Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying...

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Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing Unit Applications Conclusion References Fireworks Algorithm (FWA) for Optimization Ying TAN Peking University, China 1 / 92

Transcript of Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying...

Page 1: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 2: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 3: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 4: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 5: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 7: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 8: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 9: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 10: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 11: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 12: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 13: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 14: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 15: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 16: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 17: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 18: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 19: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 20: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 21: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 22: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 23: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 24: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 25: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 26: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 27: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 28: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 29: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 30: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 31: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 32: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 33: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 34: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 35: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 36: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 37: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 38: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 39: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 40: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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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Page 41: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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, ...)

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Page 43: Fireworks Algorithm (FWA) for Optimization - PKU · Fireworks Algorithm (FWA) for Optimization Ying TAN Introduction Conventional FWA FWA Variables FWA Based on Graphic Processing

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, ...)

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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 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.

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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

Gaussian Sparks

Random mutation is employed to replace Gaussian sparks.

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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

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

Optimization

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

Optimization

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

Optimization

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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Optimization

Ying TAN

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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Ying TAN

Introduction

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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Introduction

ConventionalFWA

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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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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