1. Mutation Operators of Fireworks Algorithm
From A Novel Swarm Intelligence Algorithm
Chao YU
Doctor of Science

2. OUTLINES
Introductions
Fireworks Algorithm (FWA)
Why the Mutation Operator
FWA with Differential Mutation Operator
FWA with Covariance Mutation Operator
Conclusions

3. 1 Introductions …… Ant Colony Optimization (ACO)
Artificial Immune System (AIS)
Bee Colony Optimization (BCO)
Bacterial Foraging Optimization (BFO)
Fish School Search (FSS)
Fireworks Algorithm (FWA)
Particle Swarm Optimization (PSO)
Water Drop Optimization (WDO)
Wild-Weed Optimization (WWO) ……

4. 1 Introductions
Fireworks Algorithm (FWA) was proposed by Tan and Zhu.*
FWA was inspired by the splendid fireworks in the sky.
* Tan, Y., & Zhu, Y. (2010). Fireworks algorithm for optimization. In Advances in Swarm Intelligence (pp ). Springer Berlin Heidelberg.

5. 1 Introductions
The conventional FWA got 525 citations from the google scholar website, whereas the water drop algorithm only got 344 citations*.
*The numbers are obtained on July 14, 2019.

6. OUTLINES
Introductions
Fireworks Algorithm (FWA)
Why the Mutation Operator
FWA with Differential Mutation Operator
FWA with Covariance Mutation Operator
Conclusions

7. 2 Fireworks Algorithm (FWA)
Initialization
Explosion Operators
Mutation Operators
Boundary Check (Mapping Rules)
The Selection Strategy
Terminal Criteria

8. 2 Fireworks Algorithm (FWA)
Repeat
Begin
Initialization
Explosion operators
Mutation operators
Mapping rules
The Selection strategy
Termination criterion met? N Y
End

9. 2 Fireworks Algorithm (FWA)
The mechanism of the explosion operator. y x o

10. 2 Fireworks Algorithm (FWA)
The mechanism of the explosion operator. 4 20
This figure was taken from the paper named “Fireworks Algorithm for Optimization” with slightly modification.

11. 2 Fireworks Algorithm (FWA)
The mechanism of the mutation operator. y + + + + x o

12. 2 Fireworks Algorithm (FWA)
The mechanism of mapping rules. *

13. 2 Fireworks Algorithm (FWA)
The mechanism of the selection strategy.
--The best individual in each cluster.
--Random if some of them are the same.

14. OUTLINES
Introductions
Fireworks Algorithm (FWA)
Why the Mutation Operator
FWA with Differential Mutation Operator
FWA with Covariance Mutation Operator
Conclusions

15. 3 Why the Mutation Operator

16. 3 Why the Mutation Operator

17. 3 Why the Mutation Operator

18. 3 Why the Mutation Operator

19. 3 Why the Mutation Operator

20. OUTLINES
Introductions
Fireworks Algorithm (FWA)
Why the Mutation Operator
FWA with Differential Mutation Operator
FWA with Covariance Mutation Operator
Conclusions

21. 4 FWA with Differential Mutation Operator
What is the differential mutation?
The selected firework
The 1st selected firework
A spark
The best firework
Sparks
The 2nd selected firework
The best firework
Gaussian mutation
Differential mutation

22. 4 FWA with Differential Mutation Operator

23. 4 FWA with Differential Mutation Operator

24. 4 FWA with Differential Mutation Operator
The video for FWADE.

25. 4 FWA with Differential Mutation Operator

26. 4 FWA with Differential Mutation Operator
Figure. The process of applying Differential Mutation to FWA

27. 4 FWA with Differential Mutation Operator

28. OUTLINES
Introductions
Fireworks Algorithm (FWA)
Why the Mutation Operator
FWA with Differential Mutation Operator
FWA with Covariance Mutation Operator
Conclusions

29. 5 FWA with Covariance Mutation Operator
The 50% better sparks in the cluster with the current best spark.
Get mean value mu and covariance matrix C.
Generate sparks in each cluster ~ N(mu, C).
Figure. The Gaussian sparks distribution with N(0, C).

30. 5 FWA with Covariance Mutation Operator
(Left) Better sparks 50 %
(Right) Better sparks 33 % y y x x O O

31. 5 FWA with Covariance Mutation Operator

32. 5 FWA with Covariance Mutation Operator

33. 5 FWA with Covariance Mutation Operator

34. 5 FWA with Covariance Mutation Operator

35. 5 FWA with Covariance Mutation Operator

36. 5 FWA with Covariance Mutation Operator

37. 5 FWA with Covariance Mutation Operator
TABLE I. CEC 2015 Comp. Functions

38. 5 FWA with Covariance Mutation Operator

39. 5 FWA with Covariance Mutation Operator
Figure. The running time of three algorithms

40. 5 FWA with Covariance Mutation Operator
Covariance mutation was introduced to fireworks algorithm.
The information of groups of sparks was used.
The algorithm named FWACM outperformed AFWA and dynFWA.

41. OUTLINES
Introductions
Fireworks Algorithm (FWA)
Why the Mutation Operator
FWA with Differential Mutation Operator
FWA with Covariance Mutation Operator
Conclusions

42. 6 Conclusions
Improving the mutation operator can improve the performance of FWA.
Mutation operator is worth researching.
Welcome to join the computational intelligence laboratory (CIL), Peking University!

43. 6 Conclusions URL：http://www.cil.pku.edu.cn/research/fwa/index.html
Writing papers concerning FWA is greatly encouraged.
Source codes in Matlab，C++，Java and Python can be downloaded at no cost.

44. Thank you for listening!
The End
Thank you for listening!