Fireworks Algorithm (FWA) for Optimization · Optimization Ying TAN Introduction Conventional FWA...
Transcript of Fireworks Algorithm (FWA) for Optimization · Optimization Ying TAN Introduction Conventional FWA...
FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Fireworks Algorithm (FWA) for Optimization
Ying TAN
Peking University, China
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Contents
1 Introduction
2 Conventional FWA
3 FWA Variables
4 FWA Based on Graphic Processing Unit
5 Applications
6 Conclusion
7 References
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Definition of Swarm Intelligence
Swarm intelligence is an artificial intelligence techniquebased on the study of collective behavior indecentralized, self-organized systems.*
Swarm intelligence is the property of a system wherebythe collective behaviours of (unsophisticated) agentsinteracting locally with their environment causecoherent functional global patterns to emerge.**
* http://en.wikipedia.org/wiki/Swarm_intelligence
** http://www.sce.carleton.ca/netmanage/tony/swarm.html
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Ant Colony Optimization (ACO)*
ACO is inspired by the phenomena of ants finding paths tofood.
*Colorni, A., Dorigo, M., & Maniezzo, V. (1991, December). Distributedoptimization by ant colonies. In Proceedings of the first Europeanconference on artificial life (Vol. 142, pp. 134-142).
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Particle Swarm Optimization (PSO)*
PSO is inspired by the birds flocking to find a food source.Both individual and social behavior are considered.
*Kennedy, J., & Eberhart, R. (1995, November). Particle swarmoptimization. In Neural Networks, 1995. Proceedings., IEEE InternationalConference on (Vol. 4, pp. 1942-1948). IEEE.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Fish School Search (FSS)*
FSS is inspired by the nature fish to find food.Simple computation in all individuals with some diversityamong individuals.
*Bastos Filho, C. J., de Lima Neto, F. B., Lins, A. J., Nascimento, A. I., &Lima, M. P. (2009). Fish school search. In Nature-Inspired Algorithms forOptimisation (pp. 261-277). Springer Berlin Heidelberg.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Fireworks Algorithm (FWA)*
FWA is inspired by the splendid fireworks in the sky.Good explosion is in a small range with plenty of sparks.
*Tan, Y., & Zhu, Y. (2010). Fireworks algorithm for optimization. InAdvances in Swarm Intelligence (LNCS 6145, pp. 355-364). SpringerBerlin Heidelberg.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Problem Description
Suppose the Fireworks Algorithm (FWA) is designedfor the general optimization problem
where x denotes a location in the potential space, f (x) is anobjective function, and xmin and xmax denote the bounds of thepotential space.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Mimicing the Fireworks
The sparks of fireworks are used to search global bestsolution.
However, the explosion of fireworks are distinguished fromgood to bad in fireworks algorithm.
For a good explosion, the generated sparks are dense andnumerous, and vice versa.
Figure: Two types of fireworks explosion
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Framework of Fireworks Algorithm
Figure: The flowchart of fireworks algorithm
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Five Steps in FWA
Calculation of Sparks Number
Calculation of Explosion Amplitude
Sparks Explosion
Sparks Gaussian Explosion
Selection
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Five Steps in FWA
Calculation of Sparks Number
Calculation of Explosion Amplitude
Sparks Explosion
Sparks Gaussian Explosion
Selection
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Calculation of Sparks Number
The number of sparks generated by eachfirework xi is defined as follow
where m is a parameter controlling the total number of sparksgenerated by the n fireworks, ymax = max(f (xi ))(i = 1, 2, ..., n)is the maximum (worst) value of the objective function amongthe n fireworks, and ξ, which denotes the smallest constant inthe computer, is utilized to avoid zero-division-error.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Calculation of Sparks Number
To avoid overwhelming effects of splendidfireworks, bounds are defined for si
where a and b are const parameters and function round(x) isto choose the nearest interger for variable x .
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Five Steps in FWA
Calculation of Sparks Number
Calculation of Explosion Amplitude
Sparks Explosion
Sparks Gaussian Explosion
Selection
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Calculation of Explosion Amplitude
Amplitude of explosion for each firework isdefined as follows
where A denotes the maximum explosion amplitude andymin = min(f (xi)) (i = 1, 2, ..., n) is the minimum (best) valueof the objective function among the n fireworks.
