAY STATION
Shrivastava Prabhat, M.ASCE1 and O’Mahony Margaret2
ABSTRACT
In the metropolitan cities of developed and developing countries, longer journeys are mostly performed
by two or more modes. In the event of availability of suburban trains and public buses, commuters prefer
to travel a longer stretch of their journeys by train, so as to avoid traffic congestion on roads, and the
remaining part by buses to reach local areas if their final destination is not in close proximity to railway
stations. Normally suburban trains have fixed corridors and buses have flexibility to serve remote local
areas. Thus design of feeder routes from railway stations to various destinations and the transfer time
from trains to buses play a very important role and can be controlled by transport planners.
A
considerable amount of research has been done on independent design of a bus route network without
considering the effect of train services. Researchers have made attempts using heuristics, simulation,
expert systems, artificial intelligence and optimization techniques for design of routes and schedules. So
far, limited effort has been made in modelling coordinated operations. In this research, a new hybrid
algorithm which exploits the benefits of Genetic Algorithms and a well tested heuristic algorithm for the
study area is discussed. More convincing results in terms of feeder routes and coordinated schedules at
the selected railway station are obtained by the proposed hybrid algorithm as compared to earlier
approaches adopted by the authors for the same study area.
CE DATABASE SUBJECT HEADINGS: Routing and scheduling, Genetic Algorithms, Optimisation,
Hybrid Algorithm, public transportation, Intermodal coordination, Heuristic Approach, Transportation
Planning
1
Professor (Transportation Engg), Civil Engg Dept., Sardar Patel College of Engg., Andheri (W), Mumbai, India
& Head Dept. of Civil, Struct & Env Engg, Director , Centre for transp Research, Trinity College, Dublin-2, Ireland
2,Professor
2
INTRODUCTION
In metropolitan cities of developed and developing countries significant growth of private and
intermediate transport has taken place. Due to this growth and limited capacity of carriageways, traffic
congestion, environmental pollution, poor level of service and longer travel times are very common.
These problems can be solved only by reducing dependency on private vehicles. The dependency can be
reduced only by making public transport more efficient. The efficiency of the public transport system can
be enhanced by better integration of its various components. Most metropolitan cities have suburban
railway and public buses as major public transport facilities. Feeder bus routes and coordinated schedules
critically determine the performance of an integrated public transport system specially when longer
journeys are made by suburban trains and public buses feed the local areas. The purpose of this paper is to
develop a methodology for development of feeder routes for public buses and also to develop coordinated
schedules of public buses for the existing schedules of suburban trains at a suburban railway station.
The heuristic approach had been very popular for bus route network design problems. In places
where practical realistic solutions are more important than optimal solutions one can opt for the heuristic
approach. Using intuition and experience the analyst may be able to guide the heuristic search process far
more efficiently than a predetermined set of rules. Good heuristics have obvious advantages over the
more standard algorithms of combinatorial optimization (Reklaitis et al, 1983). Desirable characteristics
of the heuristic process include execution in reasonable computational time, solutions which are close to
optimality on average and the simplicity of both design and computational requirements. In the case of
route design, the designer has to strike a balance between satisfaction of demand at various destinations
and shorter lengths of routes. Shrivastava and O’Mahony (2007) have discussed in detail about the
application of an heuristic approach in development of routes or network of routes.
The transit network design problems become more complex due to the difficulty in combining
user costs and operator costs in a single objective function. Non-linearity and non-convexities are
involved in the objective function along with the discrete nature of route design and various other
constraints relating to route coverage, route duplication, route length and directness of service. Thus
3
complexities involved in network design problems necessitate intelligent searches and the use of robust
optimization techniques. Application of Genetic Algorithms for route scheduling and network design
problems has been discussed in detail in Shrivastava and O’Mahony (2007) and Shrivastava and
O’Mahony (2006). .
Limited efforts have been made for the design of feeder route networks for feeder buses at
railway stations (Shrivastava and Dhingra, 2000). However, Wirasinghe (1980), Geok and Perl (1988)
attempted routing and scheduling problems for coordinated operations using analytical models. They had
considered a highway grid which is assumed to be rectangular and parallel to a single railway line which
may not always be true in practice. They had made an attempt to describe complex transit systems by
approximate analytical models. Zhao and Ubaka (2004) presented a mathematical methodology for transit
route network optimization. The objective was to minimize transfers and optimize route directness while
maximizing service coverage.
