advance in fireworks algorithm and its applicationsadvances in swarm intelligence. springer berlin...

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Advance in Fireworks Algorithm and its Applications

Ying Tan (谭营)

Peking University

Contact

ytan@pku.edu.cn

This PPT is available at

http://www.cil.pku.edu.cn/research/fwa/resources/index.html

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OUTLINES

① Brief Introduction to Swarm Intelligence

② Fireworks Algorithm (FWA)

③ FWA Variants

④ GPU-Based Parallel FWA

⑤ Latest Applications of FWA

⑥ Concluding Remarks

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1.Brief Introduction to Swarm Intelligence

Swarm Intelligence (SI) refers to

Simple individuals or information processing units

Interaction between individuals or with environment

Emerging behavior in the swarm-level

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1.Brief Introduction to SI

Some Famous SIAs

Particle Swarm Optimization (PSO)

Ant Colony Optimization (ACO)

Artificial Immune System (AIS)

Bee Colony Optimization (BCO)

Bacterial Foraging Optimization (BFO)

Fish School Search (FSS)

Seeker Optimization Algorithm (SOA)

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1.1 Motivation

① Biological population

② Social phenomena

③ Other laws in a swarm in nature

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1.1 Motivation

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1.2.1 Particle Swarm Optimization

Inspired by the

search food

of flocks.

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1.2.1 Particle Swarm Optimization

A birds flock is searching for a food, and every bird does not know where the food is. But, they know presently the distance of each bird to the food.

This seeking behavior was associated with that of an optimization

how to make a strategy that the bird can get to the

food fastest?

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1.2.1 PSO Principle

solutions

How to choose ?

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每个粒子的运动方式

v

xpg

pi

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1.2.1 Visual Demonstration of PSO

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Complicated Composition Functions

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1.2.2 Ant Colony Optimization (ACO)

Ant system searches Food from Nest

Figure. Auto-catalytic (positive feedback) process

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1.3 Fireworks Algorithm (FWA)*

Tan, Y., & Zhu, Y. (2010). Fireworks algorithm for optimization. In Advances in Swarm Intelligence (pp.

355-364). Springer Berlin. Heidelberg

• FWA is inspired by the splendid fireworks in the sky.

SearchSolution

Space

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1.4 Tendency of FWA

The number of papers concerning about FWA each year since its proposal.

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1.3 History

2010

1. FWA

2. Digital Filter Design

3. NMF

4. 0/1 Problem

5. CA-FWA

6. AcFWA

7. FWA-DE

8. EFWA

9. IFWA

10. GPU-FWA

11. Swarm Robots

12. Equations Problems

13. MOFWA

14. Spam Detection

15. Image Recognition

16. dynFWA

17. AFWA

18. FWA-DM

19. Convergence Analysis

20. BBO-FWA

2011

2012

2013

2014

2015

21. MO-FWA

22. FWA-CM

23. CoFWA

et.al.

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Tutorial materials of FWA

Y. Tan, C. Yu, S.Q. Zheng and K. Ding "Introduction to Fireworks Algorithms ," International Journal of Swarm Intelligence Researcch (IJSIR), October-December 2013, vol. 4, No. 4, pp. 39-71.

谭营, 郑少秋, "烟花算法研究进展," 《智能系统学报》, October 2014, Vol. 9, No. 5, pp. 515-528.

谭营(著)，《烟花算法引论》, 科学出版社, 2015.04. (303页)

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Fireworks Algorithm (FWA)——Proposed

Solution Space

Searching Solution Space

Tan, Ying, and Yuanchun Zhu. "Fireworks algorithm for optimization.“

Advances in Swarm Intelligence. Springer Berlin Heidelberg, 2010. 355-364.

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2. Fireworks Algorithm (FWA)

① Definition of FWA② Operators in FWA③ FWA flowcharts④ Experimental results

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2.1 Definition of FWA

Ideas

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2.1 Definition of firework

Good firework: firework can generate a big population of sparks within a small range.

Bad firework: firework that generate a small population of sparks within a big range.

The next will introduce the operators in FWA.

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Number of sparks

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Amplitude of explosion

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2.2.1 Explosion Operator

BIG RANGELITTLE SPARKS

SMALL RANGEMORE SPARKS

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2.1.2 Mutation Operator

To keep the diversity of sparks, we design another way of generating sparks, namely Gaussian explosion.

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2.1.3 Mapping Rules

Boundary [-100, 100]

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2.1.4 Selection

Crowd

Sparse

KEEP DIVERSITY!

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2.3 The flowchart of FWA

Set N firework

Obtain the sparks

Evaluate the sparks, select N fireworks

for next generation

Terminal criterion?

Repeat

N

Y

End

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2.3 The Process of FWA

Figure. The flowchart of FWA Figure. The explosion of fireworks algorithm

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2.4 Experiments Results of FWA

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2.4 Experiments Results of FWA

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2.4 Experiments Results of FWA

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2.4 Experiments Results of FWA

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3. FWA Variants

① Enhanced FWA (EFWA)② Dynamic Search FWA (dynFWA)③ Adaptive FWA (AFWA)④ FWA with Covariance Mutation (FWACM)⑤ Orienting Mutation Based FWA (dynFWA-OM)⑥ Cooperative FWA (CoFWA)

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3.1 Enhanced Fireworks Algorithm

5 improvements are proposed in EFWA to overcome the disadvantages of conventional FWA.

Improvement 1

FWA (Same distances)

EFWA (Different distances)

S. Zheng, A. Janecek and Y. Tan, "Enhanced Fireworks Algorithm "2013

IEEE Congress on Evolutionary Computation, (CEC 2013) , June 20-

23, Fiesta Americana Grand Coral Beach Hotel, Cancun, Mexico, pp.

10-19.[pdf]

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3.1 Enhanced Fireworks Algorithm

Improvement 2

FWA -------- Amplitude tends to 0.

EFWA -------- Check minimal explosion amplitude.

Figure. Linearly and non-linearly decreasing minimal explosion amplitude

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3.1 Enhanced Fireworks Algorithm

Improvement 3

FWA Gaussian explosion close to original point.

EFWA Use a new explosion strategy.

Figure. The locations of the Gaussian sparks using

the conventional FWA (Ackley function using 100

000 function evaluations)

Figure. Difference between the

Gaussian sparks operator in FWA and

EFWA

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3.1 Enhanced Fireworks Algorithm

Improvement 4

FWA ---- Mapping strategy tends to original point.

Search space [-20, 20], for a spark at -21, it is created at X = -20 + |21|%40 = 1.

EFWA ---- Apply a random mapping strategy.

Improvement 5

FWA ---- Select the individuals by density.

EFWA ---- Randomly select the individuals.

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3.2 Dynamic Search FWA (dynFWA)

Core Firework:

In each iteration, the firework at the currently best location is marked as core firework (CF).

For minimization problems, among the set C of all fireworks the firework XCF is selected as CF when

.

Core Firework(CF)

nonCF Bigger Explosion Amplitude

Global Search

Smaller Explosion Amplitude

Local Search/ Global Search

CF is always selected

[9] S.Q. Zheng, Andreas Janecek, J.Z. Li, and Y. Tan, "Dynamic Search in Fireworks Algorithm, "2014 IEEE World

Conference on Computational Intelligence (IEEE WCCI'2014) - IEEE Congress on Evolutionary Computation

(CEC'2014) , July 07-11, 2014, Beijing International Convention Center (BICC), Beijing, China, pp. 3222-3229.

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3.2 Dynamic Search FWA (dynFWA)

Fireworks

Exploitation -> Accelerate the convergence speed.

Exploration -> Move towards to global optimum, the fireworks swarm can get a better position.

Exploitation

Exploration

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3.2 Dynamic Search FWA (dynFWA)

CEC 2013

28 functions

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3.2 Dynamic Search FWA (dynFWA)

Comparison of dynFWA and EFWA dynFWA achieves better mean fitness results than EFWA on

23 functions.

The test results indicate that the improvement of dynFWA is significant compared to EFWA for 22 benchmark functions.

Comparison of dynFWA and SPSO2011 In total, dynFWA achieves better results (smaller mean

fitness) than SPSO2011 on 17 functions, while SPSO2011 is better than dynFWA on 10 functions. For one function the results are identical.

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3.3 Adaptive Fireworks Algorithm (AFWA)

To calculate an adaptive amplitude, we choose an individual and use its distance to the best individual (the firework in next generation) as the amplitude of the next explosion.

Figure. Adaptive Amplitude on Sphere Function

[10] J.Z. Li, S.Q. Zheng, and Y. Tan, "Adaptive Fireworks Algorithm, "2014 IEEE World Conference on Computational

Intelligence (IEEE WCCI'2014) - IEEE Congress on Evolutionary Computation (CEC'2014) , July 07-11, 2014, Beijing

International Convention Center (BICC), Beijing, China, pp. 3214-3221.

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3.3 Adaptive Fireworks Algorithm (AFWA)

The individual we choose subjects to the following conditions:

1) Its fitness is worse than the firework of this generation

2) Its distance to the best individual (the firework of next generation) is minimal among all individuals subjecting to the condition 1).

Figure. Amplitude of AFWA

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3.3 Adaptive Fireworks Algorithm (AFWA)

Mean error on CEC13 28 benchmark functions.

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3.3 Adaptive Fireworks Algorithm (AFWA)

Mean ranking

T-test results(AFWA vs. EFWA)

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3.3 Adaptive Fireworks Algorithm (AFWA)

Time consumed

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3.4 FWACM

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).

[4] C. Yu and Y. Tan, "Fireworks Algorithm with Covariance Mutation, " 2015 IEEE Congress on Evolutionary

Computation (CEC'2015) , May 25-28, 2015, Sendai International Center, Sendai, Japan, pp.1-8.

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3.4 FWACM

Figure. The process of generating Gaussian sparks by covariance mutation.

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3.4 FWACM

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3.5 dynFWA-OM

-100 -80 -60 -40 -20 0 20 40 60 80 100-100

-80

-60

-40

-20

0

20

40

60

80

100

J. Li and Y. Tan, "Orienting Mutation Based Fireworks Algorithm, " 2015 IEEE Congress on Evolutionary

Computation (CEC'2015) , May 25-28, 2015, Sendai International Center, Sendai, Japan, pp.1-8.

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3.5 dynFWA-OM

-100 -80 -60 -40 -20 0 20 40 60 80 100-100

-80

-60

-40

-20

0

20

40

60

80

100

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3.5 dynFWA-OM

-100 -80 -60 -40 -20 0 20 40 60 80 100-100

-80

-60

-40

-20

0

20

40

60

80

100

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3.5 dynFWA-OM

-100 -80 -60 -40 -20 0 20 40 60 80 100-100

-80

-60

-40

-20

0

20

40

60

80

100

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3.5 dynFWA-OM

-100 -80 -60 -40 -20 0 20 40 60 80 100-100

-80

-60

-40

-20

0

20

40

60

80

100

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3.5 dynFWA-OM

-100 -80 -60 -40 -20 0 20 40 60 80 100-100

-80

-60

-40

-20

0

20

40

60

80

100

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3.5 dynFWA-OM

-100 -80 -60 -40 -20 0 20 40 60 80 100-100

-80

-60

-40

-20

0

20

40

60

80

100

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3.5 dynFWA-OM

-100 -80 -60 -40 -20 0 20 40 60 80 100-100

-80

-60

-40

-20

0

20

40

60

80

100

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3.5 dynFWA-OM

Using CEC 2014 Benchmark

11 mean errors of dynFWA-OM

are significantly better than dynFWA.

Only 5 mean errors are significantly

worse.

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3.6 The Cooperative Framework for FWA (CoFWA)

Principles

Fireworks are with

different information

Fireworks are with

effective information

SQ. Zheng, JZ. Li, A. Janecek, Y. Tan, "A Cooperative Framework for Fireworks Algorithm“, IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBBSI-2015), in press.

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3.6 The Cooperative Framework for FWA (CoFWA)

The Independent Selection Method

Ensure the inherence of effective information

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3.6 The Cooperative Framework for FWA (CoFWA)

The Crowd-avoiding Cooperative Strategy

Improve the diversity of fireworks swarm

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3.6 The Cooperative Framework for FWA (CoFWA)

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4 Graphic Processing Unit Based FWA

GPU-FWA

AR-FWA

Experimental Results

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4.1 Introduce of GPU-FWA

A graphics processing unit (GPU), is a specialized electronic circuit designed to rapidly manipulate and alter memory to accelerate the creation of images in a frame buffer intended for output to a display.*

Figure. A graphics processing unit

*Owens, J. D., Houston, M., Luebke, D., Green, S., Stone, J. E., & Phillips, J. C. (2008). GPU

computing. Proceedings of the IEEE, 96(5), 879-899.

K. Ding, S.Q. Zheng and Y. Tan, "A GPU-based Parallel Fireworks Algorithm for Optimization "ACM Genetic and Evolutionary

Computation Conference (GECCO 2013) , Amsterdam, The Netherlands, July 06-10, 2013. pp. 1-8.

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GPU高性能通用计算

GPU具备如下特性：

计算核心众多

内存带宽高

GPU已进入高性能并行计算的主流行列

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4.1 Introduce of GPU-FWA

Highly parallel structure (Graphics Process Units) GPUs are more effective than general-purpose CPUs for algorithms.

Figure. Memory model on CUDA

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4.2 GPU-FWA

Two Novel Strategies

Greedy fireworks search

(Each firework is updated by its current best sparks. )

Attract repulse mutation

Figure. Attract-Repulse Mutation

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4.2 GPU-FWA

Advantages

The algorithm can find good solutions, compared to the state-of-the-art algorithms.

As the problem gets complex, the algorithm can scale in a natural and decent way.

Few control variables are used to steer the optimization.

The variables are robust and easy to choose.

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4.2 GPU-FWA

Figure. The flowchart of the GPU-FWA implementation on CUDA

K. Ding, S.Q. Zheng and Y. Tan, "A GPU-based Parallel Fireworks Algorithm for Optimization "ACM Genetic and Evolutionary

Computation Conference (GECCO 2013) , Amsterdam, The Netherlands, July 06-10, 2013. pp. 1-8.

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4.3 From GPU-FWA to AR-FWA

Progress in GPU hardware (dynamic parallelism, shuffleinstruction) Reintroduce the controlling of explosion strength More efficient GPU implementation

Advances in FWA study Adoptive amplitude control Non-uniform mutation

Parallel granularity -> Coarse-grained unable to full exploit the paralllelism in the objective

function Large population is necessary to observe great speedup

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4.4 CUDA动态并行机制

A child CUDA kernel can be called

from within a parent CUDA kernel Simplify the programming Model &

Improve the GPU utility

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4.5 AR-FWA—GPU Implementation

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4.7 Benchmark Functions

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Unimodal (0~6)

Basic Multimodal (7~22)

Hybrid (23~28)

Compostition (29~36)

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4.8 Algorithm Performance—Unimodal

77

AR-FWA v.s. EFWA and dynFWA (Unimodal)

(+1 better/0 inconclusive/-1 worse)

0 1 2 3 4 5 6

dynFWA 0 -1 -1 -1 -1 -1 +1

EFWA +1 +1 -1 -1 -1 +1 +1

For simple unimodal functions, AR-FWA shows no advances to EFWA and dynFWA

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4.8 Algorithm Performance—Multimodal

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7 8 9 10 11 12 13 14

dynFWA +1 0 +1 +1 +1 +1 +1 +1

EFWA +1 +1 +1 +1 0 +1 +1 +1

15 16 17 18 19 20 21 22

dynFWA +1 +1 +1 -1 -1 +1 +1 +1

EFWA +1 0 +1 -1 +1 +1 0 0

AR-FWA v.s. EFEA and dynFWA (Basic Multimodal)

Hybrid

23 24 25 26 27 28dynFWA +1 -1 +1 +1 +1 +1EFWA +1 -1 +1 +1 -1 0

Composition

29 30 31 32 33 34 35 36dynFWA +1 +1 +1 +1 +1 -1 -1 -1EFWA -1 +1 +1 +1 +1 +1 -1 -1

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4.8 Algorithm Performance

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Multimodal

Better Even Worse

AR-FWA vs. dynFWA 23 2 6

AR-FWA vs. EFWA 20 5 6

Overall

Better Even Worse

AR-FWA vs. dynFWA 24 2 11

AR-FWA vs. EFWA 23 5 9

AR-FWA outperforms dynFWA and EFWA in general, and greatly improves the performance on

complicated multimodal problems

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4.8 Parallel Performance—Population Size

80

2.78

4.67

6.49

8.58

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

1.40E+00

1.60E+00

1.80E+00

5 10 15 20

Sp

eed

up

Ru

nn

ing

Tim

e (

s/

iterati

on

)

# of fireworks

Sphere

CPU GPU Speedup

Large population is more suitable to achieve significant speedup.

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4.8 Parallel Performance—Complexity

Weierstrass. k𝑚𝑎𝑥 controls the complexity of the objective function. The larger k𝑚𝑎𝑥 is, the higher the complexity is.

GPU vs. CPU

With different function complexity

16.928.7

41.351.2

70.686.7

99.9114.5

130.5144.4

158.3175.8

188.5203.4210.4

224.7241.0

249.2259.7

273.1

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0.00

10.00

20.00

30.00

40.00

50.00

60.00

Sp

eed

up

Kmax

Ru

nn

ing

Tim

e(s/

)

CPU GPU 加速比

AR-FWA performance becomes better on more complicated functions.

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4.9 Summary

AR-FWA outperferm the state-of-the-art FWA on complicated multimodal optimization problems.

Thanks to the dynamic parallelism technique, AR-FWA is easy to implemented efficiently; novel hardware features improve the overall speedup.

AR-FWA can achieve significant speedup with normal population size, thus a very promising tools for real world optimization problems.

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5 The Applications of FWA

Non-negative matrix factorization (NMF)

Design of digital filters

Oil crop production

Pulse width modulated

problems

Spam detectionNon-linear equations

Document clustering

Electricity system

distribution

Others

APPLICATIONS

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5 The Applications of FWA

① FWA for Non-negative Matrix Factorization (NMF) computing

② FWA for design of digital filters

③ Multi-objective FWA for variable-rate fertilization in oil crop production

④ FWA for pulse width modulated (PWM) problems

⑤ Parametric optimization of ultrasonic machiningprocess using FWA

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5.1.1 NMF description

Lee and Seung publish a paper on Nature in 1999 about the NMF problems.

The nonlinear optimization problem underlying NMF can generally be stated as

Mathematically, we consider the problem of finding a “good” (ideally the global) solution of an optimization problem with bound constraints.

2

, ,

1min ( , ) min || || .

2W H W H Ff W H A WH

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5.1.1 NMF description

Low-rank approximations are utilized in several content based retrieval and data mining applications.

Figure. Nonnegative matrix factorization

(NMF) learns a parts-based representation of

faces

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5.1.1 NMF description

Figure - Scheme of very coarse NMF approximation with very low rank k.

Although k is significantly smaller than m and n, the typical structure of the

original data matrix can be retained (note the three different groups of data

objects in the left, middle, and right part of A).

Minimal

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5.1.1 NMF description

Figure – Illustration of the optimization process for row l of the NMF factor W. The

lthrow of A (alr) and all columns of H0 are the input for the optimization algorithms.

The output is a row-vector wlr (the lthrow of W) which minimizes the norm of dl

r,

the lthrow of the distance matrix D. The norm of dlr is the fitness function for the

optimization algorithms (minimization problem).

k

k

m≈

n

m

0r r

ll l

rH d a w

0l

rHwr

lar

lw

0H

W

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5.1.3 Experiments results of NMF

Figure – Left hand-side: average approximation error per row

(after initializing rows of W). Right hand-side: average

approximation error per column (after initializing of H). NMF rank k

= 5. Legends are ordered according to approximation error (top =

worst, bottom = best).

First W First H

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5.1.3 Experiments results of NMF

Figure Accuracy per Iteration when updating only the row of W,

m=2, c=20. Left: k=2, right: k=5

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5.1.3 Experiments results of NMF

Figure – Proportional runtimes for achieving the same accuracy as basic

MU after 30 iterations for different values of k when updating only the rows

of W. (m=2, c=20)

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5.2 FWA for Design of Digital Filters

Definition of digital filter

A digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal.

Figure. Digital filter

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5.2 FWA for Design of Digital Filters

The algorithm of culture FWA.

*Rabiner, L. R., & Gold, B. (1975). Theory and application of digital signal processing. Englewood Clis, NJ, Prentice-Hall, Inc.,

1975. 777 p., 1.

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5.2 FWA for Design of Digital Filters

Table. Comparison of four algorithms on finite impulse response (FIR) filter

PSO is particle swarm optimization. QPSO means quantum-behaved PSO.

AQPSO represents adaptive QPSO. CFWA stands for culture fireworks algorithm.

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5.3 Fertilization in Oil Crop Production

• Fertilize oil crop is a multi-objective problem.

• Objectives:

• Crop quality

• Fertilizer cost

• Energy consumption

• Solution:

• Non-dominatedarchive maintenance

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5.3 Fertilization in Oil Crop Production

Table. Solutions of multi-objective random search (MORS)

and multi-objective fireworks algorithm (MOFOA)

Figure. Distribution of the solutions in objective

space

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5.4 FWA for PWM Problems

Problem description:

There is selective harmonic elimination in pulse width modulated (PWM) inverter.

A solution:

Fireworks algorithm

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5.4.1 Simulation

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5.4.2 Experimental Results

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5.5 Parametric optimization of ultrasonic machiningprocess using fireworks algorithms

It is observed that FWA provides the best optimal results for the considered USM processes.

D. Goswami, S. Chakraborty,“Parametric optimization of ultrasonic machining process using gravitational search and fireworks algorithms” Ain Shams Engineering Journal (2014), Elsevier.

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6 Concluding Remarks

FWA outperformed typical SIAs, including standard PSO, clonal PSO, DE.

FWA successfully applied to many practical fields, such as non-negative matrix factorization(NMF), oil crop fertilization and power system distribution, etc.

The studies of FWA are widely spread all over the world, including China, America, Russia, Japan, India, Thailand, Malaysia, Serbia, Austria, Brazil, Argentina, South Africa, Iran, et al.

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7 Future researches

• Theoretical analysis

• Algorithmic improvements

• FWA for MOO, ManyOO, Combinatorial problem, etc.

• Researches on parameters’ setting

• Realization of parallelized FWA algorithm, for Big-data

• Find more and wider applications in real-world

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Reference

[1] Y. Tan, Y. Zhu. Fireworks algorithm for optimization. ICSI 2010, Part I, Springer LNCS 6145, pp. 355-364

[2] Y. Tan, C. Yu, S.Q. Zheng, & K. Ding. Introduction to Fireworks Algorithm. International Journal of Swarm Intelligence Research (IJSIR), 4(4), 2014, pp. 39-70.

[3] J. Li and Y. Tan, "Orienting Mutation Based Fireworks Algorithm, " 2015 IEEE Congress on Evolutionary Computation (CEC'2015) , May 25-28, 2015, Sendai International Center, Sendai, Japan, pp.1-8.

[4] C. Yu and Y. Tan, "Fireworks Algorithm with Covariance Mutation, " 2015 IEEE Congress on Evolutionary Computation (CEC'2015) , May 25-28, 2015, Sendai International Center, Sendai, Japan, pp.1-8.

[5] K. Ding, Y. Chen, Y. Wang and Y. Tan, "Regional Seismic Waveform Inversion Using Swarm Intelligence Algorithms, " 2015 IEEE Congress on Evolutionary Computation (CEC'2015) , May 25-28, 2015, Sendai International Center, Sendai, Japan, pp.1-8.

[6] L. Liu, S.Q. Zheng and Y. Tan, "S-metric Based Multi-Objective Fireworks Algorithm, " 2015 IEEE Congress on Evolutionary Computation (CEC'2015) , May 25-28, 2015, Sendai International Center, Sendai, Japan, pp.1-8.

[7] S. Q. Zheng, C. Yu, J. Li and Y. Tan, "Exponentially Decreased Dimension Number Strategy in Dynamic Search Fireworks Algorithm for CEC2015 Competition Problems, " 2015 IEEE Congress on Evolutionary Computation (CEC'2015) , May 25-28, 2015, Sendai International Center, Sendai, Japan, pp.1-8.