In contrast to the design of sparks number, the amplitude of agood firework explosion is smaller than a bad one.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Five Steps in FWA
Calculation of Sparks Number
Calculation of Explosion Amplitude
Sparks Explosion
Sparks Gaussian Explosion
Selection
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Sparks Explosion
Explosion sparks are generated by calculatingexplosion displacement.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Five Steps in FWA
Calculation of Sparks Number
Calculation of Explosion Amplitude
Sparks Explosion
Sparks Gaussian Explosion
Selection
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Sparks Gaussian Explosion
Gaussian Sparks are generated in a Gaussianexplosion process.
Gaussian Sparks conducts search in a localspace around a firework.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Five Steps in FWA
Calculation of Sparks Number
Calculation of Explosion Amplitude
Sparks Explosion
Sparks Gaussian Explosion
Selection
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Selection
The selection probability of a location xi isdefined as follows
where
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Pseudo Code of FWA
1 Randomly select n locations for fireworks;2 while stop criteria=false do3 Set off n fireworks respectively at the n locations:4 for each firework xi do5 Calculate the number of sparks si that the firework yields;6 Obtain locations of m common sparks of the firework;7 end for8 for k = 1: m do9 Randomly select a firework xi ;10 Generate a specific spark for the firework using Algorithm 2;11 end for12 Select the best location and keep it for next explosion generation;13 Randomly select n-1 locations from the two types of sparks and
the current fireworks according to the selection probability;14 end while
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Experiments
Benchmark Functions
Experiment Setup
Experiment Results
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Experiments
Benchmark Functions
Experiment Setup
Experiment Results
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Benchmark Functions
The feasible bounds for all functions are setas [−100, 100]D .
Table: Details of benchmark functions
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Experiments
Benchmark Functions
Experiment Setup
Experiment Results
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Experiment Setup
Parameters are set as follow.
1 Number of fireworks = 52 Parameter m = 503 Parameter a = 0.044 Parameter b = 0.85 Parameter A = 406 Parameter m = 5
Each function runs for 20 times.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Experiments
Benchmark Functions
Experiment Setup
Experiment Results
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Experiment Results
Table: Mean and standard deviation of FWA, CPSO and SPSO
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Experiment Results
FWA algorithm can reach the result within fewer functionevaluations.
Table: Accuracy of algorithms at 10000 function evaluations
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
Origination
Steps
Pseudo
Experiments
Discussion
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Discussion
Advantages
Easy to understand and realize
High population diversity
Excellent results
Disadvantages
Large time consuming
Weak on shifted functions
Lack of mathematical foundation
Complicated parameters
To overcome the disadvantages, an enhanced fireworksalgorithm is proposed.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Enhanced Fireworks Algorithm (EFWA)*
1: Initialize N fireworks and constant parameters2: repeat
3: Compute explosion number and amplitude4: Generate explosion sparks5: Generate Gaussian sparks6: Bound particles back to search space7: Evaluate fitness of newly created sparks8: Select N locations for next iteration9: until termination (time, max. # evals, convergence, ...)
*Zheng, S. Q., Janecek, A., & Tan, Y. (2013). Enhancedfireworks algorithm. IEEE International Conference onEvolutionary Computation (Vol. 1, pp. 2069-2077).
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Operator 1 - Explosion Number and Amplitude
Fireworks at good locations:
... will have a large number of sparks
... will have a small explosion amplitude
Problems
If explosion amplitude is [close to] zero, explosion sparkswill be located at [almost] same location as the fireworkitself
Location of the best firework cannot be improved untilanother firework find a better location
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Operator 1 - Explosion Number and Amplitude
Fireworks at good locations:
... will have a large number of sparks
... will have a small explosion amplitude
Problems
If explosion amplitude is [close to] zero, explosion sparkswill be located at [almost] same location as the fireworkitself
Location of the best firework cannot be improved untilanother firework find a better location
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Operator 1 - New Minimal Explosion AmplitudeCheck
Figure: Non-linear decreasing minimal explosion amplitude*
*Zheng, S. Q., Janecek, A., & Tan, Y. (2013). Enhancedfireworks algorithm. IEEE International Conference onEvolutionary Computation (Vol. 1, pp. 2069-2077).
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Framework of EFWA
1: Initialize N fireworks and constant parameters2: repeat3: Compute explosion number and amplitude4: Generate explosion sparks5: Generate Gaussian sparks6: Bound particles back to search space7: Evaluate fitness of newly created sparks8: Select N locations for next iteration9: until termination (time, max. # evals,convergence, ...)
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Operator 2 - Generating Explosion Sparks
Figure: Improvements of generate explosion sparks*
*Zheng, S. Q., Janecek, A., & Tan, Y. (2013). Enhancedfireworks algorithm. IEEE International Conference onEvolutionary Computation (Vol. 1, pp. 2069-2077).