The authors have communicated research papers on development of feeder routes for the same
study area using different approaches. This paper builds on the work of earlier research papers and
contains significant differences from previous work. In other words it inherits the best qualities of earlier
papers. In Shrivastava and Dhingra (2001) feeder routes were generated with the help of a heuristic
algorithm which was suitable for the typical case study. The heuristic algorithm does not promise an
optimal solution but it may give a near optimal or suboptimal solution. In Shrivastava and O’Mahony
(2006) a Genetic Algorithm has been used for simultaneous development of feeder routes and schedules
but it was found that demand at all nodes is not satisfied. This is because in the typical study area under
consideration some of the nodes are connected in the form of a chain without any additional connectivity
with any other node / nodes. Thus very limited alternatives are available for such nodes and even with
higher penalties demand remains unsatisfied. In Shrivastava and O’Mahony (2007), well scattered nodes
are selected as potential nodes and an heuristic algorithm is used as the repair algorithm. This research
work differs from earlier work of the authors in following ways:
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
The demand at nodes (destinations) is given priority for development of routes over the location of
nodes. Thus nodes with more than average demand are identified as potential destinations.

In the case of any network, if higher demand nodes are located on the outskirts of the study area then
the heuristic algorithm acts as repair algorithm otherwise the genetic algorithm develops a partially
optimized network giving due consideration to higher demand nodes.

After development of the partially optimized network the heuristic algorithm further modifies the
network. In the modification process using the heuristic algorithm again the demand of nodes is given
priority for development of the route system.

The proposed approach in this paper is oriented towards demand satisfaction of nodes but their
locations are also given due consideration for modification of routes which is the key idea for
development of networks especially in the context of the public transport system.

A judicious use of both genetic algorithms and heuristic approaches can be seen in this research. If
the higher demand nodes are close to the DART station then the heuristic algorithm plays a major role
and if higher demand nodes are well scattered and away from DART station then the genetic
algorithms plays the main role.
In this paper, first potential destinations having more than average demands are identified and
with k – path algorithm and Genetic Algorithms an optimized feeder route structure is developed. This
route structure is modified with heuristic algorithms so that all other nodes having less demand are
connected. Thus in this process an optimized feeder route structure is developed by Genetic and K – path
algorithms which is desirable because nodes with higher demand should be given priority over lower
demand nodes. Lower demand nodes are connected to the developed route structure by a heuristic
algorithm. Thus a judicious use of both the algorithms is shown in this paper.
In this research the Shrivastava - O’Mahony Hybrid Feeder Route Generation Algorithm
(SOHFRGA) which is a combination of Genetic Algorithms and Heuristic Approach has been developed.
It has been found that the feeder routes developed by SOHFRGA are more efficient than those developed
5
by authors using other approaches. Dun Laoghaire is a rapidly growing suburb in Dublin city of Ireland
and DART station is selected as the study area for coordination between Dublin buses and DART
services. Assessment of the number of commuters currently using DART services, the percentage of
commuters using Dublin buses after arriving by DART at Dun Laoghaire and the number of commuters
who would shift from other modes to bus is discussed in previous research papers i.e. Shrivastava and
O’Mahony (2007) and Shrivastava and O’Mahony (2006). Table 1 indicates potential demand to various
destinations which includes current demand by buses and the expected shift of commuters from other
modes. Readers are advised to refer to the above papers for further details of the study area and data
collection
PROPOSED METHODOLOGY
The overall methodology for development of feeder routes and coordinated schedules is indicated in
figure 1. As discussed in Shrivastava and O’Mahony (2006) and Shrivastava and O’Mahony (2007) the
potential demand is assessed, travel time matrices are developed, other parameters and values have been
decided (refer to steps 1, 2 and 3 of proposed methodology in the above papers). The remaining
methodology used in the research presented here can be explained in the following.
(1) Feeder routes are developed by Shrivastava – O’Mahony Hybrid Feeder Route Generation Algorithm
(SOHFRGA). Figure II indicates the various steps involved in SOHFRGA which are described
below.
Step I:
Identification of Potential Destinations
From the traffic surveys, demand at various destinations (nodes) is identified. The destinations having
more than average demand were identified as potential destinations. This has been done in order to
develop an initial feeder route network for potential destinations. In doing so the demands at potential
destinations get satisfied by shorter routes and then other nodes of which demand is less than average are
inserted / attached to developed ‘K – Paths’ using the heuristic algorithm. This is explained in later steps.
