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Spatio-Temporal Data Mining:
Agent-based Modelling
Ed Manley
Department of Civil, Environmental and Geomatic
Engineering
University College London
Today’s Talk
• Complex Systems
• Agent-based Modelling
– In Principle
– By Example
– My Research
– The Possibilities
• Development of Agent-based
Models
– Design Principles
– Software
Complex Systems
Complex Systems
System Dynamics
+ Emergence
Autonomous, decision-
making entities
“Whole is greater than the sum of it‟s parts”
Complex Systems
Non-Linear Behaviour
System behaviour is characterised by non-linear actions and
interactions
Responses to actions may be
disproportionate, n
ot easily predicted through examination of macroscopic dynamics only
“…increase in price speculation
and deliberate hoarding”
Complex Systems
Self-Organisation
Development of form and pattern through behaviours of
individuals, with no centralised coordination
Complex Systems
Learning and Adaptation
Systems remembers past events and adapts to change
Nature of system evolves over time through learning better outcomes
Architectural adaptation in Abyaneh, Iran
Complex Systems
Cascading Behaviour
Certain behaviours can cascade across networks of individuals
Behaviour can transfer quickly between individuals, not allowing
them enough time to adapt to the new conditions
Complex Systems
Inter-System Complexity
Systems do not sit in isolation, they interact with others at higher levels
A key challenge for understanding a complex system is identifying
where the boundary of influence lies
What is the cause?
Social?
Political?
Technical?
Economic?
How far does it influence?
City-wide?
Nation-wide?
World-wide?
Macroscopic phenomena emerge
through Microscopic actions and
interactions
Complex Systems
Driven by Individual Behaviour
Complex phenomena are best understood through
consideration of the behaviour of all interacting parts
• How does each individual play a part in the system?
• How does individual behaviour change reflect in the system?
• How do individuals and systems interact to cause change?
• How do interactions vary in respect to other conditions?
Why Study Complex Systems?
• Many of today’s most important
global challenges are a product of
interactions between individuals
and systems
• Social, technological, economic, ph
ysical, environmental and political
systems all can play a role
• Understanding these issues
requires an insight into the
complexity of interactions occurring
within the system
Agent-based Modelling
In Principle
Modelling Complex Systems
Traditional Methods
Traditional approaches – usually incorporating DEs – miss
out much of the relevant detail, held within the interactions
of individuals
Highly non-linear and non-equilibrium processes
High heterogeneity within the system
Individuals naturally adapt and change to new conditions
Modelling approaches must capture the full extent of
behaviour, not constrain or smooth them through
macroscopic equations
Modelling Complex Systems
Agent-based Modelling
Agent-based Modelling simulates from individual
perspective, capturing emergent phenomena through agent
behaviour
Individual agents are modelled on real-world entities, as
autonomous decision-makers that act according to a set of
rules
The behaviours and interactions of all agents results in
collective phenomena reflecting system dynamics
Modelling Complex Systems
What is an agent?
• A distinct entity, actively
involved in dynamics of the
system
• Always autonomous
• May be
human, animal, infrastructural, p
hysical, technical, basically any
kind of encapsulated individual
• Behaviour may be very
simple, or quite complex
• May be heterogeneity among
population, but not always
Modelling Complex Systems
Agent-based Modelling
Agent-based Modelling enables the exploration of how a
system changes over space and time
In many cases, spatial proximity is vital, and strongly
influences agent behaviour.
The behaviour of a system usually changes over time – this
is an explicit component of all agent-based models
Agent-based Modelling
In Principle
AGENT
Properties
Current State
Preferences
Goals
Actions
Tasks
Responses
ENVIRONMENT
Geographic
space, vector
space, grid etc.
