Developments

So far, FWA has been applied for solving practical optimization problems, combined with other optimization algorithms, improved versions, multi-objective fireworks algorithm and parallel implementation.

1 Algorithm Developments

Since the introduction of FWA, it has attracted the attentions from the researchers to develop the conversion algorithm. Zheng Yujun et al (2012). proposed a hybrid algorithm between FWA and DE by including operators from DE into FWA. The results indicate that the hybrid algorithm outperforms both, the conventional FWA and the conventional DE. However, the experiments were only conducted on functions which have their optimum at the origin and hence show similar effects as conventional FWA. Pei Yan et al. (2013) have focused on improving the conventional FWA by investigating the influence of approximation approaches for accelerating the FWA search by elite strategy. The authors compared different approximation and sampling methods, and also different sampling numbers, and analyzed the acceleration performance of FWA based on ten benchmark functions. Their results indicate that the random sampling method with a two degree polynomial model gains the best performance. We point out that different sampling methods are able to improve and speed up the FWA. However, other and probably more important operators of FWA have not been analyzed nor improved in this study. In the recent work, Zheng Shaoqiu et al (2013) proposed a new enhance fireworks algorithm, in their paper, they comprehensively analyzed the operators of FWA and pointed out the limitations. Based on the limitations, Enhance Fireworks Algorithm (EFWA) is proposed.

In addition, Liu Jianhua et al (2013) proposed another improvement version work based on using different sparks number calculation method. The above work are all improvements on single fireworks algorithm. Recently, Zheng Yujun et al (2013) proposed multi-objective fireworks algorithm, which has shown the great success for variable-rate fertilization in oil crop production.

Parallel implementation of swarm intelligence algorithm has attracted lots of attention, our lab Ding et al. (2013) proposed GPU-FWA which greatly accelerate the convergence speed and reduce the running time.

Later, Zheng Shaoqiu et al (2014), Li Junzhi et al (2014) proposed two adaptive explosion fireworks algorithm and the explosion amplitude is updated according to the optimization process information. Yu Chao et al proposed another hybrid algorithm between DE and FWA. Moreover, the convergence property is analysised by Liu Jianhua et al. Zheng Yujun et al (2014) proposed the hybrid FWA with biogeography-based optimization, BBO-FWA.

Yu Chao et al (2014), Li Junzhi et al (2015) conducted comprehensive research on mutation operator, and proposed two new mutation operators, which greatly accelerate the convergence speed for dealing with optimization problems.

Recently, Zheng et al (2015) proposed a cooperative framework for the fireworks algorithm in which a sufficient interaction among fireworks is allowed. Li et al (2016) proposed a guided fireworks algorithm using the information of the objective function provided by the explosion sparks to construct an efficient mutation operator.

2 Applications

Janecek and Tan (2011) used FWA together with Particle Swarm Optimization (PSO), Genetic Algorithms (GA), Differential Evolution (DE), and Fish School Search for improving the initialization of Non-negative Matrix Factorization (NMF). Their results indicate that FWA could not compete with the other optimization algorithms when the number of dimensions (i.e., the rank of NMF) was small, but achieved good results when the number of dimensions was increased. Bureerat (2011) compared twelve different optimization algorithms on 35 benchmark functions with different dimensions ranging from 2 to 30. FWA was ranked as the 6-th best algorithm for optimizing these benchmark functions, which is better than GA and PSO. Gao Hongyuan and Ming Diao (2011) proposed the Cultural Firework Algorithm (CFA) which combines ideas from Cultural Algorithms (CAs) and FWA. CFA acquires problem-solving knowledge (beliefs) from the explosion of fireworks and in return makes use of that knowledge to better guide the search . Results indicate that CFA is well suited for optimizing FIR and IIR digital filters, and outperforms various PSO variants for this type of optimization problem. W.R.He et al. used FWA for the parameters optimization in the process of pattern extraction for spam detection while Zheng Shaoqiu and Tan Ying(2013) used FWA for the parameters determination of the combination of the difference orientation patterns. Both of the results indicate that the optimization of FWA gains improvements. Recently, FWA has been used for selective harmonic elimination, network eeconfiguration mass and minimisation of trusses.