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The preference is given to small number of routes with higher percentage of demand satisfaction with
lower travel time. Large number of routes will be generated if K- Paths are developed for each
destination. Large number of routes will require more buses and also some routes will be very short and
some may be very long, which will pose problems in the scheduling process. Buses will have to be
scheduled on many routes where demand may not be substantial which will lead to uneconomical
operations. In view of this K – Paths were developed for destinations with demand more than average
with upper limits on lengths of routes.
Step II:
Development of K –Paths between Origin (DART station) and Potential Destinations
There were five potential destinations having more than average demand from the DART station. With
the help of K-path algorithms (Eppstein, 1994) five short paths between origin (DART station) and each
potential destination were developed. Thus between each pair of origin (DART station) and potential
destination five alternative paths were available for further analysis as explained in the next step.
As there were 16 destinations to which demand from DART station exists, out of these 16 destinations
five had more than average demand and thus selected as potential destinations, remaining 11 nodes
(destinations) were used for development of short paths to potential destinations. It can be seen in Table 2 that variation in lengths between first (smallest) and fifth (largest) path for each pair is considerable
therefore, if more than five paths are developed for each destinations there will be additional paths with
higher travel times. Routes with higher travel times are not desirable as there will not be any improvement
in result. In view of this five ‘k’ paths are developed for each destination. The value of ‘k’ can be
selected higher if more nodes are available as there will be possibility of having more number of short
paths without considerable variation in travel time between shortest and longest path.
Step III:
Determination of optimized K-Paths and Schedules
A computer program to calculate the penalised objective function (summation of objective function and
penalties due to violation of constraints) was developed in the ‘C++’ environment. The developed ‘K’
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paths are used with the objective function program. The provision is made so that each alternative path
out of five ‘K’ paths for each potential destination is selected with random frequencies generated by
Genetic Algorithms. The alternative paths and frequencies corresponding to minimum penalized objective
functions are selected as optimized feeder routes and frequencies.
Thus frequencies ‘fj’ and a set of routes (with different lengths ‘lj’) are the decision variables. The
time of departure of buses is decided on the basis of frequencies and the scheduled arrival time of DARTs
from either direction at the DART station. The typical analysis in the paper has been carried out for peak
hour only. From the traffic surveys it was found that from each train during the peak hour almost the same
numbers of passengers alight and relatively similar percentages of passengers would select buses to their
destinations for further travel. Due to this uniformity in the alighting pattern, the frequencies of
connecting feeder buses are also found to be same, for example, on route number ‘1’ each bus is
scheduled at 6 minute headway starting from 8.07 am to 8.55 am. This frequency will change as per
demand and with the distribution of commuters at any other time interval. In off peak hours, the headway
between trains will increase due to lower demand. This frequency will change as per demand in other
time intervals. During off-peak periods there will be less DART commuters and thereby headway
between buses will increase which will lead to a lower requirement of buses. The binary digit coding to
represent routes and schedules together has been adopted (Shrivastava et al 2002).
Details of Objective Function, Penalties and use of GAs in SOHFRGA
The objective function is adopted as the minimization of user and operator costs. The user cost is the
summation of the in-vehicle time cost and the transfer time cost between DARTs and buses. The operator
cost is associated with the running cost (vehicle operation cost) of buses. Constraints are related to load
factor, fleet size and unsatisfied demand. Readers are requested to refer Shrivastava and O’Mahony
(2007) as mathematical representation of objective function, constraints, and penalties along with detailed
discussion is given there. In this paper, the same objective function and constraints are solved by using a
different approach which differs in the way it selects potential destinations.
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The developed objective function is used with LibGA software (Lance Chambers, 1995) for Genetic
Algorithms in the Linux environment. The objective function and constraints pose a multi-objective
problem. Some of the
constraints are in favor of users and some are in favor of the operator. For
example, lower load factor and higher load factor constraints are in favor of users and operators
respectively. If the load factor is above ‘1’ some of the users may not be able to get a seat but the operator
will earn a profit. The fleet size constraint ensures that the scheduling of buses should be done within the
limited fleet size and this is in favor of the operator. The unsatisfied demand constraint ensures that all
commuters should be able to get on a bus, thus this constraint is in favor of the operator. Assigning a
very high penalty to one of the constraint results in a biased solution. Thus these penalties are decided so
as to keep the load factors between the minimum and maximum values, the fleet size within a specified
limit and the unsatisfied demand to zero. The adopted set of penalties for the feasible solutions is decided
so as to get a judiciously balanced solution.