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Framework of EFWA
1: Initialize N fireworks and constant parameters2: repeat3: Compute explosion number and amplitude4: Generate explosion sparks5: Generate Gaussian sparks6: Bound particles back to search space7: Evaluate fitness of newly created sparks8: Select N locations for next iteration9: until termination (time, max. # evals,convergence, ...)
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Operation 3 - Generating Gaussian Sparks
Figure: Improvements of generate Gaussian sparks*
*Zheng, S. Q., Janecek, A., & Tan, Y. (2013). Enhancedfireworks algorithm. IEEE International Conference onEvolutionary Computation (Vol. 1, pp. 2069-2077).
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Operation 3 - Generating Gaussian Sparks
Figure: Sparks of no shift and shift function*
*Zheng, S. Q., Janecek, A., & Tan, Y. (2013). Enhancedfireworks algorithm. IEEE International Conference onEvolutionary Computation (Vol. 1, pp. 2069-2077).
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Framework of EFWA
1: Initialize N fireworks and constant parameters2: repeat3: Compute explosion number and amplitude4: Generate explosion sparks5: Generate Gaussian sparks6: Bound particles back to search space7: Evaluate fitness of newly created sparks8: Select N locations for next iteration9: until termination (time, max. # evals,convergence, ...)
41 / 92
FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Operator 4 - Mapping
Mapping in conventional FWA:
Xik
= X kmin + |Xi |k %
(X k
max − X kmin
)If search space is equally distributed X k
min ≡ −X kmax and a
new location exceeds allowed search space only by a smallvalue, the new position is close to the origin point.
Example: search space [-20, 20], the new spark is createdat X k = 21 (dimension k)
⇒ Mapping: Xik
= −20 + |21|%40⇒ Xik
= 1
Mapping in EFWA: Xik
= X kmin + rand ∗
(X k
max − X kmin
)Uniform random mapping operator
Maps the sparks to any location in the search space withuniform distribution
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Framework of EFWA
1: Initialize N fireworks and constant parameters2: repeat3: Compute explosion number and amplitude4: Generate explosion sparks5: Generate Gaussian sparks6: Bound particles back to search space7: Evaluate fitness of newly created sparks8: Select N locations for next iteration9: until termination (time, max. # evals,convergence, ...)
43 / 92
FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Operator 5 - Selection
Conventional FWA: distance based selection strategy
Favors to select fireworks/sparks in less crowded solutionspace
Diversity increases with expensive computation ⇒ Themost time consuming part
EFWA: Elitism-Random Selection
Optima of the set will be selected first, while otherindividuals are selected randomly.
Linear complexity - reduces runtime of EFWA significantly
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Shifted Index
Table: Shifted index (SI) and shifted value (SV)
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Experiment Results on Schwefel 1.2 Function
Figure: Comparison of FWA, SPSO and twotypes of EFWA
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Another Improved Fireworks Algorithm (IFWA)*
1: Initialize N fireworks and constant parameters2: repeat3: Compute sparks number and amplitude4: Generate sparks by explosion5: Generate Gaussian sparks6: Bound particles back to search space7: Evaluate fitness of newly created sparks8: Select N locations for next iteration9: until termination (time, max. # evals, convergence, ...)
*Liu, J., Zheng, S., & Tan, Y. (2013). The Improvementon Controlling Exploration and Exploitation of FireworkAlgorithm. In Advances in Swarm Intelligence (Vol. 7928,pp. 11-23). Springer Berlin Heidelberg.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Sparks Number and Amplitude
Sparks number is represented as Sn
Amplitude is stated as An
The transfer function is defined as f (x)
Parameter a varies from 20 to 1 evenly in the iteration.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Another Improved Fireworks Algorithm (IFWA)*
1: Initialize N fireworks and constant parameters2: repeat3: Compute sparks number and amplitude4: Generate sparks by explosion5: Generate Gaussian sparks6: Bound particles back to search space7: Evaluate fitness of newly created sparks8: Select N locations for next iteration9: until termination (time, max. # evals, convergence, ...)
*Liu, J., Zheng, S., & Tan, Y. (2013). The Improvementon Controlling Exploration and Exploitation of FireworkAlgorithm. In Advances in Swarm Intelligence (Vol. 7928,pp. 11-23). Springer Berlin Heidelberg.
49 / 92
FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Gaussian Sparks
Random mutation is employed to replace Gaussian sparks.
50 / 92
FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Another Improved Fireworks Algorithm (IFWA)*
1: Initialize N fireworks and constant parameters2: repeat3: Compute sparks number and amplitude4: Generate sparks by explosion5: Generate Gaussian sparks6: Bound particles back to search space7: Evaluate fitness of newly created sparks8: Select N locations for next iteration9: until termination (time, max. # evals, convergence, ...)
*Liu, J., Zheng, S., & Tan, Y. (2013). The Improvementon Controlling Exploration and Exploitation of FireworkAlgorithm. In Advances in Swarm Intelligence (Vol. 7928,pp. 11-23). Springer Berlin Heidelberg.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Selection
Method 1 =⇒ Random Fitness Selection
The best individual is selected for next generation.
Other individuals are selected by possibility
where ymax is the fitness of the worst individual and f (xi ) isthe fitness of individual xi .
Method 2 =⇒ Best Fitness Selection
The best sparks are selected for next generation.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Experiment Results on Shifted Sphere Function
Figure: Comparison of PSO, FWA, IFWAFS and IFWABS
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
More Deatiled Results are in the Paper
Table: Part of Statistic Results of Mean, Std and bestof Benchmark Functions in 10 Dimension
*FES stands for the times of function evaluation.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Empirical Study on Fireworks Algorithm (ESFWA)*
1: Initialize N fireworks and constant parameters2: repeat3: Compute explosion number and amplitude4: Generate explosion sparks5: Generate Gaussian sparks6: Bound particles back to search space7: Evaluate fitness of newly created sparks8: Resampling9: Select N locations for next iteration10: until termination (time, max. # evals, convergence, ...)
*Pei, Y., Zheng, S., Tan, Y., & Takagi, H. (2012, October). An empirical studyon influence of approximation approaches on enhancing fireworks algorithm. InSystems, Man, and Cybernetics (SMC), 2012 IEEE International Conference on(pp. 1322-1327). IEEE.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Experiment Functions
Table: The attributes of benchmark functions
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Shifted Value and Environment
Table: The shifted index and value
The experimental platform is Visual Studio 2012 and theprogram is running on 64bit Window 8 operation systemwith a Intel Core i7-3820QM; 2.70GHz and 2GB RAM.
Each experiment is all running 30 times of over 300,000function evaluations.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Comparison of FWA Variables with PSO
Table: Part of the experiment results
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
EFWA
IFWA
ESFWA
Comparison ofFWA Variablesand PSO
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Result Analysis
From the experiment results, it can be concludedas follows.
EFWA, IFWAFS, IFWABS and LS2-BST10 are superior toconventional FWA on most functions.
SPSO achieves better results on large shifted indexes.
EFWA is fast on 11 functions and SPSO is quicker than otheralgorithms on 2 other functions.
Conventional FWA consumes more time than all the otheralgorithms.
GPU-FWA greatly reduced the computational time for eachfunction.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
The Principle ofGPU
Experiments
Applications
Conclusion
References
The principle of GPU
A graphics processing unit (GPU), is a specialized electroniccircuit designed to rapidly manipulate and alter memory toaccelerate the creation of images in a frame buffer intended foroutput 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.
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FireworksAlgorithm(FWA) for
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Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
The Principle ofGPU
Experiments
Applications
Conclusion
References
What is CUDA
NVIDIA’s Computing Unified Device Architecture (CUDA) is ahigh level general purpose parallel computing platform andprogramming model.
Figure: Memory model on CUDA
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
The Principle ofGPU
Experiments
Applications
Conclusion
References
Running GPU-FWA on CUDA
Figure: The Flowchart of the GPU-FWA Implementation onCUDA
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
The Principle ofGPU
Experiments
Applications
Conclusion
References
GPU-FWA
Two Novel Strategies
Greedy fireworks search
Attract repulse mutation
Advantages
The algorithm can find good solutions, compared to thestate-of-the-art algorithms.
As the problem gets complex, the algorithm can scale in anatural and decent way.
Few control variables are used to steer the optimization.