The development of FWA can be grouped as the following:

(1) Basic Algorithm

  • Fireworks Algorithm
  • Tan, Ying, and Yuanchun Zhu. "Fireworks algorithm for optimization." Advances in Swarm Intelligence. Springer Berlin Heidelberg, 2010. 355-364. [pdf]

(2) Algorithms and developments

  • Single objective
  • [1] Pei, Yan, Zheng Shaoqiu, Tan Ying and Takagi H.. "An empirical study on influence of approximation approaches on enhancing fireworks algorithm." Systems, Man, and Cybernetics (SMC), 2012 IEEE International Conference on. IEEE, 2012. [pdf]
    [2] Zheng, Shaoqiu, Andreas Janecek, and Ying Tan. "Enhanced fireworks algorithm." Evolutionary Computation (CEC), 2013 IEEE Congress on. IEEE, 2013. 2069-2077.[pdf]
    [3]Liu, Jianhua, Shaoqiu Zheng, and Ying Tan. "The improvement on controlling exploration and exploitation of firework algorithm." Advances in swarm intelligence. Springer Berlin Heidelberg, 2013. 11-23. [pdf]
    [4] Zheng Shaoqiu, Janecek Andreas, Li Junzhi, Tan Ying. Dynamic search in fireworks algorithm[C]//Evolutionary Computation (CEC), 2014 IEEE Congress on. IEEE, 2014: 3222-3229. [pdf]
    [5] Li Junzhi , Zheng Shaoqiu and Tan Ying , Adaptive Fireworks Algorithm[C]//Evolutionary Computation (CEC), 2014 IEEE Congress on. IEEE, 2014: 3214-3221. [pdf]
    [6] Yu Chao , Kelley Lingchen ,Zheng Shaoqiu and Tan Ying , Fireworks algorithm with differential mutation for solving the cec 2014 competition problems[C]//Evolutionary Computation (CEC), 2014 IEEE Congress on. IEEE, 2014: 3238-3245. [pdf]
    [7] Liu Jianhua, Zheng Shaoqiu and Tan Ying, Analysis on global convergence and time complexity of fireworks algorithm[C]//Evolutionary Computation (CEC), 2014 IEEE Congress on. IEEE, 2014: 3207-3213.[pdf]
    [8] Zhang B, Zhang M, Zheng Yujun. Improving Enhanced Fireworks Algorithm with New Gaussian Explosion and Population Selection Strategies[M]//Advances in Swarm Intelligence. Springer International Publishing, 2014: 53-63.[pdf]
    [9] Si T, Ghosh R. Explosion sparks generation using adaptive transfer function in firework algorithm[C]// IEEE Third International Conference on Signal Processing, Communications and NETWORKING. 2015:305-314. [pdf]
    [10] Shaoqiu Zheng, Chao Yu, Junzhi Li and Y. Tan, "Exponentially Decreased Dimension Number Strategy in Dynamic Search Fireworks Algorithm for CEC2015 Competition Problems, " 2015 IEEE Congress on Evolutionary Computation (CEC'2015) , May 25-28, 2015, Sendai Internatonal Center, Sendai, Japan, pp.1-8 [pdf]
    [11] Junzhi Li and Y. Tan, "Orienting Mutation Based Fireworks Algorithm, " 2015 IEEE Congress on Evolutionary Computation (CEC'2015) , May 25-28, 2015, Sendai Internatonal Center, Sendai, Japan, pp.1-8 [pdf]
    [12] Pei Y, Zheng S, Tan Y, et al. Effectiveness of approximation strategy in surrogate-assisted fireworks algorithm[J]. International Journal of Machine Learning and Cybernetics, 2015, 6(5):795-810. [pdf]
    [13] Zhang B, Zheng Y J, Zhang M X, et al. Fireworks Algorithm with Enhanced Fireworks Interaction[J]. Ieee-Acm Transactions on Computational Biology and Bioinformatics, 2015, 32(6):1-1. [pdf]