The demand satisfaction and load factors on various routes are two dominating factors for both users and
operators. It has been found during the interviews with commuters that they prefer to have connecting
buses within five minutes of waiting after arriving at bus stops but most of them even accept ten minutes
of waiting as a reasonable time. Thus the variation of penalty coefficients for a minimum load factor is
related to the percentage satisfaction of demand within ten minutes of waiting. The coefficient for the
minimum load factor is selected because it is observed that the load factor frequently goes below 0.4
(minimum value) due to low demand which is not compatible to the adopted existing bus capacity (74).
This typical variation is observed when the penalty coefficient corresponding to the minimum load factor
(less than 0.4) is varied keeping other coefficients the same. A weighted factor is calculated by awarding
equal weights to the overall load factor and the percentage demand satisfaction within ten minutes of
waiting. The penalty coefficient corresponding to the higher weighted factor is selected for further
analysis.
Step IV:
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Check whether the entire demand is satisfied and routes are within the specified length. If the entire
demand is satisfied and routes are within the specified lengths then developed feeder routes and the
frequencies are optimum. The frequencies are used to calculate coordinated schedules for the existing
schedules of the DART.
Step V:
If the entire demand is not satisfied and routes are within specified lengths then these routes are used for
modification. Destinations leading to unsatisfied demand are inserted in routes by node selection and
insertion strategies. If the lengths of routes are not within specified limits (very small due to higher
demands close to a railway station) then these routes are discarded.
If the potential destinations are very close to a DART station then they lead to very short routes
mushrooming near to a station (Shrivastava and Dhingra, 2001 & Baaj and Mahamassani, 1995). Such
short routes are not acceptable in actual practice. Thus in the proposed case study a length of 2.5 km
equivalent to travel time of 10 minutes is adopted as the minimum length of feeder routes and the routes
less than or equal to this value are discarded. The nodes present on discarded routes and not duplicated in
other routes are also used for heuristic insertion/attachment process along with other nodes with
unsatisfied demand (destinations not included in any developed feeder route). Readers are requested to
refer to Shrivastava and Dhingra (2001) where the full description of node selection and insertion /
attachment process along with various insertion strategies are discussed in detail.
Use of Genetic Algorithms for the objective function and constraints
The proposed objective function is used with LibGA software (Lance Chambers, 1995) of Genetic
Algorithms in the Linux environment to determine optimal routes and frequencies in SOHFRGA and
thereafter for determination of final frequencies leading to coordinated schedules on developed feeder
route network. The details of Genetic Algorithms, its application and adopted values of various operators
etc is discussed in Shrivastava and O’Mahony (2007).
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RESULTS AND DISCUSSION
In the initial stage of SOHFRGA, nodes having more than average demand were selected as potential
destinations and feeder routes with frequencies for feeder buses (leading to coordinated schedules) were
developed simultaneously using Genetic Algorithms. There were six destinations having more than
average demand. These destinations were Dun Laoghaire College (2), Sallynogin (3), Monkstown (4),
Deans Grange (5), Stillorgan (8) and Loughlinstown (12). Selection of these nodes as potential
destinations developed six routes with 12.85% unsatisfied demand. Selection of five nodes i.e. Dun
Laoghaire College (2), Sallynogin (3), Deans Grange (5), Stillorgan (8) and Lough Linstown (12) also
gave 12.85% unsatisfied demand with five feeder routes. Therefore these five destinations were selected
as potential destinations and five k-paths as indicated in table 2 were developed for each of these potential
destinations originating from the DART station. These k – paths were used with LibGA software of
Genetic Algorithms in Linux and feeder routes with frequencies leading to coordinated schedules were
developed simultaneously. The following feeder routes were obtained (with codes as given in table 1).