[8] C. Yu, L. Kelley and Y. Tan, "Dynamic Search Fireworks Algorithm with Covariance Mutation for Solving the CEC 2015 Learning Based Competition Problems, " 2015 IEEE Congress on Evolutionary Computation (CEC'2015) , May 25-28, 2015, Sendai International Center, Sendai, Japan, pp.1-8.

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Reference[9] S.Q. Zheng, Andreas Janecek, J.Z. Li, and Y. Tan, "Dynamic Search in Fireworks Algorithm, "2014 IEEE World Conference on Computational Intelligence (IEEE WCCI'2014) - IEEE Congress on Evolutionary Computation (CEC'2014) , July 07-11, 2014, Beijing International Convention Center (BICC), Beijing, China, pp. 3222-3229.

[10] J.Z. Li, S.Q. Zheng, and Y. Tan, "Adaptive Fireworks Algorithm, "2014 IEEE World Conference on Computational Intelligence (IEEE WCCI'2014) - IEEE Congress on Evolutionary Computation (CEC'2014) , July 07-11, 2014, Beijing International Convention Center (BICC), Beijing, China, pp. 3214-3221.

[11] K. Ding and Y. Tan, "Comparison of Random Number Generators in Particle Swarm Optimization Algorithm, "2014 IEEE World Conference on Computational Intelligence (IEEE WCCI'2014) - IEEE Congress on Evolutionary Computation (CEC'2014) , July 07-11, 2014, Beijing International Convention Center (BICC), Beijing, China, pp. 2664-2671.

[12] C. Yu, L.C. Kelley, S.Q. Zheng, and Y. Tan, "Fireworks Algorithm with Differential Mutation for Solving the CEC 2014 Competition Problems, "2014 IEEE World Conference on Computational Intelligence (IEEE WCCI'2014) - IEEE Congress on Evolutionary Computation (CEC'2014) , July 07-11, 2014, Beijing International Convention Center (BICC), Beijing, China, pp. 3238-3245.

[13] C. Yu, and Y. Tan, "Improving Enhanced Fireworks Algorithm with Differential Mutation, "The 2014 IEEE International Conference on Systems, Man, and Cybernetics, October 5-8, 2014,Paradise Point Resort and Spa, San Diego, California, USA. pp. 270-275.

[14] K. Ding, and Y. Tan, "cuROB: A GPU-Based Test Suit for Real-Parameter Optimization " The Fifth International Conference on Swarm Intelligence (ICSI 2014) , Hefei, China, October 17-20, 2014. Springer, LNCS 8794, pp. 66-78.

[15] S.Q. Zheng, L. Liu, C. Yu, J.Z. Li, and Y. Tan, "Fireworks Algorithm and Its Variants for Solving ICSI 2014 Competition Problems " The Fifth International Conference on Swarm Intelligence (ICSI 2014) , Hefei, China, October 17-20, 2014. Springer, LNCS 8794, pp. 442-451.

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《烟花算法引论》

ISBN：978-7-03-044085-3，303页，

TP-6972.01，40万字，售价：120元

2015年4月

谭营著

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简介

该书系统地描述了作者所提出的烟花算法的产生、算法实现、理论分析、算法改进及其应用，为读者勾勒出了烟花算法的全景图像。

内容包括：烟花算法及其性能分析、收敛性和时间复杂度分析、多种改进算法、混合方法、多目标烟花算法、离散烟花算法、烟花算法的并行化实现、以及几种应用实例。书中重点介绍了烟花算法及其参数设定，各种改进方法、并行化实现、与典型群体智能算法的性能对比分析等。同时，书中还包括了烟花算法的最新资料、一些重要算法的流程图、及其源代码的链接，供感兴趣读者参阅和使用。

本书适合作为智能科学与计算机科学的高年级本科生和研究生的教材，也可作为烟花算法学习的入门参考书。

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简介

全书分四个部分，共17章

第一部分是基础理论包括第1章到第4章，

第二部分是改进算法研究包括第5章到第10章，

第三部分是高级研究主题研究包括第11章到第13章，

第四部分是烟花算法的应用研究包括第14章到第17章。

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附录

最后是5个附录。

附录1给出了标准测试函数集及其图像；

附录2给出了与烟花算法有关的各种网络资源链接列表；

附录3给出了全书术语列表；

附录4是本书的图表目录；

附录5是本书的索引。

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Ying Tan, Fireworks Algorithm: A Swarm

Intelligence Optimization Method,

Springer, 2015.05.

