metaheuristic tabu pso algorithms

1. Particle Swarm optimisation
Metaheuristic

2. Particle Swarm optimisation
Tabu Search

3. Particle Swarm optimisation
Tabu Search is an improvement over basic local search that
attempts to get over local search problems by not being stuck
in a local minima.
allowing the acceptance of non-improving moves, in order to
not be stuck in a locally optimum solution, and in the hope of
finding the global best.
Tabu search also allows us to escape from sub-optimal
solutions by the use of a tabu list.
A tabu list : is a list of possible moves that could be performed
on a solution.
These moves could be swap operations (as in TSP) .
its move is made tabu for a certain number of iterations
When a move is made tabu , it is added to the tabu list with a
certain value called the Tabu Tenure (tabu length).
With each iteration, the tabu tenure is decremented.
Only when the tabu tenure of a certain move is 0, can the
move be performed and accepted.

4. Particle Swarm optimisation
Intensification/Diversifica
tion
•Intensification: penalize
solutions far from the current
solution
•Diversification: penalize
solutions close to the current
solution

5. Particle Swarm optimisation

6. Particle Swarm optimisation
Tabu Search: Finding the Minimal Value of
Peaks Function

7. Particle Swarm optimisation

8. Particle Swarm optimisation

9. Particle Swarm optimisation
TRAVELING
SALESMAN
PROBLEMThe Travelling Salesman Problem (TSP) is
an NP-Hard problem. It goes as follows,
given a set of cities, with paths connecting
each city with every other city, we need to
find the shortest path from the starting city,
to every other city and come back to the
starting city in the shortest
distance without visiting any city along the
path more than once.
This problem is easy to state, but hard to
solve .It has been proved that the TSP is

10. Particle Swarm optimisation
The largest solved traveling salesman problem,
n 85,900-city route at 30/01‫3‏102/‏‬ -

11. Particle Swarm optimisation

12. Particle Swarm optimisation

13. Particle Swarm optimisation

14. These slides adapted from a presentation
by Maurice.Clerc@WriteMe.com - one of the
main researchers in PSO
PSO invented by Russ Eberhart (engineering
Prof) and James Kennedy (social scientist)
in USA

15. Explore PSO and its parameters with my app
at http://www.macs.hw.ac.uk/~dwcorne/mypages/apps/pso.html

16. Cooperation example

17. Particle Swarm optimisation
Particle’s velocity
PSO Algorithm
socialcognitiveInertia)1( ++=+kiv
GBest
Inertia
cognitive
social
PBest
x(k)
x(k+1)
v(k+1)
v(k)

18. Particle Swarm optimisation
PSO solution update in
2D
Current solution (4, 2)
Particle’s best solution (9,
1)
Global best solution (5, 10)
Inertia: v(k)=(-2, 2)
x(k) - Current solution (4, 2)
PBest - Particle’s best solution (9, 1)
GBest-Global best solution (5, 10)
GBest
PBest

19. Particle Swarm optimisation
PSO solution update in
2D
Current solution (4, 2)
Particle’s best solution (9,
1)
Global best solution (5, 10)
 Inertia: v(k)=(-2,2)
 Cognitive:
PBest-x(k)=(9,1)-(4,2)=(5,-1)
 Social:
GBest-x(k)=(5,10)-(4,2)=(1,8)
x(k) - Current solution (4, 2)
PBest - Particle’s best solution (9, 1)
GBest-Global best solution (5, 10)
GBest
PBest

20. Particle Swarm optimisation
PSO solution update in
2D
x(k) - Current solution (4, 2)
PBest - Particle’s best solution (9, 1)
GBest-Global best solution (5, 10)
 Inertia: v(k)=(-2,2)
 Cognitive:
PBest-x(k)=(9,1)-(4,2)=(5,-1)
 Social:
GBest-x(k)=(5,10)-
(4,2)=(1,8)
v(k+1)=(-2,2)+0.8*(5,-1)
+0.2*(1,8) = (2.2,2.8)
GBest
PBest
v(k+1
)

21. Particle Swarm optimisation
PSO solution update in
2D
GBest
PBest
x(k+1
)
x(k) - Current solution (4, 2)
PBest - Particle’s best solution (9, 1)
GBest-Global best solution (5, 10)
 Inertia: v(k)=(-2,2)
 Cognitive:
PBest-x(k)=(9,1)-(4,2)=(5,-1)
 Social:
GBest-x(k)=(5,10)-
(4,2)=(1,8)
 v(k+1)=(2.2,2.8)
x(k+1)=x(k)+v(k+1)=
(4,2)+(2.2,2.8)=(6.2,4.8)

22. Particle Swarm optimisation
Pseudocode
http://www.swarmintelligence.org/tutorials.php
Equation (a)
v[] = c0 *v[]
+ c1 * rand() * (pbest[] - present[])
+ c2 * rand() * (gbest[] - present[])
(in the original method, c0=1, but many
researchers now play with this parameter)
Equation (b)
present[] = present[] + v[]

23. Particle Swarm optimisation
Parameters
Number of particles (swarmsize)
C1 (importance of personal best)
C2 (importance of neighbourhood best)
Vmax: limit on velocity

24. Particle Swarm optimisation
Pseudocode
http://www.swarmintelligence.org/tutorials.php
For each particle
Initialize particle
END
Do
For each particle
Calculate fitness value
If the fitness value is better than its peronal best
set current value as the new pBest
End
Choose the particle with the best fitness value of all as gBest
For each particle
Calculate particle velocity according equation (a)
Update particle position according equation (b)
End
While maximum iterations or minimum error criteria is not attained

25. Particle Swarm optimisation