Mutation Operators of Fireworks Algorithm From A Novel Swarm Intelligence Algorithm Chao YU Doctor of Science Email: chaoyu@pku.edu.cn

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

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) ……

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. 355-364). Springer Berlin Heidelberg.

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.

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

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

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

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

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.

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

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

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

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

3 Why the Mutation Operator

3 Why the Mutation Operator

3 Why the Mutation Operator

3 Why the Mutation Operator

3 Why the Mutation Operator

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

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

4 FWA with Differential Mutation Operator

4 FWA with Differential Mutation Operator

4 FWA with Differential Mutation Operator The video for FWADE.

4 FWA with Differential Mutation Operator

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

4 FWA with Differential Mutation Operator

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

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).

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

5 FWA with Covariance Mutation Operator

5 FWA with Covariance Mutation Operator

5 FWA with Covariance Mutation Operator

5 FWA with Covariance Mutation Operator

5 FWA with Covariance Mutation Operator

5 FWA with Covariance Mutation Operator

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

5 FWA with Covariance Mutation Operator

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

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.

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

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!

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.

Thank you for listening! The End Thank you for listening! http://www.cil.pku.edu.cn/research/fwa/index.html