ISBN: 978-3-662-46352-9.

[TOC with samples], [Book at

Springer.Com],

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烟花算法论坛

URL：http://www.cil.pku.edu.cn/research/fwa/index.html

FWA的原理，导论材料

有关FWA的所有论文

有关FWA的重要算法的源代码，包括：Matlab，C++，Java

FWA有关的学术交流活动

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Special Issue at IJSIR-6(2), April - June 2015

International Journal of Swarm

Intelligence Research (IJSIR)

Volume 6, Issue 2, April - June 2015

Special Issue on Developments and

Applications of Fireworks Algorithm

Guest Editors:Ying Tan, Peking University, China,

Andreas Janecek, University of Vienna, Austria,

Jianhua Liu, Fujian University of Technology, China

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Special Issue on Developments and Applications of Fireworks Algorithm

GUEST EDITORIAL PREFACE

Special Issue on Developments and Applications of

Fireworks AlgorithmYing Tan (Peking University, China),

Andreas Janecek (University of Vienna, Austria),

Jianhua Liu (Fujian University of Technology, China)

To obtain a copy of the Guest Editorial Preface, click on the link below.

www.igi-

global.com/pdf.aspx?tid=133575&ptid=118723&ctid=15&t=Special Issue

on Developments and Applications of Fireworks Algorithm

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Special Issue on Developments and Applications of Fireworks Algorithm

ARTICLE 1

Attract-Repulse Fireworks Algorithm and its CUDA Implementation Using Dynamic ParallelismKe Ding (Key Laboratory of Machine Perception (MOE), Peking University, Beijing, China & Department of Machine Intelligence,

School of Electronics Engineering and Computer Science, Peking University, Beijing, China),

Ying Tan (Key Laboratory of Machine Perception (MOE), Peking University, Beijing, China & Department of Machine Intelligence,

School of Electronics Engineering and Computer Science, Peking University, Beijing, China)

ARTICLE 2

Parallelization of Enhanced Firework Algorithm using MapReduceSimone A. Ludwig (Department of Computer Science, North Dakota State University, Fargo, ND, USA),

Deepak Dawar (Department of Computer Science, North Dakota State University, Fargo, ND, USA)

ARTICLE 3

Analytics on Fireworks Algorithm Solving Problems with Shifts in the Decision Space and

Objective SpaceShi Cheng (Division of Computer Science, The University of Nottingham Ningbo, Ningbo, China),

Quande Qin (College of Management, Shenzhen University, Shenzhen, China),

Junfeng Chen (Hohai University, Changzhou, China),

Yuhui Shi (Department of Electrical and Electronic Engineering, Xi'an Jiaotong-Liverpool University, Suzhou, China),

Qingyu Zhang (Shenzhen University, Shenzhen, China)

ARTICLE 4

Binary Fireworks Algorithm Based Thermal Unit CommitmentLokesh Kumar Panwar (MNIT, Jaipur, India),

Srikanth Reddy K (MNIT, Jaipur, India),

Rajesh Kumar (MNIT, Jaipur, India)

ARTICLE 5

Application of Fireworks Algorithm in Gamma-Ray Spectrum Fitting for Radioisotope IdentificationMiltiadis Alamaniotis (Nuclear Engineering Program, University of Utah, Salt Lake City, UT, USA & Applied Intelligent Systems

Laboratory, School of Nuclear Engineering, Purdue University, West Lafayette, IN, USA),

Chan K. Choi (School of Nuclear Engineering, Purdue University, West Lafayette, IN, USA),

Lefteri H. Tsoukalas (School of Nuclear Engineering, Purdue University, West Lafayette, IN, USA)

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Thank you

http://www.cil.pku.edu.cn/research/fwa/index.html