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Advance in Fireworks Algorithm and its Applications
Ying Tan (谭营)
Peking University
Contact
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
76
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
78
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