Nodes in feeder routes
Length in terms of travel time in ‘minutes’
1–2
8
1–3
7
1–4–5
15
1–6–7–8
25
1 – 3 – 17 – 11 – 12
30
Since the developed feeder route network does not satisfy 100% demand, the next stage of further
modification of feeder routes using node selection and insertion strategies is adopted. The frequencies
associated with feeder routes in the earlier stage are discarded since fresh frequencies are required to be
determined due to the modification of routes. The travel time on the first two feeder routes is even less
than ten minutes (minimum specified length of 2.5 km) Hence the first two routes are discarded and node
‘2’ which leads to unsatisfied demand is selected for the insertion process in the next stage for
modification of routes along with other unsatisfied nodes. Thus the 3rd, 4th and 5th routes were selected for
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modification and nodes having unsatisfied demand are inserted priority-wise using a heuristic approach.
Finally, the following three feeder routes, as indicated in figure 3 were developed.
Nodes in feeder routes
Length in ‘km’
1 – 4 – 2 – 5 – 10 – 9 – 16
10.76
1 – 6 – 7 – 8 – 15 – 14 – 13
14.60
1 – 3 – 17 – 11 – 12
7.72
It can be seen that the developed feeder routes are well within the specified minimum (2.5 km) and
maximum (15 km) lengths of routes. These lengths of routes are decided based on locations of nodes to
which demand exists as identified in typical traffic survey. The upper limit of the length of routes can be
revised and shorter lengths can be adopted if a similar exercise of coordination is repeated at other DART
stations also. This is due to the fact that a particular node may have connectivity with more than one
DART station which may lead to shorter and better routes from one station, as compared to another one.
For example, nodes 13, 14 and 15 are very close to the Blackrock DART station as compared to Dun
Laoghaire. Thus feeder routes for these destinations from Blackrock will be shorter.
In the next stage for determination of coordinated schedules for feeder buses for the existing
schedules of DARTs these feeder routes were used. Genetic Algorithms are implemented for determining
optimal frequencies and coordinated schedules were derived from these frequencies. Table 3 shows
details of coordinated schedules of feeder buses for the existing schedules of DARTs and load factors. It
can be seen in the table that the average load factor on each route is more than 0.40 and the overall load
factor (average of load factors on all the three routes) is 0.47. The load factors on the routes and overall
load factor have much improved values against the existing scenario in which the load factor hardly
increases above 0.3.
In the case study the capacity of feeder buses is taken as 74 (Scott Wilson, 2000) which is on
higher side as compared to the number of DART commuters transfer to buses. The load factor will be
more (greater than ‘1’) if coordinating buses are held for longer time. Commuters from later DART trains
will be able to seek transfer to a particular bus due to a longer holding period. Longer holding increases
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transfer time between DARTs and feeder buses which is not desirable to users and will also increase the
value of the objective function. Thus the two contradictory conditions regarding higher load factors in
favor of the operator and the lower transfer time for users are satisfied by striking a balance between the
two. As the load factor decreases below ‘1’ penalties are imposed because the constraint for the minimum
load factor is violated. Thus the load factors obtained in the study are less than ‘1’ but transfer time
remains within desirable limits. Busses with lower seating capacity will improve the load factor. Also the
load factor will be higher if the model is implemented to places where higher numbers of train commuters
seek transfer to buses.
Thus the decision of bus dispatch time not only depends on arrival time of DARTs but also on the
number of passengers transferring from DARTs to buses. As discussed above, the dispatch time of buses
is decided upon by means of striking a balance between transfer time and the acceptable value of the load
factor. If the load factor is lower, then buses are held for more time so as to acquire more commuters from
later DART trains. Other factors influencing the schedule of buses are the available fleet size and the
percentage demand satisfied. The coordinated buses are dispatched only after five minutes of scheduled
arrival of DART at station because it takes about five minutes for passengers to reach bus stops after
arriving on a DART train. It can be seen in table 3 that the first bus is at 8.07 which is five minutes after
the arrival of the south bound DART scheduled at 8.02; on route number 1, the second bus is at 8.13
which is five minutes after the arrival of the first north bound DART at 8.08. Some buses are scheduled
later than five minutes after the arrival of a DART train. This is done in order to compromise with the
load factor by holding the bus, as discussed above. The other coordinated schedules can be explained on
the basis of the above reasoning.