    [14] Junfeng Chen, Qiwen Yang, Jianjun Ni, Yingjuan Xie, Shi Cheng, "An Improved Fireworks Algorithm with Landscape Information for Balancing Exploration and Exploitation". 2015 IEEE Congress on Evolutionary Computation (CEC'2015) , May 25-28, 2015, Sendai Internatonal Center, Sendai, Japan, pp.1-8 [pdf]
    [15] Qin Q, Cheng S, Shi Y, et al. Analytics on Fireworks Algorithm Solving Problems with Shifts in the Decision Space and Objective Space[J]. International Journal of Swarm Intelligence Research, 2015, 6(2):52-86. [pdf]
    [16] Zheng S, Li J, Janecek A, et al. A Cooperative Framework for Fireworks Algorithm[J]. IEEE/ACM Transactions on Computational Biology & Bioinformatics, 2015:1-1. [pdf]
    [17] Li J, Zheng S, Tan Y. The Effect of Information Utilization: Introducing a Novel Guiding Spark in the Fireworks Algorithm[J]. 2016:1-1. [pdf]
  • Multi-objective
  • [1] Zheng Yujun, Qin Song, and Sheng-Yong Chen. Multiobjective fireworks optimization for variable-rate fertilization in oil crop production[J]. Applied Soft Computing, 2013, 13(11): 4253-4263. [pdf]
    [2] Lang Liu, Shaoqiu Zheng and Y. Tan, "S-metric Based Multi-Objective Fireworks Algorithm, " 2015 IEEE Congress on Evolutionary Computation (CEC'2015) , May 25-28, 2015, Sendai Internatonal Center, Sendai, Japan. [pdf]
  • Parallel implementation
  • [1] Ding Ke, Zheng Shaoqiu and Tan Ying, "A GPU-based Parallel Fireworks Algorithm for Optimization "ACM Genetic and Evolutionary Computation Conference (GECCO 2013)- a recombiination of 22nd International Conference on Genetic Algorithms (ICGA) and the 18th Annual Genetic Programming Conference (GP) , Amsterdam, The Netherlands, July 06-10, 2013. pp. 1-8. [pdf]
    [2] Ding K, Tan Y. Attract-Repulse Fireworks Algorithm and its CUDA Implementation Using Dynamic Parallelism[J]. International Journal of Swarm Intelligence Research, 2015, 6(2):1-31. [pdf]
    [3] Ludwig S A, Dawar D. Parallelization of Enhanced Firework Algorithm using MapReduce[J]. International Journal of Swarm Intelligence Research, 2015, 6(2):32-51. [pdf]
  • Hybrid FWA with other algorithms
  • [1] Gao Hongyuan, and Ming Diao. "Cultural firework algorithm and its application for digital filters design." International Journal of Modelling, Identification and Control 14, no. 4 (2011): 324-331. [pdf]
    [2] Zhang B, Zhang M X, Zheng Y J. A hybrid biogeography-based optimization and fireworks algorithm[C]//Evolutionary Computation (CEC), 2014 IEEE Congress on. IEEE, 2014: 3200-3206.[pdf]
    [3] Yu C, Li J, Tan Y. Improve enhanced fireworks algorithm with differential mutation[C]//Systems, Man and Cybernetics (SMC), 2014 IEEE International Conference on. IEEE, 2014: 264-269. [pdf]
    [4] Yu C, Kelley L, Zheng S, et al. Fireworks algorithm with differential mutation for solving the cec 2014 competition problems[C]//Evolutionary Computation (CEC), 2014 IEEE Congress on. IEEE, 2014: 3238-3245. [pdf]
    [5] Zheng Yujun, Xu X., and Ling H., Zheng Y J, Xu X L, Ling H F, et al. A hybrid fireworks optimization method with differential evolution operators[J]. Neurocomputing, 2015, 148: 75-82. [pdf]
    [6] Chao Yu, Ling Chen Kelley and Y. