Bus Route Network Design Procedures

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


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


Weighted sum

Bi level mixed integer

Pareto optimality


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.


Constraints

Single

Objective

Multi

Objective

Passenger

Operator


Weighted sum


Pareto optimality


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


Pareto optimality




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:


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


BRNDP – Example


Objective function Multi objective function

Weighted sum approach


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


Demand estimation

Constraints

Single

Objective

Multi

Objective




Heuristics

Meta- Heuristics

Passenger

Operator





Network Design

2. Data required

Design variables

Decision variables






Route Construction









Demand parameters





Demand estimation

Decision Variables

Design Variables

1. Data required


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


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


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





Pareto optimality




1



2


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



Demand estimation

Constraints

Single

Objective

Multi

Objective




Heuristics

Meta- Heuristics

Passenger

Operator





Network Design

2. Data required

Design variables

Decision variables






Route Construction









Demand parameters





Assignment Models


BRNDP – Passenger demand Assignment












Pareto optimality

Data required



1



2


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



Demand estimation

Constraints

Single

Objective

Multi

Objective




Heuristics

Meta- Heuristics

Passenger

Operator





Network Design

2. Data required

Design variables

Decision variables






Route Construction









Demand parameters






BRNDP – Optimization

Heuristics

Meta- Heuristics




K-shortest path algorithm / Yen’s



Route construction

Optimization algorithms


Step 1

Step 2

Step 3

BRNDP –Route construction procedure


Candidate route set generation Identify initial route set using shortest path algorithms


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





Pareto optimality

Data required



1



2


Load factor

Fleet size

Trip length

Bus lanes

Transfer

3

4

5

6

7





Shortest path algorithm Connectivity check

Example:

Depth-first search

breadth-first search

Initial Route set:

BRNDP – Example


Objective function

Data required



1



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





Pareto optimality

Data required



1



2


Load factor

Fleet size

Trip length

Bus lanes

Transfer

3

4

5

6

7


Small Network test

Real size Network test

Key issues to optimum solution in BRND


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






Pareto optimality Data required Design variables

Decision variables






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


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


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Bus Route Network Design Procedures

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