The variables are robust and easy to choose.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
The Principle ofGPU
Experiments
Applications
Conclusion
References
Experimental Environment
Operation System:Windows 7 Professional x64 with 4G DDR3 Memory (1333MHz)
CPU: Intel core I5-2310 (2.9 GHz, 3.1 GHz)
GPU: NVIDIA GeForce GTX 560 Ti with 384 CUDA cores
CUDA runtime version: 5.0
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FireworksAlgorithm(FWA) for
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Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
The Principle ofGPU
Experiments
Applications
Conclusion
References
Benchmark Functions for GPU-FWA
Table : Benchmark functions
ID Function Expression Feasible bounds Dimension optima
f1 Sphere f1 =∑D
i=1 x2i [−5.12, 5.12]D 30 0
f2 Hyper-ellipsoid f2 =∑D
i=1 i · x2i [−5.12, 5.12]D 30 0
f3 Schwefel 1.2 f3 =∑D
i=1
(∑ij=1 xj
)2[−65.536, 65.536]D 30 0
f4 Rosenbrock f4 =∑D−1
i=1
[100 ·
(xi+1 − x2
i
)2+ (1− xi )
2]
[−2.048, 2.048]D 30 0
f5 Rastrigin f5 = 10 · D +∑D
i=1
[x2i − 10 cos (2πxi )
][−5.12, 5.12]D 30 0
f6 Schwefel f6 =∑D
i=1
[−xi sin
(√|xi |)]
[−500, 500]D 30 -1.3e+04
f7 Griewangk f7 = 14000
∑Di=1 x
2i −
∏Di=1 cos
(xi√i
)+ 1 [−600, 600]D 30 0
f8 Ackley f8 = −a · exp
(−b ·
√1D
∑Di=1 x
2i
)− exp
(1D
∑Di=1 cos (cxi )
)+ a + exp(1) [−32.768, 32.768]D 30 0
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
The Principle ofGPU
Experiments
Applications
Conclusion
References
Experiment Results
Table : Precision comparison
Fun GPU-FWA FWA PSOAvg. Std. Avg. Std. Avg. Std.
f1 1.31E-09 1.85E-09 7.41E+00 1.98E+01 3.81E-08 7.42E-07f2 1.49E-07 6.04E-07 9.91E+01 2.01E+02 3.52E-11 1.15E-10f3 3.46E+00 6.75E+01 3.63E+02 7.98E+02 2.34E+04 1.84E+04f4 1.92E+01 3.03E+00 4.01E+02 5.80E+02 1.31E+02 8.68E+02f5 7.02E+00 1.36E+01 2.93E+01 2.92E+00 3.16E+02 1.11E+02f6 -8.09E+03 2.89E+03 -1.03E+04 3.77E+03 -6.49E+03 9.96E+03f7 1.33E+00 1.78E+01 7.29E-01 1.24E+00 1.10E+00 1.18E+00f8 3.63E-02 7.06E-01 7.48E+00 7.12E+00 1.83E+00 1.26E+01
Table : p-values of t-test
f1 f2 f3 f4 f5 f6 f7 f8
GPU-FWA vs. FWA 1.00E-06 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 5.16E-01 0.00E+00
GPU-FWA vs. PSO 3.46E-01 1.21E-04 0.00E+00 2.15E-02 0.00E+00 6.50E-03 8.03E-01 1.21E-02
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
The Principle ofGPU
Experiments
Applications
Conclusion
References
Experiment Results
GPU-FWA is the fastest algorithm among FWA and PSO.
Table : Running time and speedup of function Rosenbrock
n FWA(s) PSO(s) GPU-FWA(s) SU(FWA) SU(PSO)
48 36.420 84.615 0.615 59.2 137.6
72 55.260 78.225 0.624 88.6 125.4
96 65.595 103.485 0.722 90.8 143.3
144 100.005 155.400 0.831 120.3 187.0
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
The Principle ofGPU
Experiments
Applications
Conclusion
References
Comparison of GPU-FWA and Conventional FWA
The speedup is up to 190.
Figure: Speedup of GPU-FWA compared with conventionalFWA
The horizontal axis represents the number of fireworks, while the vertical axis means the speedup.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
The Principle ofGPU
Experiments
Applications
Conclusion
References
Comparison of GPU-FWA and PSO
The speedup is up to 250.
Figure: Speedup of GPU-FWA compared with PSO
Again, the horizontal axis represents the number of fireworks, while the vertical axis means the speedup.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
The Applications of FWA
Five applications are listed below.
1 FWA for Non-negative Matrix Factorization(NMF) computing
2 FWA on spam detection
3 FWA on design of digital filters
4 FWA solve non-linear equations
5 Multiobjective FWA for variable-ratefertilization in oil crop production
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
FWA for NMF computing[1−3]
Definition of NMF
The Non-negative Matrix Factorization (NMF) refers to aslow-rank approximation and has been utilized in several variousareas like content based retrieval and data mining applications,etc.
NMF can reduce storage and runtime requirements, and alsoreduce redundancy and noise in the data representation whilecapturing the essential associations.
