Presentation 3rd CSUM

3rd Conference on Sustainable Urban Mobility
26-27 May, 2016, Volos, Greece
A Hybrid Approach to the Problem of Journey Planning with
the Use of Mathematical Programming and Modern
Techniques
With the contribution of the LIFE programme of the European Union - LIFE14 ENV/GR/000611

Authors
• Georgios K.D. Saharidis
• Dimitrios Rizopoulos
• Afroditi Temourtzidou
• Antonios Fragkogios
• Nikolaos Cholevas
• Asimina Galanou
• George Emmanouelidis
• Chrysostomos Chatzigeorgiou
• Labros Bizas
Department of
Mechanical Engineering
Polytechnic School
University of Thessaly

Presentation structure
• GreenYourMove Project
• The journey planning problem
• Proposed method
• Conclusion

GreenYourMove Project
• GreenYourMove (GYM) is a European Research Project co-funded
by LIFE, the EU financial instrument for the environment - LIFE14
ENV/GR/000611.
• GreenYourMove’s main objective is the development and
promotion of a co-modal journey application to minimize GHG
emission in Europe. GreenYourMove develops a multi-modal
transport planner (both routing & ticketing system) considering all
kinds of urban public transportation (urban and sub-urban buses,
metro, tram, trolley, trains), where the user gets alternative routes
combining more than one transport modes if necessary. The
routes are the environmentally friendliest ones, since emissions
are calculated for different scenarios
• Target: Creation of a web platform and smartphone app.

GreenYourMove Project
• Partners:
– University of Thessaly
– AVMAP
– CHAPS (Czech Republic)
– EMISIA
– PLANNERSTACK (The Netherlands)
– TRAINOSE
• Total Budget: 1,245,052 €
– Start: September 2015
– Finish: August 2018

The journey planning problem
• The computation of an optimal,
feasible and personalized
journey from a starting point A
to an ending point B. Generally,
the important task is to
calculate the path from a point
A to another point B, such that
the total distance/time travelled
from A to B will be the
minimum.

• Multi-Modal Journey Planning (MMJP)
– In public transportation networks, the multi-modal
journey planning problem (MMJP) seeks for journeys
combining schedule-based transportation (buses, trains)
with unrestricted modes (walking, driving).

– Earliest Arrival Problem (EAP): Given a source stop A, a
target stop B and a departure time T, the problem asks
for a journey that departs from A, no earlier than T, and
arrives at B as early as possible.
– Range Problem (RP): Takes as input a time range (e.g. 6-
9am) and asks for the journey with the least travel time
that depart within that range.

– Multi-Criteria Problem (MCP): Different optimization
criteria:
• The number of transfers
• The total journey cost
• Ecological footprint (Environmental MMJP): Minimization of
GreenHouse Gas (GHG) emissions
• Etc.
Journey, which is the most environmental friendly

Proposed Method
• Hybrid approach, because it is a combination of:
– Dijkstra’s algorithm
– Mathematical model for the MMJP

Proposed Method
The user inserts the starting and
ending points as well as the
departure time of his journey
Dikjstra's algorithm is applied to find the closest public
network node S (stop or station) to the starting point and the
closest node T to the ending point
The mathematical model is built and solved in order to
compute the optimal journey between S and T
The optimal journey minimizing
both travel time and environmental
cost is delivered to the user

Proposed Method
Dijkstra’s algorithm
Mathematical Model

Proposed Method
• Dijkstra’s Algorithm
– The mostly known Shortest Path algorithm, which is a
label setting algorithm introduced by Dijkstra in 1959.
Source Target
Total distance: 28

Proposed Method
• Dijkstra’s Algorithm
– Scan nodes near Source and Target until you hop on a
stop of the Public Transportation network.

Proposed Method
• Mathematical model for the MMJP
– Mixed Integer Linear Program (MILP) in order to
compute the optimal journey between the departure
and arrival stops of the public network.
– In-between those two stations, the model prompts the
user to use up to a number of different modes of
transport, depending on his/her input. While in the
network, the user follows an optimal journey that
minimizes the travel time and the environmental cost.

Proposed Method
– Indices
• i, j, h Nodes of the network.
• k Modes or transport.
• n Trips.

Proposed Method
– Data
• Ci,j,k Environmental cost of moving from i to j with mode k.
• TTi,j,k Time of transfer from i to j with mode k.
• ToDi,j,k Time of departure of trip n with mode k from i to j.
• N Number of nodes.
• M Number of modes of transport.
• L Maximum Number of trips in all available modes.
• S The departure station.
• T The arrival station.
• a Coefficient in the objective function.
• b Coefficient in the objective function.
• DT Departure time of the user from the starting point.
• AT Latest arrival time of the user to the ending point.
• WT1 Walking Time from starting point to S.
• WT2 Walking Time from T to ending point.

