A Review of Bus Route Network Design Procedures:
Multi-objective optimization using Evolutionary Algorithms
S. M. Hassan Mahdavi M Research Scholar, Transportation Engineering, Department of Civil Engineering, Indian Institute of Technology Delhi, India
K. Ramachandra Rao Department of Civil Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India
Geetam Tiwari Department of Civil Engineering, Indian Institute of Technology Delhi, Room 815, 7th Floor Main Building, Hauz Khas, New Delhi 110 016, India
Indian Institute of Technology Delhi, India
Department of Civil Engineering
Transportation Engineering
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
Bus route network design (BRND)
Configuration and performance of Bus route network
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
Approach
Efficient utilization of resources depending upon optimal
networking of routes and frequency of buses.
Meta-heuristic approaches
Transitions in optimization procedures over time
Mathematical and heuristic
Multi-objective optimality Single objective optimality
Multi-Objective Approach
How efficient all components of bus transit system are being integrated?
Depending on stages
involved in procedure
Efficiency
Bus route network design stages and components
1. Objective function
Demand estimation
Constraints
Single
Objective
Multi
Objective
3. Assignment models
Shortest path algorithms
4. Optimization algorithms
Heuristics
Meta- Heuristics
Passenger
Operator
Type 1: Pareto optimality models
Type 2: Bi level mixed integer models
Type 3: Weighted sum models
Components of Bus Route
Network Design
2. Data required
Design variables
Decision variables
Type 1: Genetic Algorithm
Type 2: Simulated annealing
Dijkstra shortest path algorithm
K-shortest path algorithm
Yen’s kth shortest path algorithm
Route Construction
Hybrid transit trip assignment
Capacity-constrained traffic assignment
All-or-Nothing demand assignments
Hyper path transit assignment
Stochastic User Equilibrium assignment
Multiple transit trip assignment
Evolutionary algorithms
Type 3: Immune Clone Annealing
Demand parameters
Network structure parameters
Transfer related parameters
Travel time parameters
Operational parameters
BRNDP - Multi-Objective functions
Constraints
Single
Objective
Multi
Objective
Passenger
Operator
1. Objective function
Weighted sum
Bi level mixed integer
Pareto optimality
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
Type 1: Weighted sum approach
Year Author
1998 Pattnaik et al
1998 Rao
1999 Tom
2001 Chien et al.
2003 Tom and Mohan
2003 Chakroborty
2004 Agrawal and Mathew
2004 Carrese and Gori
2005 Hu et al.
2006 Zhao
2006 Zhao and Zeng
2006 Fan and Machemehl
2009 Mauttone and Urquhart
2009 Beltran et al.
2009 Fan
2010 Fan and Mumford
2011 Szeto and Wu
2012 Cipriani et al.
2012 Ciaffi et al.
2012 Yu et al.
1 1
1 1 1 1
:j n j ni n i n
ij ij ij ij
i j i i j i
Minimize Z A d p B d t
Objectives being aggregated in a weighted
function and converted into single
objective function.