[1] Janecek, A., & Tan, Y. (2011). Swarm Intelligence for Non-Negative Matrix Factorization. InternationalJournal of Swarm Intelligence Research (IJSIR), 2(4), 12-34.[2] Janecek, A., & Tan, Y. (2011). Using population based algorithms for initializing nonnegative matrixfactorization. In Advances in Swarm Intelligence (pp. 307-316). Springer Berlin Heidelberg.[3] Janecek, A., & Tan, Y. (2011, July). Iterative improvement of the Multiplicative Update NMF algorithmusing nature-inspired optimization. In Natural Computation (ICNC), 2011 Seventh International Conferenceon (Vol. 3, pp. 1668-1672). IEEE.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
Problem and Solution
Problem
The nonlinear optimization problem underlying NMF cangenerally be stated asminW ,H f (W ,H) = minW ,H
12 ||A−WH||2F .
Solution
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
Experiment Result
The best algorithm is optimal fireworks search (opt-FS).
Figure: Convergence curves for six different algorithms
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
Spam Detection*
Definition
Spam detection is an action to put those spams away fromgeneral emails.
Problem
In previous research, parameters in the anti-spam process areset simply and manually.
Solution
A new framework of fireworks algorithm was proposed thatautomatically optimizes parameters in anti-spam model.
*He, W., Mi, G., & Tan, Y. (2013). Parameter Optimization of Local-Concentration Model for SpamDetection by Using Fireworks Algorithm. In Advances in Swarm Intelligence (pp. 439-450). Springer BerlinHeidelberg.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
Flowchart of FWA on Spam Detection
Figure: Flowchart of FWA on spam detection
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
Experiment Result
Table: Comparison of fireworks algorithm and local concentrationmethod (LC)
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
FWA for Digital Filters Design
Definition
A digital filter is a system that performs mathematicaloperations on a sampled, discrete-time signal to reduce orenhance certain aspects of that signal.*
Problem
Filters designed by other intellligent algorithms havedisadvantages.
Solution
Design digital filters by fireworks algorithm is proposed.**
*Rabiner, L. R., & Gold, B. (1975). Theory and application of digital signal processing. Englewood Cliffs,NJ, Prentice-Hall, Inc., 1975. 777 p., 1.**Gao, H., & Diao, M. (2011). Cultural firework algorithm and its application for digital filters design.International Journal of Modelling, Identification and Control, 14(4), 324-331.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
Solution
Figure: The flow chart of design digital filters by culturefireworks algorithm
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
Experiment Result
Table: Comparison of four algorithms on FIR filter
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
FWA for Solving Nonlinear Equations
Four equations are listed below.
Zhang J. (2012). Artificial bee colony algorithm for solving nonlinear equation and system. ComputerEngineering and Applications, 48(22), 45-47.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
Solution
Step 1: Randomly generates n individuals at initial.
Step 2: Generate common sparks and Gaussian sparks thesame as fireworks algorithm.
Step 3: Choose the best individual for next generation andthe next (N - 1) individuals are choose the same likefireworks algorithm.
Step 4: If the terminal condition is met, end theprocedure. If not, go back to step 2.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
Experiment Result
Table: Comparison of ABC and FWA algorithms on fourequations
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
Multiobjective FWA for variable-rate fertilization inoil crop production
Oil crop fertilization is a multiobjective problem.
Three objectives
1 Crop quality
2 Fertilizer cost
3 Energy consumption
Solution
Multiobjective fireworks algorithm
Differential evolution strategies
Zheng, Y. J., Song, Q., & Chen, S. Y. (2013). Multiobjective fireworks optimization for variable-ratefertilization in oil crop production. Applied Soft Computing.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
Framework of Multiobjective Fireworks Algorithm
(1) Initialization.
1.1) Randomly generate a population P of p feasible solutions.1.2) Create the empty non-dominated solution archive NP and select those non-dominated solutions from Pto update NP.
(2) Iterative improvement.
2.1) For each individual (2.1) For each individual xi in P do:2.1.1) Calculate number of sparks si for xi .2.1.2) Calculate amplitude of sparks Ai for xi .2.1.3) Generate si sparks of xi .2.1.4) Generate a specific spark of xi .2.1.5) Compute fitness for all sparks.2.1.6) Update NP based on the new solutions (sparks).
2.2) Select p solutions from the fireworks and sparks, where the selection probability of each solution xi isf (xi )/sum(f (xi ));
2.3) For i = 1 to p2.3.1) Apply the mutation, crossover and selection operators to xi and get a trial solution ui .2.3.2) If the DE result indicates that xi is to be replaced by ui , then use ui to update NP.