Proposed Method
– Decision variables
• Xi,j,k,n Binary Variable used to represent whether a
transfer is made from i to j with mode k and trip n.
X is equal to 1 when transfer is made and 0 when
it is NOT.
• Si,j,k,n Non-negative continuous variable used to
represent the departure time from i to j with k
and n. If the transfer is NOT made S is equal to 0

Proposed Method
– Constraints
, , ,
1 1 1
1
N M L
S j k n
j k n
X  

1. Connection from point S to a next point happens
, , ,
1 1 1
0
N M L
i S k n
i k n
X  

2. Once a journey has departed from S, it will never go through S again
, , ,
1 1 1
1
N M L
i T k n
i k n
X  

3. A connection between any point and T is made

Proposed Method
– Constraints
4. The journey reaches the target node and it never departs from it again
, , ,
1 1 1
0
N M L
T j k n
j k n
X  

, , ,
1 1 1
1, ,
N M L
i j k n
i k n
i i TX  
  
5. The journey goes through each node at most once
, , , , , ,
1 1 1 1 1 1
0, , ,
N M L N M L
i h k n h j k n
i k n j k n
h h S TX X     
    
6. Whatever node of the network we visit, we have to leave from it as well

Proposed Method
– Constraints
7. When X is 1, then S gets equal to ToD. The constraint relaxes, when X is 0
8. The departure that corresponds to X will not happen if ToD is 0, meaning there is
no transfer available
9. Time continuity in the problem
, , , , , ,, , , , , ,
*(1 ) *(1 ), , , ,i j k n i j k ni j k n i j k n
M M i j k nS ToDX X      
, , , , , ,
, , ,i j k n i j k n
i j k nToDX  
, , , , ,, , , , , ,
1 1 1 1 1 1 1 1 1
( * ) , ,
N M L N M L N M L
i h k i h k ni h k n h j k n
i k n i k n j k n
h h S TS STT X        
     

Proposed Method
– Constraints
10. The departure time from the first node is the smallest
11. It initializes S to 0 if there is no transfer between i and j with mode k and trip n
12. The time of departure from the node before T is the largest time of departure
in the journey delivered
, , ,, , , , , ,
1 1 1 1 1 1 1 1 1
(1 )* ,
N M L N M L N M L
i j k nS j k n i j k n
j k n j k n j k n
M i SS S X        
      
, , ,, , ,
* , , ,i j k ni j k n
M i j k nS X 
, , , , , ,
1 1 1 1 1 1
0,
N M L N M L
i T k n i j k n
i k n i k n
j TS S     
    

Proposed Method
– Constraints
13. Uses the solution from Dijkstra’s algorithm, which we have run before the
construction of the mathematical model.
It makes sure that the first departure from a node of the network happens after the
departure time of the traveler plus the walking time from the starting point to the
station S
, , ,
1 1 1
1
N M L
S j k n
j k n
WT DTS  
 

Proposed Method
– Objective Function
Minimization of 2 criteria, the total environmental cost and the total travel time of the
journey, which is proposed to the user. Coefficients a and b are predefined by the user.
The Environmental Cost Ci,j,k is pre-computed for each arc i-j and mode k of the
public transportation network. This pre-computation is made using emission calculation
models, that take into consideration several parameters, such as the type of fuel
(gasoline, diesel, electricity etc.) and the fuel consumption, which concern the vehicle
of the public means of transport. Other parameters concern the trip, which the vehicle
follows, such as the distance and the gradient between the stops.
, , , , ,, ,
1 1 1 1
( * * )*
N N M L
i j k i j k ni j k
i j k n
Min z a bC TT X   
 

Conclusion
• Novel approach for solving the Environmental
Multi-Modal Journey Planning problem. The
proposed hybrid algorithm combines the Dijkstra’s
algorithm with a Mixed Integer Linear Program
(MILP) in order to deliver the journey with the least
travel time and environmental cost.
• Research is still ongoing for the improvement of our
algorithm. The mathematical formulation is still
under modification and there may be slight changes
in the algorithm.

Conclusion
• Future work
– The objective function shall be split into two, one for the
minimization of the travel time and one for the
minimization of the environmental cost. Thus, the
computation of a Pareto set of optimal journeys will be
possible so that the user has more options to consider.
– Addition of more objective functions for the
minimization of number of transfers, the total fare of the
journey etc.

Conclusion
• Future work
– A decomposition method, such as Benders
Decomposition method, shall be implemented on the
MILP so that it will be easier to solve for big data sets.
– Finally, the integration of the algorithm in an online
platform having data from the public transportation
network of Greece will make possible the wide use of it
by the passengers with a large benefit both for them and
the environment

Thank you for your attention
Learn more at:
http://www.greenyourmove.org/

Presentation 3rd CSUM

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