This document describes a major technical project on vehicle sharing. It involves clustering cities using the K-means algorithm to assign user requests for transportation between sources and destinations to drivers. The project formalizes the routing and allocation problem and describes implementing an optimization module to solve it, with references provided for related work. Future work involves tailoring an algorithm to the specific project needs.

1. Vehicle Sharing
Major Technical Project
Damini Singal (B10107)
Sanchit Khattry (B10029)
Final Year, Computer Science and Engineering

2. User ID
Source
Destination
Date of Journey
Time of Journey
Max Detour Dist
Preferences
User ID
:user1
Source
:Chandigarh
Destination
:Delhi
Date of Journey :14 November 2014
Time of Journey :21:00
Max Waiting Time:15 minutes
Preferences
:Age > 35, Male
:user2
:Mandi
:Roorkee
:14 November 2014
:19:30
:6 km
:None

3. Number of Clusters
3

4. City Name
Coordinates
Cluster id
Cluster centroid
Mandi
31.70817,76.93137
0
31.470200000000006,76.61453285714286
Hamirpur
31.6861,76.52131
0
31.470200000000006,76.61453285714286
Ner Chowk
31.60852,76.91533
0
31.470200000000006,76.61453285714286
Chandigarh
30.73331,76.77942
1
30.550172500000002,76.21847500000001
Shimla
31.10461,77.17342
0
31.470200000000006,76.61453285714286
Patiala
30.32062,76.39513
1
30.550172500000002,76.21847500000001
Dehradun
30.31649,78.03219
2
29.972666,77.836818
Muzaffarnagar
29.47268,77.70851
2
29.972666,77.836818
Rishikesh
30.08693,78.26761
2
29.972666,77.836818
Roorkee
29.85426,77.888
2
29.972666,77.836818
Ghumarwin
31.44192,76.71208
0
31.470200000000006,76.61453285714286
Hoshiarpur
31.52798,75.91375
0
31.470200000000006,76.61453285714286
Garhshankar
31.2141,76.13447
0
31.470200000000006,76.61453285714286
Ludhiana
30.90096,75.85728
1
30.550172500000002,76.21847500000001
Sangrur
30.2458,75.84207
1
30.550172500000002,76.21847500000001
Yamunanagar
30.13297,77.28778
2
29.972666,77.836818
Using K Means
Algorithm
To Cluster the
Cities
(K = 3)

5. Clustering Problem

Clustering problem – Classifying similar data items into clusters (high
similarity among the points, dissimilar to points in other clusters)

Input: Collection of nodes with the inputs
User ID, Source, Destination, Time of journey, Tolerances (Time and
distance)

Output: User ID with the assigned Cluster ID

Naïve ways to select features:
•
Geographical location (Source)
•
Chronological order (Time of Journey)

6. But the question that arises is how can we
combine the features of both Time and
Geographical Locations to create clusters for
the given problem?

7. What if there is a passenger at
Chandigarh or Shimla?
Path taken by these
Can pickup passengers at
points without any change in
Driver without
route
extra passengers

8. What problems arise?
Say the driver picks up the
passenger at Chandigarh
following an alternate route
Detour Tolerance of the
Driver
The system thus demands an
Passenger Wait Time
optimal routing algorithm which
takes care of these and various
Feasibility of the alternate
other such factors involved
route (traffic, road
conditions etc.)
Seat availability

9. But what about
Hamirpur which is
outside the
tolerance limit by
just 50 m?
Problem!
Say, Rupnagar, Chandigarh
and Ambala Cantt are
within the tolerance limit
When will a passenger not
get picked up?
 When lying outside the
tolerance limit
Set of requests close to the driver route
 When the driver denies
Close here means within the
detour tolerance of the
driver.

10. Algorithm overview
Start2
Start1
Laydown driver paths
Destination1
Those lying within the routes
are routed without any
problem and the path is
But what about these?
Expand the width of the route as
modified
per the drivers detour tolerance
Detour
Tolerance2
Detour
Tolerance1
Destination2
Fetch the set of requests
Where is one request

11. Formalizing the problem

Given sets of driver journey details:
Di = {d_id, s, d, det, cap}
Di = Driver i
d_id = Driver ID
s = Source Location
d = Destination
det = Detour Tolerance
cap = Car capacity

Given sets of passenger requests:
Pi = {p_id, s, d, wt, num}
Pi = Passenger i
p_id = Passenger ID
s = Source Location
d = Destination
wt = Wait Tolerance
num = Number of Passengers

12. Formalizing the problem (contd.)

The engine will give output sets as follows:
Let D = {D1, D2, D3, … , Di}
P = {P1, P2, P3, … , Pi}
(J, RemP) = f(D, P)
J = Sets of journeys {J1, J2, … , Ji}
Ji = {j_id, d_id, p_id}
f = Routing and Allocation algorithm function
j_id = Journey ID
D = Driver
P = Passenger
RemP = Set of passengers who remain unallocated at the end of the current
iteration

13. Routing and Allocation Implementation

For routing and allocation in the first iteration we are using the
implementation of “round trip and A-Z trip” over Google Maps API.
A working module could be found at http://optimap.net/

The module implements the following algorithms:
* Brute Force: Runtime O(n-1!)
* Ant Colony along with local K2 optimization: Runtime
O(numWaves * numAnts * n ^ 2) for ACO and
O(numWaves * numAnts * n ^ 3) for rewiring

Future Plan: Plugging in an algorithm to the module tailored to the project

14. Project Implementation

15. References
1.
Manel, Sghaier, et al. "A distributed dijkstra's algorithm for the implementation of
a Real Time Carpooling Service with an optimized aspect on siblings." the 14Th
International IEEE Annual Conference on Intelligent Transportation Systems (ITSC
2011). 2011.
2.
Chekuri, C., Korula, N., & Pál, M. (2012). Improved algorithms for orienteering and
related problems. ACM Transactions on Algorithms (TALG), 8(3), 23.
3.
Agatz, N. A. H., Erera, A., Savelsbergh, M. W. P., & Wang, X. (2010).Sustainable
passenger transportation: Dynamic ride-sharing (No. ERS-2010-010-LIS). Erasmus
Research Institute of Management (ERIM).
4.
Chao, I., Golden, B. L., & Wasil, E. A. (1996). A fast and effective heuristic for the
orienteering problem. European Journal of Operational Research, 88(3), 475-489.
5.
Chao, I., Golden, B. L., & Wasil, E. A. (1996). The team orienteering
problem.European journal of operational research, 88(3), 464-474.
6.
Lyft, Peer-to-peer ridesharing mobile application, http://www.lyft.com