2.4) Update P by including the best solution and other (p − 1) ones randomly selected according todistance-based propability.
2.5) If the termination condition is satisfied, then the algorithm stops; else go to step 2.1).
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
1.NMFComputing
2.SpamDetection
3.Digital FiltersDesign
4.NonlinearEquations
5.CropFertilization
Conclusion
References
Experiment Results
Table: Solutions of Multiobjective random search (MORS) andMultiobjective fireworks algorithm (MOFOA)
Figure: Distribution of the solutions in objective space
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Conclusion
For fireworks algorithm, there are both advantages anddisadvantages.
Advantages
1 Effectively solve most optimization problems
2 Less running time when parallelized
3 Many variables algorithm and varied applications
Disadvantages
1 Lack of necessary mathematical foundation
2 Difficult to choose proper parametersr
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FireworksAlgorithm(FWA) for
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Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Future Works and Acknowledgement
Future Works
Mathematical foundation
More improvements
Research on parameters setting
Deeply research on realization of parallelized algorithm
The applications of fireworks algorithm
Acknowledgement
The following people offered great help.
They are Chao Yu, Shaoqiu Zheng, Ke Ding, ZhongyangZheng, Guyue Mi, Weiwei Hu, Xiang Yang and Lang Liu.
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Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
References
[1] Banerjee, S., & Caballe, S. (2011, November). Exploring Fish School Algorithm for ImprovingTurnaround Time: An Experience of Content Retrieval. In Intelligent Networking and Collaborative Systems(INCoS), 2011 Third International Conference on (pp. 842-847). IEEE.[2] Bastos Filho, C. J., de Lima Neto, F. B., Lins, A. J., Nascimento, A. I., & Lima, M. P. (2009). Fishschool search. In Nature-Inspired Algorithms for Optimisation (pp. 261-277). Springer Berlin Heidelberg.[3] Bureerat, S. (2011). Hybrid population-based incremental learning using real codes. In Learning andIntelligent Optimization (pp. 379-391). Springer Berlin Heidelberg.[4] Bureerat, S. (2011). Improved population-based incremental learning in continuous spaces. In SoftComputing in Industrial Applications (pp. 77-86). Springer Berlin Heidelberg.[5] Colorni, A., Dorigo, M., & Maniezzo, V. (1991, December). Distributed optimization by ant colonies. InProceedings of the first European conference on artificial life (Vol. 142, pp. 134-142).[6] Ding, K., Zheng, S. Q., & Tan, Y. (2013). A GPU-based parallel fireworks algorithm for optimization.Genetic and Evolutionary Computation Conference.[7] Du, Z. X. (2013) Fireworks algorithm for solving nonlinear equation and system. Modern Computer (pp.18-21).[8] Gao, H., & Diao, M. (2011). Cultural firework algorithm and its application for digital filters design.International Journal of Modelling, Identification and Control, 14(4), 324-331.[9] Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning.[10] Hackwood, S., & Beni, G. (1992, May). Self-organization of sensors for swarm intelligence. In Roboticsand Automation, 1992. Proceedings. 1992 IEEE International Conference on (pp. 819-829). IEEE.
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ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
References
[11] He, W., Mi, G., & Tan, Y. (2013). Parameter Optimization of Local-Concentration Model for SpamDetection by Using Fireworks Algorithm. In Advances in Swarm Intelligence (pp. 439-450). Springer BerlinHeidelberg.[12] Janecek, A.,& Tan, Y. (2011). Feeding the fishweight update strategies for the fish school searchalgorithm. In Advances in Swarm Intelligence (pp. 553-562). Springer Berlin Heidelberg.[13 Janecek, A., & Tan, Y. (2011). Swarm Intelligence for Non-Negative Matrix Factorization. InternationalJournal of Swarm Intelligence Research (IJSIR), 2(4), 12-34.[14] Janecek, A., & Tan, Y. (2011). Using population based algorithms for initializing nonnegative matrixfactorization. In Advances in Swarm Intelligence (pp. 307-316). Springer Berlin Heidelberg.[15] Janecek, A., & Tan, Y. (2011, July). Iterative improvement of the Multiplicative Update NMF algorithmusing nature-inspired optimization. In Natural Computation (ICNC), 2011 Seventh International Conferenceon (Vol. 3, pp. 1668-1672). IEEE.[16] Karaboga, D., & Basturk, B. (2008). On the performance of artificial bee colony (ABC) algorithm.Applied soft computing, 8(1), 687-697.[17] Kennedy, J., & Eberhart, R. (1995, November). Particle swarm optimization. In Neural Networks, 1995.Proceedings. IEEE International Conference on (Vol. 4, pp. 1942-1948). IEEE.[18] Liu, J., Zheng, S., & Tan, Y. (2013). The Improvement on Controlling Exploration and Exploitation ofFirework Algorithm. In Advances in Swarm Intelligence (Vol. 7928, pp. 11-23). Springer Berlin Heidelberg.[19] Lou, Y., Li, J., Jin, L., & Li, G. (2012). A Co-Evolutionary Algorithm Based on Elitism andGravitational Evolution Strategies. Journal of Computational Information Systems, 8(7), 2741-2750.[20] Lou, Y., Li, J., Shi, Y., & Jin, L. (2013). Gravitational Co-evolution and Opposition-based OptimizationAlgorithm. International Journal of Computational Intelligence Systems, 6(5), 849-861.
