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Particle Swarm Optimization AlgorithmsMohamed Tounsi

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Learning Outcomes At the end of the presentation, you will

Get an idea about origin of PSO algorithm Understand the concept behind Swarm

optimization algorithms Get an idea about existing research around

PSO algorithms Know how PSO algorithm can be used for

solving path planning problems Learn one PSO algorithm for path planning

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Outline History Concepts of PSO Algorithms Related Works PSO Algorithm and Path Planning Path Planning Algorithm using PSO

Algorithm

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PSO PSO is a robust stochastic optimization technique

based on the movement and intelligence of swarms.

PSO applies the concept of social interaction to problem solving.

It was developed in 1995 by James Kennedy (social-psychologist) and Russell Eberhart (electrical engineer).

“Best strategy to find the food is to follow the bird which is nearest to the food”

Getting the best solution from the problem by taking particles and moving them around in the search space

PSO is a simple but powerful search technique.

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PSO Search Scheme It uses a number of agents, i.e.,

particles, that constitute a swarm moving around in the search space looking for the best solution.

Each particle is treated as a point in a N-dimensional space which adjusts its “flying” according to its own flying experience as well as the flying experience of other particles.

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PSO Model pbest the best solution achieved so far by that

particle. gbest the best value obtained so far by all particles

The basic concept of PSO lies in accelerating each particle toward its pbest and the gbest locations, with a random weighted acceleration at each time.

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Particle Flying Model

kskpbest

kgbest

kv1kv

1ks

kpbestd

kgbestd

1 2

k kpbestk gbestd dv w w 11 ()c rw and 22 ()c rw and

kv

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Particle Flying Model Each particle tries to

modify its position using the following information: the current positions, the current velocities, the distance between the

current position and pbest, the distance between the

current position and the gbest. Source: [2][3]

kskpbest

kgbest

kvkv1kv 1kv

1ks

kpbestd

kgbestd

1 2

k kpbestk gbestd dv w w 11 ()c rw and 22 ()c rw and

kv kv

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Particle Flying Model

1 1k k ki i is s v

1 2() ( ) () ( )k k k k ki i i iv c rand pbest s c rand gbest s

*

**

Source: [2][3]

kskpbest

kgbest

kvkv1kv 1kv

1ks

kpbestd

kgbestd

1 2

k kpbestk gbestd dv w w 11 ()c rw and 22 ()c rw and

kv kv

𝑉 𝑎2+𝑏2=𝑐2❑𝑘+ 1𝑎21k k ki i iv v v =

W

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PSO AlgorithmFor each particle    Initialize particleEND

Do   For each particle        Calculate fitness value        If the fitness value is better than the best fitness value (pbest) in history        Set current value as the new pbest   End

   Choose the particle with the best fitness value of all the particles as the gbest   For each particle        Calculate particle velocity according equation (*)        Update particle position according equation (**)   End While maximum iterations or minimum error criteria is not attained

(Adapted from : [1][4])

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About Parameters: Swarm size = 20 - 50 ([1]) Typical values for parameters are w=0.9, and

c1=c2=1. Maximum velocities for some small robots

noted in the literature are 20 cm/sec, 100 cm/sec and 1 m/sec.

A large W favors global search while a small wi favors local search

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Comparison With GA No selection operation mechanisms All particles in PSO are kept as members of the

population through the execution PSO is the only algorithm that does not

implement the survival of the fittest. No crossover operation in PSO. No mutation operation in PSO

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Application Optimization Telecommunications power systems signal processing Artificial neural network training Fuzzy system control

….Where Genetic Algorithm can be applied.

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Features Easy to perform Few parameters to adjust Efficient in global search Fast Convergence Larger w: greater global search ability Smaller w: greater local search ability.

15 stut

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PSO to Robot Path Planning The positions of globally best particle in

each iteration are selected, and reached by the robot in sequence

The optimal path is generated with this method when the robot reaches its target

Related works: PSO for Robotic Obstacle-avoidance Path Planning for Soccer

Robots Using Particle Swarm Optimization (2006) Obstacle avoidance with multi-objective

optimization by PSO in dynamic environment (2005)

Robot Path Planning using Particle Swarm Optimization of Ferguson Splines (2006)

Path planning for mobile robot using the particle swarm optimization with mutation operator (2004)

Parallel Learning in Heterogeneous Multi-Robot Swarms (2006,2007)

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Examples of Fitness FunctionsFitness

function: Euclidian Distance Euclidian Distance +

Smoothness

Euclidian Distance + Number obstacles

Neighborhood Generation

Goal

Range of connectivity

New velocity heuristics which solved the premature convergence

Credit Assignment heuristic which solve the Local minimum problem

Hot Zone/Area heuristic Communication Range(Multi Robots)

(Pugh and Martinoli, 2006; Bogatyreva and Shillerov, 2005)

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Variants of PSO for Path Planning

Credit Assignment and Boundary Condition idea:

Reward and Punishment Suspend factor

Robots positions would be suspended each time that they cross boundary lines (similar to TS)

By this conditions they can escape from the areas that they are stuck in it and it is as useful as reinitializing the robot states in the environment.

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Source: [3][4]

Hot Zone/Area Heuristic The idea is based on dividing the environment

to sub virtual fixed areas with various credits.

Areas credit defined the proportion of goals and obstacles positioned in the area.

particles know the credit of first and second layer of its current neighborhood

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Source: [4]

Multi Robot: Communication Methodology Robots can only communicate with those who

are in their communication range. Various communication ranges could be used. This heuristic has major effect on the sub

swarm size. Help request signal can provide a chain of

connections.

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Comparison Faster than GA Converge Quickly than GA / Djikstra Efficient in obstacle avoidance problem Good for Multi-Robot Path Planning

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References1) Kennedy, J. and Eberhart, R. (1995). “Particle Swarm

Optimization”, Proceedings of the 1995 IEEE International Conference on Neural Networks, pp. 1942-1948, IEEE Press.

2) Xin, C., Li, Y.M.: Smooth Path Planning of a Mobile Robot Using Stochastic Particle Swarm Optimization. In: Proceedings of the 2006 IEEE International Conference on Mechatronics and Automation, pp. 1722–1727. Luoyang, China (2006)

3) Li W.; Yushu L.; Hongbin D. and Yuanqing X.; Obstacle-avoidance Path Planning for Soccer Robots Using Particle Swarm Optimization", Proc. IEEE Int. Conf. on Rob. and Biomimetics (ROBIO '06). (2006) pp. 1233- 1238.

4) Saska, M.; Macas, M.; Preucil, L. and Lhotska, L. Robot Path Planning using Particle Swarm Optimization of Ferguson Splines", Proc. IEEE/ETFA '06, (2006) pp. 833-839.

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5) Xin C. and Yangmin L.; "Smooth Path Planning of a Mobile Robot Using Stochastic Particle Swarm Optimization" Proc. IEEE on Mechatronics and Aut., (2006) pp. 1722-1727.

6) Yuan-Qing Q.; De-Bao S.; Ning L. and Yi-Gang C.; Path planning for mobile robot using the particle swarm optimization with mutation operator Proc. Int. Conf. on Machine Learning and Cybernetics, (2004) pp. 2473 – 2478.

7) Hettiarachchi, S. (2006). Distributed online evolution for swarm robotics. Autonomous Agents and Multi Agent Systems.