Table 4 gives a comparison between existing and proposed route network. It can be seen that on
average 89 % of the total demand is satisfied within 5 minutes of effective waiting time and 99% of
demand is satisfied within 10 minutes of effective waiting time. Only 1 % of commuters are required to
wait up to 15 minutes. Route wise details indicate that 100 % demand on route 1 is satisfied within 5
minutes of effective waiting time and on route 2 and 3, 96 % of demand is satisfied within 10 minutes of
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effective waiting time. Only 4 % of commuters have to wait up to 15 minutes. Thus if a monetary value is
assigned to a saving in transfer time then about a 70% saving can be expected in transfer time due to the
proposed system. In the existing scenario there are 6 bus routes travelling through identified nodes
whereas in the proposed model three bus routes cover identified demand nodes. The saving in in-vehicle
time and operating cost can be expected to be 50% due to the proposed model against the existing
scenario. Table 4 briefly summarises the above discussions.
CONCLUSIONS
In the proposed research, feeder routes are developed using a hybrid approach which makes use of the
benefits of optimisation using genetic algorithms and a heuristic approach.
For the development of
feeder routes, priority is given to nodes having higher demands. In view of this, nodes having higher
demand (more than average) are considered as potential destinations and optimisation is carried out by
GAs. Nodes having lower demand are attached to (or inserted in) developed routes keeping the length (or
deviation) within reasonable limits. Coordinated schedules are determined by genetic algorithms.
The
following conclusions can be drawn from the proposed modelling exercise.
1. It has been observed that for the given influence area of a DART train station a combination of
genetic algorithms and the proposed heuristic approach develops an improved feeder route structure.
In the influence area of the railway station destinations closer to the railway stations have higher
demands and other destinations are well-scattered with limited connectivity between them. By using
this approach, a lower number of feeder routes is developed as compared to earlier approaches for the
same influence area and demand. The proposed model also provides improved load factors with a
higher percentage of demand satisfaction and lower waiting time.
2. The lengths of feeder routes are well controlled in the model. They are checked after the first stage
i.e. after simultaneous development of routes and schedules using GAs and also using the heuristic
approach route lengths are controlled by the ‘maximum demand deviation shorter path time criterion’
and the ‘path extension time criterion’.
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3. The model strikes a balance between user need and operator requirements. The objective function
incorporates user costs in terms of time spent in buses and the transfer time between DARTs and
buses; the operators cost is the vehicle operation cost which is directly proportional to the distance
travelled by buses. Similarly constraints are also as per the requirements of users and operators. The
load factor constraint is kept within minimum and maximum values so as to maintain a better level of
service for users and economic operation to satisfy operators. The fleet size constraint is also a
realistic constraint from the operator’s point of view. The constraint for unsatisfied demand increases
the probability of availability of seats to commuters though it is not very important when the load
factor remains less than a minimum value as has been experienced for the study area.
4. The same modelling exercise can be carried out at other DART stations with large scale data
collection for the whole day. A fully integrated system with DART as the main line haul carrier and
buses as feeder services can be developed. Schedules and thus the requirement of buses can be found
for peak and off-peak periods of the day. Even the route structure can be appropriately designed as
per demand at various destinations for different periods of the day.
5. The application of all three algorithms i.e. K – Path, Genetic and Heuristic Algorithms makes this
approach acceptable for all types of networks i.e. networks with well connected nodes and networks
in which all the nodes have limited connectivity. Planners have limited options available in the
formation of alternative routes in the case of networks with limited connectivity. Combinations of
Genetic Algorithms and K –Path algorithms have been successfully implemented for well connected
networks. The heuristic approach is developed keeping in mind networks in which nodes are not well
connected. Thus this method can be implemented for a network which is well connected and also for
a network in which nodes do not posses better connectivity with other nodes. Thus this methodology
is not developed only for a given case study but it can be implemented to other networks also. If the
higher demand destinations are located away from the origin (railway station), well scattered and well
connected then optimised feeder routes and coordinated schedules will be developed in the first stage
of model in which optimisation of feeder routes and coordinated schedules is done simultaneously
15
using Genetic Algorithms. Thus the proposed model can be used for any influence area if demands at
various destinations and network connectivity details are known.
REFERENCES
1. Baaj M.H. and Mahmassani H.S. (1995). Hybrid Route Generation Heuristic Algorithm for the
Design of Transit Networks, Transpn. Res.C, 3, 1, 31 – 50.