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FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
References
[21] Lu, G., Tan, D. J., & Zhao, H. M. (2002, November). Improvement on regulating definition of antibodydensity of immune algorithm. In Neural Information Processing, 2002. ICONIP’02. Proceedings of the 9thInternational Conference on (Vol. 5, pp. 2669-2672). IEEE.[22] Owens, J. D., Houston, M., Luebke, D., Green, S., Stone, J. E., & Phillips, J. C. (2008). GPUcomputing. Proceedings of the IEEE, 96(5), 879-899.[23] Pei, Y., Zheng, S., Tan, Y., & Takagi, H. (2012, October). An empirical study on influence ofapproximation approaches on enhancing fireworks algorithm. In Systems, Man, and Cybernetics (SMC), 2012IEEE International Conference on (pp. 1322-1327). IEEE.[24] Storn, R., & Price, K. (1995). Differential evolution-a simple and efficient adaptive scheme for globaloptimization over continuous spaces, Berkeley. CA, Tech. Rep. TR-95-012.[25] Storn, R., & Price, K. (1997). Differential evolutiona simple and efficient heuristic for globaloptimization over continuous spaces. Journal of global optimization, 11(4), 341-359.[26] Tan, Y., & Xiao, Z. M. (2007, September). Clonal particle swarm optimization and its applications. InEvolutionary Computation, 2007. CEC 2007. IEEE Congress on (pp. 2303-2309). IEEE.[27] Tan, Y., & Zhu, Y. (2010). Fireworks algorithm for optimization. In Advances in Swarm Intelligence(pp. 355-364). Springer Berlin Heidelberg.[28] Zhang J. (2012). Artificial bee colony algorithm for solving nonlinear equation and system. ComputerEngineering and Applications, 48(22), 45-47.[29] Zhang J. Q. (2011). Fireworks algorithm for solving 0/1 knapsack problem. Journal of WuhanEngineering Institute 23(3), 64-66.[30] Zheng, S. Q., Janecek, A., & Tan, Y. (2013). Enhanced fireworks algorithm. IEEE InternationalConference on Evolutionary Computation (Vol. 1, pp. 2069-2077).
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Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
References
[31] Zheng, Y. J., Ling, H. F., & Guan, Q. (2012). Adaptive parameters for amodified comprehensive learning particle swarm optimizer. MathematicalProblems in Engineering, 2012.[32] Zheng, Y. J., Song, Q., & Chen, S. Y. (2013). Multiobjective fireworksoptimization for variable-rate fertilization in oil crop production. Applied SoftComputing.[33] Zheng, Y. J., Xu, X. L., & Ling, H. F. (2013). A hybrid fireworksoptimization method with differential evolution operators. Neurocomputing.[34] Zheng, Z. Y., & Tan, Y. (2013). Group explosion strategy for searchingmultiple targets using swarm robotic. IEEE Congress on EvolutionaryComputation.[35] Zhou, Y., & Tan, Y. (2009, May). GPU-based parallel particle swarmoptimization. In Evolutionary Computation, 2009. CEC’09. IEEE Congress on(pp. 1493-1500). IEEE.[36] Zhou, Y., & Tan, Y. (2011). GPU-based parallel multi-objective particleswarm optimization. Int. J. Artif. Intell. v7 iA11, 125-141.
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FireworksAlgorithm(FWA) for
Optimization
Ying TAN
Introduction
ConventionalFWA
FWA Variables
FWA Basedon GraphicProcessingUnit
Applications
Conclusion
References
Thank you!
Email: [email protected]: http://www.cil.pku.edu.cn/research/fa/
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