BRNDP - Multi-Objective functions
Constraints
Single
Objective
Multi
Objective
Passenger
Operator
1. Objective function
Weighted sum
Bi level mixed integer
Pareto optimality
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
Type 2: Bi level Mixed integer
Year Author
2007 Chen et al
2008 Mudchanatongsuk et al
2009 Sun et al
2010 Shimamoto et al Weighted sum or Pareto
Passenger trip assignment models
Model of the leader and follower game
Upper level of the model
Lower level of the model
Constraints
Single
Objective
Multi
Objective
Passenger
Operator
Weighted sum
Bi level mixed integer
Pareto optimality
1. Objective function
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
BRNDP - Multi-Objective functions
Type 3: Pareto optimality
Year Author
2011 Blum and Mathew
2011 Miandoabchi et al
2009 Lang et al
1 1
1 1 1 1
:j n j ni n i n
p ij ij ij ij
i j i i j i
Minimize C A d p B d t
1
:r
o l
l
Minimize C L
Passengers perspective
Operator perspective
There is no single global solution
Passenger and operator costs traded
off as dual objectives
BRNDP – Three Multi-Objective Perspectives followed:
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
User + Operator perspective Based on:
1
Minimizing Total User’s travel cost Total Operating Cost
Minimizing Users’ costs Operator’s costs (External Cost)
Minimizaing
Passenger cost [satisfied demand [in-vehicle travel time + waiting time + transfer penalty]
unsatisfied demand]
+ Operator Cost [Round trip time + waiting time at r
ound trip + frequency of kth route]
Including Externalities Based on:
2
Including Transfer, Unsatisfied demand, Round trips Based on:
3
BRNDP - Variation of Constraints
Frequency feasibility 1
2
4
6
7
8
9
10
12
14
Load Factor
Fleet size
Transfer related
Budget constraints of operating agencies
Demand allocation constraints
Unsatisfied transit demand
Accessibility
Route directness
Maximum number of nodes and routes
Trip length 3
Length of bus lanes 5
Geographical & land use 13
Round trip 11
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
BRNDP – Example
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
Objective function Multi objective function
Weighted sum approach
Bi level mixed integer
Pareto optimality
Data required
Initial route set construction
Passenger Demand Assignment
Optimization Procedure
1
Small and Big network testing
Sensitivity Analysis
2
Constraints Frequency
Load factor
Fleet size
Trip length
Bus lanes
Transfer
3
4
5
6
7
1 1
1 1 1 1
:j n j ni n i n
ij ij ij ij
i j i i j i
Minimize Z A d p B d t
1
:r
o l
l
Minimize C L
min max
max
, max
Constraints:
frequency constraint
Capacity Cosntraint
Fleet size constraint
Maximum transfer constraint
k
k
i j
f f f
S C
F
x x
Bus route network design components
1. Objective function
Demand estimation
Constraints
Single
Objective
Multi
Objective
3. Assignment models
Shortest path algorithms
4. Optimization algorithms
Heuristics
Meta- Heuristics
Passenger
Operator
Type 1: Pareto optimality models
Type 2: Bi level mixed integer models
Type 3: Weighted sum models
Components of Bus Route
Network Design
2. Data required
Design variables
Decision variables
Type 1: Genetic Algorithm
Type 2: Simulated annealing
Dijkstra shortest path algorithm
K-shortest path algorithm
Yen’s kth shortest path algorithm
Route Construction
Hybrid transit trip assignment
Capacity-constrained traffic assignment
All-or-Nothing demand assignments
Hyper path transit assignment
Stochastic User Equilibrium assignment
Multiple transit trip assignment
Evolutionary algorithms
Type 3: Immune Clone Annealing
Demand parameters
Network structure parameters
Transfer related parameters
Travel time parameters
Operational parameters
Demand estimation
Decision Variables
Design Variables
1. Data required
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
BRNDP – Parameters (Passenger Demand)
Demand parameters
Network structure
Transfer parameter
Travel time parameter
Operational parameter
Parameters
Demand estimation as
Multi-dimensional approach
Depending on factors determined by
user and operators
Level of service +
Perception of operational agency +
Configuration of Bus transit network
structure + …
BRNDP – Demand Estimation issues
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
Variable demand versus Fixed demand
Variable relationship between Transit demand and network