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Information
and
Finding the
Computer
k shortest paths. Tech. Report 94-26, Department of
Science,
University
of
California,
USA.
http://www.ics.uci.edu/~eppstein/pubs/Epp-TR-94-26.pdf accessed on 25.09.2004
3. Geok K, and Jossef P. (1988). Optimization of feeder bus routes and bus stop spacing. Journal of
Transportation Engineering, 114, 3, ASCE, Reston, VA, 341-354.
4. Chambers, L. (1995). “Practical Handbook of Genetic Algorithms Applications. Volume I”, CRC
Press, 555.
5. Reklaitis, G.V. Ravindran, A. and Ragsdell K.M. (1983), “Engineering Optimization – methods and
applications”, Wiley, New York, N.Y.
6. Scott Wilson (2000). “Final Report on Bus Network Strategy Appraisal Report for Greater Dublin
Area”. www.dublinbus.ie/about_us/pdf/swilson.pdf Accessed May 13, 2004.
7. Shrivastava P. and Dhingra S.L (2000). An overview of bus routing and scheduling techniques.
Highway Research Bulletin, 62, 65 – 90.
8. Shrivastava P. and Dhingra S.L. (2001), Development of feeder routes for suburban railway stations
using heuristic approach Journal of Transportation Engineering, ASCE, USA, July/August 2001,
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Coordinated Schedules – A Genetic Algorithms Approach, Transport Policy, 13, 5, 413-425.
16
11. Shrivastava P. and O’Mahony M. (2007), Design of Feeder Route Network Using Combined Genetic
Algorithm and Specialized Repair Heuristic, Journal of Public Transport, 10, 2, 99-123
12. Wirasinghe, S.C. (1980), Nearly optimal parameters for a rail feeder bus system on a rectangular
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route directness, Journal of Public Transportation, 7, 67 – 82
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Table 1 Potential Demand to Various Destinations
Node
No.
(code)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Destinations
Dun Laoghaire DART Station
Dun Laoghaire College
Sallynoggin
Monks town
Deans Grange
Temple Hill
Black Rock
Stillorgan
Leopards town
Foxrock
Maple Manor / Cabinteely
Lough Linstown
Mount Merrion
University College of Dublin
Dundrum
Sandyford
Rouches Town Avenue
Potential demand to various
destinations
7 – 8 a.m.
8 – 9 a.m.
7-9 a.m.
0
0
0
39
202
241
17
103
120
10
63
73
16
93
109
2
6
8
8
46
54
13
77
90
2
8
10
2
8
10
2
4
6
13
78
91
2
15
17
4
23
27
6
31
37
3
15
18
2
4
6
18
Table 2 Developed ‘K’ paths between DART station and Potential Destinations
Origin
Potential Destination
1
2
1
3
1
5
1
8
1
12
Nodes in ‘k’ paths
( k=5 )
1, 2
1,3,2
1,4,2
1,6,4,2
1,4,5,2
1,3
1,2,3
1,4,2,3
1,4,5,2,3
1,2,5,3
1,2,5
1,3,2,5
1,4,5
1,2,4,5
1,3,5
1,6,8
1,7,8
1,6,7,8
1,7,6,8
1,2,5,8
1,3,17,12
1,2,3,17,12
1,3,11,12
1,2,17,12
1,3,17,11,12
Travel time
min
8
10
15
20
20
7
11
18
23
23
13
15
15
16
17
21
24
25
26
26
23
27
28
30
30
19
Table 3 Details of Bus Schedules with Load Factors
Train Timings
North
Bound
DARTS
8.08
8.15
8.23
8.29
8.33
8.38
8.43
8.49
8.58
South
Bound
DARTS
8.02
8.09
8.20
8.25
8.31
8.36
8.45
8.53
-
Trains after 9 a.m.
Bus Timings
Route
1
Route
2
8.07
8.07
8.13
8.19
8.19
8.31
8.25
8.43
8.31
8.55
8.37
8.43
8.49
8.55
Buses to be
scheduled after
9 a.m.
Average load factors on individual routes
Load Factors
Route
3
8.07
8.19
8.31
8.43
8.55
Buses to
be
scheduled
after 9
a.m.
Route
1
Route
2
Over
all load
factor
Route
3
0.46
0.23
0.22
0.16
0.31
0.30
0.46
0.62
0.60
0.62
0.70
0.67
0.62
0.39
0.38
0.62
Load factor
0.78
for Buses
0.16
to
be
0.62
scheduled
Load factor for
Buses
to
be after 9 a.m.
scheduled after
9 a.m.