SYSTEMS
Apply Influence
EVENT SCHEDULER
Prompts all in environment to update state
Population reflective
of heterogeneity
identified in real
population
Agent Behaviour Simulation Environment
SYSTEM OUTPUT
Agent-based Modelling
Modelling Behaviour
• Agent behaviour may be simple or sophisticated
• However, this does not necessarily reflect in the degree
of complexity viewed at the system level
• We’ll now go through some examples of simple and
complex agent behaviour, demonstrating how
accumulated behaviour reflect in macroscopic
phenomena
• Models developed in NetLogo software
Agent-based Modelling
By Example
Agent-based Modelling
By Example
Ant Nest Model
Simple ant foraging behaviour
Simple model demonstrating ant communication
behaviours around food sources
Heterogeneity across population only lies in agents’
actions – yet macroscopic patterns still resolve
Ants move randomly in search for food, once found
they return to the nest, leaving a pheromone trail for
other ants to follow
Other ants, on sensing the pheromone, follow it
towards the food source to carry out the same
procedure
AGENT
Properties
-
Actions
Move Randomly
Return to Nest
Leave Pheromone
Follow Pheromone
Agent-based Modelling
By Example
Ant Nest Model
Things to Notice:
• Route are established through the initial discovery by one single
ant – this is non-linear and self-organisational behaviour
• Generally only one route is operating at a given time, with it being
more difficult to establish other routes while most ants are
preoccupied
• Altering the pheromone behaviours causes significant changes to
rate at which food is found and transported back to nest
Agent-based Modelling
By Example
Schelling’s Segregation Model (1978)
The „first‟ Agent-based Model
Model of evolution of racial segregation in American
cities during 1970s
Two types of simple agents, behaviour leads to
patterns developing in urban realm
Grid-based spatial representation of environment
System outputs showing % unhappy and % similar
AGENT
Properties
Agent Type
% Similar Wanted
Happy?
Similar Nearby %
Other Nearby %
Actions
Assess Area
Find Random Spot
Agent-based Modelling
By Example
Schelling’s Segregation Model (1978)
Things to Notice:
• Individuals move randomly, assessing each location
independently, but yet order is established – self-organisation
• The random nature of movement means that the arrival of a single
green agent may lead to the departure of a number of red agents –
non-linear response to a simple action
• Space is very important – if space is available agents may cluster
into completely homogenous groups, if not then allowances have to
be made
Agent-based Modelling
By Example
El Farol Bar (1994)
Exploring Agent Predictive Power
Popular bar in Sante Fe, New Mexico – Thursday
night is Irish music night! However, the bar often gets
uncomfortably crowded putting potential visitors off.
Agents use a prediction strategy to decide whether
to go to the bar, prediction is based on a weighting of
previous weeks’ attendances
Agents utilise their best performing prediction
strategies in deciding whether to attend or not.
AGENT
Properties
Strategies
Best Strategy
Current Prediction
Attend?
Actions
Create Strategy
Make Prediction
Go to Bar
Agent-based Modelling
By Example
El Farol Bar (1994)
Things to Notice:
• Representation of inductive reasoning by agents, bounded in their
knowledge of the problem
• Game theoretic representation of behaviour, predicting actions of
others in order to select own behaviour
• Increased number of strategies leads to less variation in patterns
• When agents have memory of only previous week’s attendance
then the system descends into a chaotic loop of attendance and
non-attendance
Agent-based Modelling
By Example
Virus Spreading Model
Cascading Virus Spreading through a Network
Abstract representation of virus spreading through a
network, demonstrates the SIR
(susceptibility, infected, resistance) model of
epidemics
Virus spreads between network nodes, according to
defined spread probabilities, with checks carried out
every tick
Network configuration is vital in determining virus
movement patterns
AGENT
Properties
Infected?
Resistant?
Actions
Become
Susceptible
Become Infected
Become Resistant
Spread Virus
Agent-based Modelling
By Example
Virus Spreading Model
Things to Notice:
• Good demonstration of potential for problem to swiftly cascade
through a network of agents
• But, some agents are able to adapt to the virus, causing it to
eventually die out
• Networked model introduces a new element of systemic
behaviour, demonstrating importance of connectivity
• Behaviour of virus – in terms of contagiousness – and agent
behaviour – rate of recovery – are both vital in establishing
infection patterns
Agent-based Modelling
By Example
Economic Disparity Land Use Model
Selection of Residence Area by Socio-Economic
Status
More sophisticated model of land use
development, incorporating four types of agent –
representing human behaviour and influence of
internal systems
‘Rich’ and ‘poor’ agents calculate the utility of a
residential location by quality of land measure, cost of
living and proximity to services
Service location and land squares considered agents
too – behaving independently, impacting on system
dynamics
AGENT
Properties
Type
Actions
Calculate Utility
Find New Location
Die
Human Agents
Agent-based Modelling
By Example
Economic Disparity Land Use Model
Things to Notice:
• Good demonstration of development of spatio-temporal patterns
based on agent preference and behaviour
• Demonstrates mixture of agents and systems and their
interactions – land value development, location of jobs, selection of
residence
• Behaviour of agents leads to development of quite different urban
structures – either sprawl or clustering
• Development of Schelling’s segregation model, with more complex
mechanisms driving dynamics
Agent-based Modelling
By Example
My Research
Evolution of Urban Traffic Systems in response to Unexpected Road
Closures
Complex model of agent behaviour, developed using a more
sophisticated modelling platform
Agent design incorporates heterogeneity in terms of spatial knowledge
and route choice – based on analysis of movement data
Individual responses towards road closure and congestion by agents
results in evolution of traffic patterns over space and time
Agent-based Modelling
The Possibilities
Recent Conference on ABM included some of the following
themes:
• Pedestrian Simulation, indoor and outdoor
• Education Planning
• Housing Choice and Housing Policy
• Impact of forest composition on spread of disease in Red Colobus populations
• Operation of HVAC systems in commercial buildings
• Land-use change in the Elbow River watershed in southern Alberta
• Agent based model of urban retail system
• An Agent-Based Model for Analysing Conflict, Disasters, and Humanitarian Crises in East Africa
• Spatio-temporal Dynamics of Slum Formation in Mumbai, India
• Climate Change, Land Acquisition, and Household Dynamics in Southern Ethiopia
• An Agent-Based Understanding of City Size Distributions
• Simulating Residential Dynamics in London's Housing Market
A world of possibilities!