configuration
2
Re-estimation of demand based on:
Peak time and non-peak time
Demand forecasting models
4 step model or
Descrite choice models
Fixed Demand
Assuming demand given in network 1
+
Toward optimum solution
BRNDP – Parameters – Design and Decision Variables
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
Demand Parameters
Operational Parameters
Transfer related Parameters
Travel time Parameters
Network structure Parameters
Passenger travel demand between OD pairs
Percentage demand satisfied without any transfers
with one transfer
with one transfer
Value of unsatisfied travel demand
Min – Max allowable frequency of buses or headways
Maximum fleet size, Bus capacity, Bus fares
Maximum operating hours, Budget limit
Cost of operating hours
Bus travel speed
Transfer penalty
Travel time between OD pairs
Maximum travel time
Maximum allowable round trip time
Length of the routes
Number of lanes
Maximum Number of routes
BRNDP – Procedure and components
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
Objective function Multi objective function
Weighted sum approach
Bi level mixed integer
Pareto optimality
Initial route set construction
Passenger Demand Assignment
Optimization Procedure
1
Small and Big network testing
Sensitivity Analysis
2
Constraints Frequency
Load factor
Fleet size
Trip length
Bus lanes
Transfer
3
4
5
6
7
Data required Design variables
Decision variables
Parameters Demand
Operational
Transfer related
Travel time related
Network structure
Demand Estimation
Modeling
Bus route network design components
1. Objective function
Demand estimation
Constraints
Single
Objective
Multi
Objective
3. Assignment models
Shortest path algorithms
4. Optimization algorithms
Heuristics
Meta- Heuristics
Passenger
Operator
Type 1: Pareto optimality models
Type 2: Bi level mixed integer models
Type 3: Weighted sum models
Components of Bus Route
Network Design
2. Data required
Design variables
Decision variables
Type 1: Genetic Algorithm
Type 2: Simulated annealing
Dijkstra shortest path algorithm
K-shortest path algorithm
Yen’s kth shortest path algorithm
Route Construction
Hybrid transit trip assignment
Capacity-constrained traffic assignment
All-or-Nothing demand assignments
Hyper path transit assignment
Stochastic User Equilibrium assignment
Multiple transit trip assignment
Evolutionary algorithms
Type 3: Immune Clone Annealing
Demand parameters
Network structure parameters
Transfer related parameters
Travel time parameters
Operational parameters
Assignment Models
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
BRNDP – Passenger demand Assignment
Hybrid transit trip assignment
Capacity-constrained traffic assignment
All-or-Nothing demand assignments
Hyper path transit assignment
Stochastic User Equilibrium assignment
Multiple transit trip assignment
BRNDP – Procedure and components
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
Objective function Multi objective function
Weighted sum approach
Bi level mixed integer
Pareto optimality
Data required
Passenger Demand Assignment
Optimization Procedure
1
Small and Big network testing
Sensitivity Analysis
2
Constraints Frequency
Load factor
Fleet size
Trip length
Bus lanes
Transfer
3
4
5
6
7
Initial route set construction Route Construction Module
Shortest path algorithm
Feasibility Assessment
Connectivity Assessment
Bus route network design components
1. Objective function
Demand estimation
Constraints
Single
Objective
Multi
Objective
3. Assignment models
Shortest path algorithms
4. Optimization algorithms
Heuristics
Meta- Heuristics
Passenger
Operator
Type 1: Pareto optimality models
Type 2: Bi level mixed integer models
Type 3: Weighted sum models
Components of Bus Route
Network Design
2. Data required
Design variables
Decision variables
Type 1: Genetic Algorithm
Type 2: Simulated annealing
Dijkstra shortest path algorithm
K-shortest path algorithm
Yen’s kth shortest path algorithm
Route Construction
Hybrid transit trip assignment
Capacity-constrained traffic assignment
All-or-Nothing demand assignments
Hyper path transit assignment
Stochastic User Equilibrium assignment
Multiple transit trip assignment
Evolutionary algorithms
Type 3: Immune Clone Annealing
Demand parameters
Network structure parameters
Transfer related parameters
Travel time parameters
Operational parameters