0.50
0.45
0.43
0.47
20
Table 4: Comparison between existing and proposed Route Network
Property for comparison
Existing Route network in the
study area
Not a feeder route network
Less than 0.3
Proposed route network for the
study area
Type of route network
Feeder route network
Average load factor on routes
Greater than 0.4 on all routes,
over all load factor is 0.47
Waiting time / percentage Average waiting time is more 89% demand is satisfied with in
demand satisfaction
than 20 minutes
5 minutes, 99 % with in 10
minutes and 100 % is satisfied
with in 15 minutes of effective
waiting.
Transfer Cost
About 70% saving in transfer cost can be achieved per head due to
proposed network and coordinated scheduling
In vehicle cost and Operating There will be about 50 % saving in in-vehicle cost and operating cost
Cost
Total Cost
The total saving can be expected to be more than 50%
21
Identification of data requirement
Details of existing bus and DART network
- Coded bus and DART network
- Link lengths & link travel time
- Characteristics of Dublin buses
TRAFFIC SURVEYS
Surveys for assessing
existing distribution of
DART Commuters on
Different Modes
Existing Road Network
Assessment of potential
demand to different
destinations from DART
station using willingness
to shift surveys
Potential O - D Matrix
SHRIVASTAVA – O’MAHONY HYBRID FEEDER
ROUTE GENERATION ALGORITHM
(SOHFRGA)
Feeder routes
for DART station
SCHEDULE OPTIMISATION MODEL
Minimisation of distance travelled by Dublin buses (Operator Cost) and
Transfer time between DART and coordinating feeder public buses (User
cost) with the constraints related to load factor, transfer time and
unsatisfied demand.
Coordinated Schedules of Public Buses
Figure 1: Proposed Methodology for development of feeder routes and coordinated
Schedule
Existing
DART
timings
22
Figure 2: Proposed Shrivastava – O’Mahony Hybrid Feeder Route Generation Algorithm
(SOHFRGA)
Existing Road Network
Link connectivity matrix
Demand Matrix obtained
by Traffic surveys
Selection of Potential
destinations based on
average demand
Development of K –paths
between DART station and
potential destinations
Optimization of penalized objective function using Genetic Algorithms
Objective function: Minimization (Transfer time between DARTs and
Buses + in Vehicle time + Vehicle operating cost)
Constraints: Related to Minimum and Maximum load factors, fleet
size and unsatisfied demand
Existing
DART
timings
Optimized Feeder routes and
coordinated schedules
Yes
No
Is entire demand
Satisfied?
Yes
Are the lengths of
feeder routes with in
acceptable limits?
Print optimized feeder routes and
coordinated schedules
A
23
A
Discard the routes having less than minimum
specified
Length / Travel time (2.5 km / 10 min for case
study).
Available routes for modification
Sort all the available nodes due to following in decreasing
order of demand:
 Could not be used by developed feeder routes and
give rise to unsatisfied demand
 Available due to discarding of smaller feeder routes.
Select first node among arranged in decreasing order of
demand
Stop,
Yes
Is last node has been
inserted?
Print Routes
No
Node selection and
insertion strategies
Find out the route in which selected node has to be
inserted /attached as per node selection and insertion
strategies and Insert / attach the selected node in the
identified route.
Is route length with in
specified limit?
Insert the node in selected route and delete from
node list
Select next
route
Take next node
Figure 2 : Proposed Shrivastava – O’Mahony Hybrid Feeder Route Generation Algorithm
(SOHFRGA) (Continued)
24
Figure 3 is available on request from the authors
List of Tables
Table 1 Potential Demand to Various Destinations
Table 2 Developed ‘K’ paths between DART station and Potential Destinations
Table 3 Details of Bus Schedules with Load Factors
Table 4 Comparison between existing and proposed Route Network
List of Figures
Figure 1 Proposed Methodology for development of feeder routes and coordinated schedule
Figure 2 Proposed Shrivastava – O’Mahony Hybrid Feeder Route Generation Algorithm
(SOHFRGA)
Figure 2 Proposed Shrivastava – O’Mahony Hybrid Feeder Route Generation Algorithm
(SOHFRGA) (Continued)
Figure 3 Developed feeder route network for Dun Laoghaire DART station