Development of
Agent-based Models
Development
Principles
1. Identify the most relevant actors and processes operating
within your system of interest
– Who is playing an active influence on system dynamics?
– What behaviours need to be captured?
– Where does the system end? Where are its boundaries?
2. Identify whether the relevant behaviours can be modelled
– Do methods exist for the modelling of this behaviour?
– Can behaviour be measured and quantified? Or reduced into a number of
rules?
– Can models reflecting this behaviour be easily validated?
Development
Principles
3. Over which kind of space and time will your agents
interact?
– Will they move over geographic space, or a vector space?
– Will they connect through networks (social, physical) or only by
proximity?
– Can the space be readily discretised?
– How long should the simulation run for? How long a time step?
4. Identify the system-level measures that will indicate the
effectiveness of your model
5. Select the most appropriate platform on which to build
your model based on your specification
Development
Principles
• Keep it Simple!
• Greater sophistication does not necessarily lead to a
better model, but will lead to slower processing times
• Model only the key agents and key behaviours
• Build agent behaviour from data where possible
• Validate both agent behaviour and system patterns
• Get the design right: Garbage In, Garbage Out!
Development
Software
• Large number of frameworks, suitability for your work
should depend on the following aspects:
– Nature of model (size, complexity, desired output etc.)
– Level of programming expertise
– Established programming skills
– Framework maturity (including access to resources, help)
– (Maybe) Operating System
• Most available for free (open source), built within
academia
• Many employ design frameworks, scheduling and
simulation engine functionality
Development
Software
Name Language Maturity Notes
NetLogo Proprietary High
Easy-to-use, highly flexible platform;
Widely used; Great ‘toy’ model
platform, but scalability issues.
Repast Simphony Java and Groovy High
Flexible, scalable platform; Excellent
GUI with good GIS features; Includes
ANN/GA implementations.
MASON Java Medium
Lightweight platform;
Less feature-rich than Repast.
JADE Java High Standardised development platform
Swarm Objective-C Medium
Similar design to Repast but with
less functionality
Final Word
Final Word
Agent-based Modelling
• ABM is an excellent platform for modelling phenomena
where individual behaviour is central to defining system
characteristics
• Enables the prediction and examination of expected AND
unexpected behaviours
• Applicable to a range of situations, able to incorporate
human, technical and ecological agents
• Careful agent design is vital, and validation should be a
priority
• The range of platforms available means ABM is open to
all
Thank You
Questions?
Ed Manley
ucesejm@ucl.ac.uk
Blog: www.UrbanMovements.co.uk
Twitter: @EdThink
References
Bonabeau, E. 2002. ‘Agent-based modeling: Methods and techniques for simulating
human systems’. Proceedings of National Academy of Sciences. 99(3): 7280–7287.
Epstein, J. 2009. ‘Modelling to contain pandemics’. Nature 460, 687.
The Economist. 2010. ‘Agents on Change’.
http://www.economist.com/node/16636121.
Gilbert, N. and Terna, P. 2000. ‘How to build and use agent-based models in social
science’. Mind & Society. 1(1), 57-72.
Castle, C.J.E. and Crooks, A.T. 2006. Principles and Concepts of Agent-Based
Modelling for Developing Geospatial Simulations. http://eprints.ucl.ac.uk/3342.