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
BRNDP – Optimization
Heuristics
Meta- Heuristics
Type 1: Genetic Algorithm
Type 2: Simulated annealing
Dijkstra shortest path algorithm
K-shortest path algorithm / Yen’s
Evolutionary algorithms
Type 3: Immune Clone Annealing
Route construction
Optimization algorithms
Shortest path algorithms
Step 1
Step 2
Step 3
BRNDP –Route construction procedure
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
Candidate route set generation Identify initial route set using shortest path algorithms
Dijkstra shortest path algorithm
Applying heuristics to check Feasibility checking
Connectivity checking
Route evaluation modules
Frequency setting > Simultaniously or Separately
1
2
K-shortest path algorithm / Yen’s
Applying optimization procedure Find optimum set of solutions
3 Heuristic
Meta-Heuristic
BRNDP – Example
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
Objective function Multi objective function
Weighted sum approach
Bi level mixed integer
Pareto optimality
Data required
Passenger Demand Assignment
Optimization Procedure
1
Small and Big network testing
Sensitivity Analysis
2
Constraints Frequency
Load factor
Fleet size
Trip length
Bus lanes
Transfer
3
4
5
6
7
Initial route set construction Route Construction Module
Shortest path algorithm
Feasibility Assessment
Connectivity Assessment
Shortest path algorithm Connectivity check
Example:
Depth-first search
breadth-first search
Initial Route set:
BRNDP – Example
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
Objective function
Data required
Initial route set construction
Passenger Demand Assignment
1
Small and Big network testing
Sensitivity Analysis
2
3
4
5
6
7
Optimization Procedure Meta-Heauristic approach
Evolutionary algorithm
Genetic algorithm
Simulated annealing
Immune clone annealing
Genetic algorithm operation
Optimum solution
Evolutionary algorithms as a population
based methods
BRNDP – Example
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
Objective function Multi objective function
Weighted sum approach
Bi level mixed integer
Pareto optimality
Data required
Passenger Demand Assignment
Optimization Procedure
1
Small and Big network testing
Sensitivity Analysis
2
Constraints Frequency
Load factor
Fleet size
Trip length
Bus lanes
Transfer
3
4
5
6
7
Initial route set construction
Small Network test
Real size Network test
Key issues to optimum solution in BRND
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
Demand Estimation methods 1
Route construction heuristics 2
Route Evaluation parameters
Effect of more complex parameters in
optimum solution set 3
Bus stop spacing, accessibility to bus stops
Effect of different operators in Evolutionary
algorithms 4
BRNDP – Procedure and components
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013
Objective function Multi objective function
Weighted sum approach
Bi level mixed integer
Pareto optimality Data required Design variables
Decision variables
Initial route set construction Route Construction Module
Shortest path algorithm
Feasibility Assessment
Connectivity Assessment
Passenger Demand Assignment
Optimization Procedure Meta-Heauristic approach
Evolutionary algorithm
Genetic algorithm
Simulated annealing
Immune clone annealing
1
Small and Big network testing Different types of network
Sensitivity Analysis Sensitivity to evolutionary algorithm operators
Sensitivity to parameters
2
Constraints Frequency
Load factor
Fleet size
Trip length
Bus lanes
Transfer
Parameters Demand
Operational
Transfer related
Travel time related
Network structure
Demand Estimation 3
4
5
6
7
S. M. Hassan Mahdavi M Research Scholar, Transportation Engineering, Department of Civil Engineering, Indian Institute of Technology Delhi, India
K. Ramachandra Rao Department of Civil Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016, India
Geetam Tiwari Department of Civil Engineering, Indian Institute of Technology Delhi, Room 815, 7th Floor Main Building, Hauz Khas, New Delhi 110 016, India
A Review of Bus Route Network Design Procedures: Multi-objective optimization using Evolutionary Algorithms
E-Mail: [email protected]
Title
Thank You
Indian Institute of Technology Delhi, India
Department of Civil Engineering
Transportation Engineering
URBAN MOBILITY CONFERENCE INDIA - RESEARCH SYMPOSIUM, 05 December 2013