swarm behaviour and traffic simulations
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Swarm behaviour and traffic simulationsUsing stigmergy to solve algorithmic problems, predict and improve vehicle traffic
Overview (1)
Swarms in nature Social insects and Stigmergy Ant algorithms and application examples:
Foraging in ants Using foraging behaviour to solve the TSP
Labour division among social insects Mailmen using adaptive task allocation model
Overview (2)
Traffic simulation by cellular automata Adopting the stigmergic process Prediction of driver behaviour Traffic infrastructure optimization
Drivers as ant agents Signal lights as social insects
Other real world applications
Swarms in nature
What is a swarm ???
Pictures of swarms (1)
Pictures of swarms (2)
Pictures of swarms (3)
Characteristics of swarms Aggregation of animals with similar size and often
similar orientation
Interaction of animals leads to new intelligent forms of behaviour that are not inherited in the individuals
E.g. insects, birds, fish, bacteria
The main actor of the presentation
Social insects and stigmergy
Social insect societies are distributed systems with highly structered social organization
They can accomplish complex tasks that far exceed the individuals abilities
Here: focus on stigmergy as important means of indirect communication paradigm
Stigmergy Originally defined by Grassé:
Stimulation of workers by the performance they have achieved
Method of indirect communication in a self-organizing emergent system where its individual parts communicate with each other by modifying their local environment
Here: Pheromones diffusing chemical substance
Stigmergy example
Example: termites buildung nest pillars with soil pellets
Stimulus response
Autocatalytic process
Stigmergy behaviour of ants
Stigmergy behaviour in ants and their transfer to
computer algorithms:
Foraging and the TSP
Labour Division and adaptive task allocation
Foraging in ants Foraging means searching for food
Ants manage to find the shortest path between their nest and a food source
Achieved through trail-laying and trail–following behaviour with pheromones Stigmergy
Foraging example Two paths with
different lengths
Ants follow way with most pheromones
Autocatalytic process leads to „differential length effect“
The Travelling Salesman Problem Consists of a set of given cities
Goal is to visit all cities in a closed loop of shortest length
Every city must be visited only once!
E.g. 15 biggest cities of Germany
TSP represented by graph theoryTSP defined more generally by graph theory: Graphs consist of vertices V and edges E Cities are vertices, edges are connections between cities In the TSP each city is connected to each other! Each edge has a certain length
Example: 4 cities A,B,C,D
represented by vertices;
6 connnections with lengths
represented by edges
Ants solving the TSP Artificial ants exploring the TSP graph Artificial pheromones added by ants after completion of a
complete loop proportional to 1/length of route Probabilistic transition rule for ant k to next city j:
City j visited? Length of edge gives desirability measure ηij = 1/length
Amount of pheromones τij(t) on edge (i, j)
Evaporation of pheromones over time lets system forget bad information
Labour division in ants Fundamental in social insects: Division of
reproductive castes from worker castes
Further divisions: subcastes of workers specialists subcastes of age and morphology again dividing subcastes into behavioural castes
Plasticity: Workers switch tasks in response to internal and external pertubations
Labour division model
Based on idea of response threshold
Stimulus exceeds individuals response threshold individual engages in task performance
Stimulus plays role of Stigmergy here (can be pheromones, amount of encounters, …)
Extended labour division model
More realistic:
Extend previous model by threshold varying in time.
if an individual performs a certain task its threshold related to this task decreases
the thresholds related to all other tasks, not performed meanwhile, are increasing
Example: Express mail retrieval (1)
Group of mailmen has to
pick up letters in a city
Goal: Allocation of mailmen to appearing demands should be optimal realized with adaptive task allocation model
Each mailmen i reacts with a certain probability p to arising demands, depending on: response threshold Ө related to area j with demand the distance d to the area with demand the intensity s of the demand stimulus
Example: Express mail retrieval (2)
Figure (a): demand of a certain area over time
At t = 2000 the mailman that is specialized on this area gets removed
Figure (b): response threshold of another mailmen that is reacting to the loss of the specialist
Traffic simulations
Why would one do that?
to predict drivers behaviour in order to adjust dynamic traffic signs, or propose alternative routes in navigation devices or radio
to improve traffic infrastructure and traffic light plans in big, complicated traffic networks like cities
Cellular automata traffic models (1)
Two major approaches on traffic simulation: Fluid-dynamical, with continuous traffic macroscopic Discretized cellular automata model microscopic
Focus in presentation: discretized cellular automata models
Discretized: Street is diveded into fixed sites, cars have integer velocities Each site can be occupied by a car or can be empty
car 1 car 2
x meters
site n site n+1 site n +2 site n +3 site n + 4
e.g. one lane traffic
Cellular automata traffic models (2)
Assuming a simple one lane model:
One update of the system consists of the following steps performed with each car in parallel: Acceleration or slowing down:
Depending on maximal speed and distance to next car Randomization:
To contribute human behaviour and external influences Car motion:
The advancment of sites, according to the speed
Model shows nontrivial and realistic behaviour
Adopting Stigmergy Cars adopt the pheromone laying and sniffing behaviour of
ants
Leads to very realistic and dynamic system
Reduces communication between cars to local information creation and retrieval stigmergy
Computational costs can be reduced for collision checking
Still, information about traffic signs and other environmental signals are non-local
„cellular automata ant cars“
How cars behave like ants Each car leaves and sniffs pheromones on the road Pheromones fade over time, like with ants Faster cars leave longer trails then slower cars (a)
Additional pheromone dropping necessary for stopped cars (b)
quick deceleration lane changing (c)
like using signal andbrake lights
(a)
(b)
(c)
Traffic prediction Measurement devices like cameras determine the vehicles
entering an area Implementing foraging behaviour of ants leads to realistic
system of interacting drivers
drivers follow other drivers and try to escape jams Various types of driver support:
Adjustment of dynamic traffic signs to avoid congestions Knowledge of growth of traffic jams allows to give reasonable
redirections Through use of foraging behaviour alternative routes can be given
more effectively, cars spread more
Optimizing traffic light plans
Microscopic traffic model by individual cars with individual aims
1st Approach: Cars as agents facilitate change of light plans by voting Evolutionary process improves overall light plans
2nd Approach: Groups of ligths at an intersection behave like social
insects Adaptive task allocation is responsible for running plans
Cars voting for traffic ligths Each car keeps track of two variables:
total driving time dtot
total waiting time wtot
waiting measure:
Statistics give information about overall fitness overall waiting measure:
Cars that are stopped at a light vote for it
Lights with many votes are more probable to be mutated quicker adaption in the evolutionary process
Probabilistic mutations of traffic light timings Mutation changes length of correlated light phases at
an intersection (e.g. N–S and E-W)
Simulation of each branch of a new generation Survival of the fittest with least waiting time of
cars
Evolutionary process
simulation 1
simulation 2
simulation 3
choose fittest
mutate
. . . .
mutate
Traffic Simulation under SuRJESuRJE: Swarms Under R&J using Evolution Design environment to build, test and optimize traffic
scenarios Uses swarm based approach and
evolutionary adaption Features:
Enables to build multi-lane road maps Car seeding areas define the
input and output of cars Initial lights settings for starting point Evolutionary adaption parameters can be set
Simulation example in SuRJE
Example network: „Looptown“ (a) Figure (b) shows the decrease of overall waiting time
over generations
Traffic lights as social insects
Traffic lights are implemented as social insects
all lights at an intersection form one insect Insect has to perform one traffic light plan out of
several for its intersection Traffic can be modeled by any microscopic traffic
simulator Cars emit pheromones when crossing and waiting at
an intersection to provide stimulus
Use of adaptive task allocation Adaptive task allocation model is applied to insects
light-plans are chosen through stimulus – response strategies communication of intersections only by Stigmergy
Each insect/intersection has individual thresholds related to available light-plan
Stimulus for light-plan j provided by cars:
Reinforcement learning is used to specialize intersections: Threshold j of intersection i: Learning coefficient:
Example of stimulus evaluation 4 way intersection with two light-plans:
1st plan gives priority to North-South leading lanes 2nd plan has priority for West-East leading lanes
Traffic situation: Many cars are driving on West – East direction Few cars on North-South direction
Initially plan 1 is driven: Big amount of pheromones for W-E (many, waiting cars) Small amount for N-S (few, almost not waiting cars)
evaluation of stimulus yields higher value for 2nd plan!
N
W E
S
Traffic simulation - Recapitulation Traffic prediction:
Simulation into future by using swarm based approach Giving the driver useful information about choosing the best route
Traffic light timing improvment by cars as agents: Cars are modeled with swarm based approach Improvement of traffic light plans through evolution Good for simple traffic lights with static timing program
Dynamic traffic light adoption through social insects: Cars are modeled by any microscopic traffic simulation Intersections choose their light plan through adaptive task allocation Good for traffic lights with sensors for counting cars
Examples for real world applications
Scheduling Problems, e.g. subway, train
Vehicle Routing, e.g. bus, taxi
Connection-oriented network routing, e.g. internet, TCP/IP
Connection-less network routing, e.g. bluetooth, infrared
Optical networks routing
Thank you for your attention!
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