Grimm, V. and Railsback S. 2012. ‘Agent-Based and Individual-Based Modeling: A
Practical Introduction’. Princeton University Press.
Heppenstall, A,. Crooks, A., See, L. and Batty, M. (eds), ‘Agent-based Models of
Geographical Systems’. Springer.
Gilbert, N. 2010. ‘Agent-based models’. Sage.

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Introduction to Agent-based Modelling

  • 1. Spatio-Temporal Data Mining: Agent-based Modelling Ed Manley Department of Civil, Environmental and Geomatic Engineering University College London
  • 2. Today’s Talk • Complex Systems • Agent-based Modelling – In Principle – By Example – My Research – The Possibilities • Development of Agent-based Models – Design Principles – Software
  • 4. Complex Systems System Dynamics + Emergence Autonomous, decision- making entities “Whole is greater than the sum of it‟s parts”
  • 5. Complex Systems Non-Linear Behaviour System behaviour is characterised by non-linear actions and interactions Responses to actions may be disproportionate, n ot easily predicted through examination of macroscopic dynamics only “…increase in price speculation and deliberate hoarding”
  • 6. Complex Systems Self-Organisation Development of form and pattern through behaviours of individuals, with no centralised coordination
  • 7. Complex Systems Learning and Adaptation Systems remembers past events and adapts to change Nature of system evolves over time through learning better outcomes Architectural adaptation in Abyaneh, Iran
  • 8. Complex Systems Cascading Behaviour Certain behaviours can cascade across networks of individuals Behaviour can transfer quickly between individuals, not allowing them enough time to adapt to the new conditions
  • 9. Complex Systems Inter-System Complexity Systems do not sit in isolation, they interact with others at higher levels A key challenge for understanding a complex system is identifying where the boundary of influence lies What is the cause? Social? Political? Technical? Economic? How far does it influence? City-wide? Nation-wide? World-wide?
  • 10. Macroscopic phenomena emerge through Microscopic actions and interactions Complex Systems Driven by Individual Behaviour Complex phenomena are best understood through consideration of the behaviour of all interacting parts • How does each individual play a part in the system? • How does individual behaviour change reflect in the system? • How do individuals and systems interact to cause change? • How do interactions vary in respect to other conditions?
  • 11. Why Study Complex Systems? • Many of today’s most important global challenges are a product of interactions between individuals and systems • Social, technological, economic, ph ysical, environmental and political systems all can play a role • Understanding these issues requires an insight into the complexity of interactions occurring within the system
  • 13. Modelling Complex Systems Traditional Methods Traditional approaches – usually incorporating DEs – miss out much of the relevant detail, held within the interactions of individuals Highly non-linear and non-equilibrium processes High heterogeneity within the system Individuals naturally adapt and change to new conditions Modelling approaches must capture the full extent of behaviour, not constrain or smooth them through macroscopic equations
  • 14. Modelling Complex Systems Agent-based Modelling Agent-based Modelling simulates from individual perspective, capturing emergent phenomena through agent behaviour Individual agents are modelled on real-world entities, as autonomous decision-makers that act according to a set of rules The behaviours and interactions of all agents results in collective phenomena reflecting system dynamics
  • 15. Modelling Complex Systems What is an agent? • A distinct entity, actively involved in dynamics of the system • Always autonomous • May be human, animal, infrastructural, p hysical, technical, basically any kind of encapsulated individual • Behaviour may be very simple, or quite complex • May be heterogeneity among population, but not always
  • 16. Modelling Complex Systems Agent-based Modelling Agent-based Modelling enables the exploration of how a system changes over space and time In many cases, spatial proximity is vital, and strongly influences agent behaviour. The behaviour of a system usually changes over time – this is an explicit component of all agent-based models
  • 17. Agent-based Modelling In Principle AGENT Properties Current State Preferences Goals Actions Tasks Responses ENVIRONMENT Geographic space, vector space, grid etc. SYSTEMS Apply Influence EVENT SCHEDULER Prompts all in environment to update state Population reflective of heterogeneity identified in real population Agent Behaviour Simulation Environment SYSTEM OUTPUT
  • 18. Agent-based Modelling Modelling Behaviour • Agent behaviour may be simple or sophisticated • However, this does not necessarily reflect in the degree of complexity viewed at the system level • We’ll now go through some examples of simple and complex agent behaviour, demonstrating how accumulated behaviour reflect in macroscopic phenomena • Models developed in NetLogo software
  • 20. Agent-based Modelling By Example Ant Nest Model Simple ant foraging behaviour Simple model demonstrating ant communication behaviours around food sources Heterogeneity across population only lies in agents’ actions – yet macroscopic patterns still resolve Ants move randomly in search for food, once found they return to the nest, leaving a pheromone trail for other ants to follow Other ants, on sensing the pheromone, follow it towards the food source to carry out the same procedure AGENT Properties - Actions Move Randomly Return to Nest Leave Pheromone Follow Pheromone
  • 21. Agent-based Modelling By Example Ant Nest Model Things to Notice: • Route are established through the initial discovery by one single ant – this is non-linear and self-organisational behaviour • Generally only one route is operating at a given time, with it being more difficult to establish other routes while most ants are preoccupied • Altering the pheromone behaviours causes significant changes to rate at which food is found and transported back to nest
  • 22. Agent-based Modelling By Example Schelling’s Segregation Model (1978) The „first‟ Agent-based Model Model of evolution of racial segregation in American cities during 1970s Two types of simple agents, behaviour leads to patterns developing in urban realm Grid-based spatial representation of environment System outputs showing % unhappy and % similar AGENT Properties Agent Type % Similar Wanted Happy? Similar Nearby % Other Nearby % Actions Assess Area Find Random Spot
  • 23. Agent-based Modelling By Example Schelling’s Segregation Model (1978) Things to Notice: • Individuals move randomly, assessing each location independently, but yet order is established – self-organisation • The random nature of movement means that the arrival of a single green agent may lead to the departure of a number of red agents – non-linear response to a simple action • Space is very important – if space is available agents may cluster into completely homogenous groups, if not then allowances have to be made
  • 24. Agent-based Modelling By Example El Farol Bar (1994) Exploring Agent Predictive Power Popular bar in Sante Fe, New Mexico – Thursday night is Irish music night! However, the bar often gets uncomfortably crowded putting potential visitors off. Agents use a prediction strategy to decide whether to go to the bar, prediction is based on a weighting of previous weeks’ attendances Agents utilise their best performing prediction strategies in deciding whether to attend or not. AGENT Properties Strategies Best Strategy Current Prediction Attend? Actions Create Strategy Make Prediction Go to Bar
  • 25. Agent-based Modelling By Example El Farol Bar (1994) Things to Notice: • Representation of inductive reasoning by agents, bounded in their knowledge of the problem • Game theoretic representation of behaviour, predicting actions of others in order to select own behaviour • Increased number of strategies leads to less variation in patterns • When agents have memory of only previous week’s attendance then the system descends into a chaotic loop of attendance and non-attendance
  • 26. Agent-based Modelling By Example Virus Spreading Model Cascading Virus Spreading through a Network Abstract representation of virus spreading through a network, demonstrates the SIR (susceptibility, infected, resistance) model of epidemics Virus spreads between network nodes, according to defined spread probabilities, with checks carried out every tick Network configuration is vital in determining virus movement patterns AGENT Properties Infected? Resistant? Actions Become Susceptible Become Infected Become Resistant Spread Virus
  • 27. Agent-based Modelling By Example Virus Spreading Model Things to Notice: • Good demonstration of potential for problem to swiftly cascade through a network of agents • But, some agents are able to adapt to the virus, causing it to eventually die out • Networked model introduces a new element of systemic behaviour, demonstrating importance of connectivity • Behaviour of virus – in terms of contagiousness – and agent behaviour – rate of recovery – are both vital in establishing infection patterns
  • 28. Agent-based Modelling By Example Economic Disparity Land Use Model Selection of Residence Area by Socio-Economic Status More sophisticated model of land use development, incorporating four types of agent – representing human behaviour and influence of internal systems ‘Rich’ and ‘poor’ agents calculate the utility of a residential location by quality of land measure, cost of living and proximity to services Service location and land squares considered agents too – behaving independently, impacting on system dynamics AGENT Properties Type Actions Calculate Utility Find New Location Die Human Agents
  • 29. Agent-based Modelling By Example Economic Disparity Land Use Model Things to Notice: • Good demonstration of development of spatio-temporal patterns based on agent preference and behaviour • Demonstrates mixture of agents and systems and their interactions – land value development, location of jobs, selection of residence • Behaviour of agents leads to development of quite different urban structures – either sprawl or clustering • Development of Schelling’s segregation model, with more complex mechanisms driving dynamics
  • 30. Agent-based Modelling By Example My Research Evolution of Urban Traffic Systems in response to Unexpected Road Closures Complex model of agent behaviour, developed using a more sophisticated modelling platform Agent design incorporates heterogeneity in terms of spatial knowledge and route choice – based on analysis of movement data Individual responses towards road closure and congestion by agents results in evolution of traffic patterns over space and time
  • 31.
  • 32. Agent-based Modelling The Possibilities Recent Conference on ABM included some of the following themes: • Pedestrian Simulation, indoor and outdoor • Education Planning • Housing Choice and Housing Policy • Impact of forest composition on spread of disease in Red Colobus populations • Operation of HVAC systems in commercial buildings • Land-use change in the Elbow River watershed in southern Alberta • Agent based model of urban retail system • An Agent-Based Model for Analysing Conflict, Disasters, and Humanitarian Crises in East Africa • Spatio-temporal Dynamics of Slum Formation in Mumbai, India • Climate Change, Land Acquisition, and Household Dynamics in Southern Ethiopia • An Agent-Based Understanding of City Size Distributions • Simulating Residential Dynamics in London's Housing Market A world of possibilities!
  • 34. Development Principles 1. Identify the most relevant actors and processes operating within your system of interest – Who is playing an active influence on system dynamics? – What behaviours need to be captured? – Where does the system end? Where are its boundaries? 2. Identify whether the relevant behaviours can be modelled – Do methods exist for the modelling of this behaviour? – Can behaviour be measured and quantified? Or reduced into a number of rules? – Can models reflecting this behaviour be easily validated?
  • 35. Development Principles 3. Over which kind of space and time will your agents interact? – Will they move over geographic space, or a vector space? – Will they connect through networks (social, physical) or only by proximity? – Can the space be readily discretised? – How long should the simulation run for? How long a time step? 4. Identify the system-level measures that will indicate the effectiveness of your model 5. Select the most appropriate platform on which to build your model based on your specification
  • 36. Development Principles • Keep it Simple! • Greater sophistication does not necessarily lead to a better model, but will lead to slower processing times • Model only the key agents and key behaviours • Build agent behaviour from data where possible • Validate both agent behaviour and system patterns • Get the design right: Garbage In, Garbage Out!
  • 37. Development Software • Large number of frameworks, suitability for your work should depend on the following aspects: – Nature of model (size, complexity, desired output etc.) – Level of programming expertise – Established programming skills – Framework maturity (including access to resources, help) – (Maybe) Operating System • Most available for free (open source), built within academia • Many employ design frameworks, scheduling and simulation engine functionality
  • 38. Development Software Name Language Maturity Notes NetLogo Proprietary High Easy-to-use, highly flexible platform; Widely used; Great ‘toy’ model platform, but scalability issues. Repast Simphony Java and Groovy High Flexible, scalable platform; Excellent GUI with good GIS features; Includes ANN/GA implementations. MASON Java Medium Lightweight platform; Less feature-rich than Repast. JADE Java High Standardised development platform Swarm Objective-C Medium Similar design to Repast but with less functionality
  • 40. Final Word Agent-based Modelling • ABM is an excellent platform for modelling phenomena where individual behaviour is central to defining system characteristics • Enables the prediction and examination of expected AND unexpected behaviours • Applicable to a range of situations, able to incorporate human, technical and ecological agents • Careful agent design is vital, and validation should be a priority • The range of platforms available means ABM is open to all
  • 41. Thank You Questions? Ed Manley ucesejm@ucl.ac.uk Blog: www.UrbanMovements.co.uk Twitter: @EdThink
  • 42. References Bonabeau, E. 2002. ‘Agent-based modeling: Methods and techniques for simulating human systems’. Proceedings of National Academy of Sciences. 99(3): 7280–7287. Epstein, J. 2009. ‘Modelling to contain pandemics’. Nature 460, 687. The Economist. 2010. ‘Agents on Change’. http://www.economist.com/node/16636121. Gilbert, N. and Terna, P. 2000. ‘How to build and use agent-based models in social science’. Mind & Society. 1(1), 57-72. Castle, C.J.E. and Crooks, A.T. 2006. Principles and Concepts of Agent-Based Modelling for Developing Geospatial Simulations. http://eprints.ucl.ac.uk/3342. Grimm, V. and Railsback S. 2012. ‘Agent-Based and Individual-Based Modeling: A Practical Introduction’. Princeton University Press. Heppenstall, A,. Crooks, A., See, L. and Batty, M. (eds), ‘Agent-based Models of Geographical Systems’. Springer. Gilbert, N. 2010. ‘Agent-based models’. Sage.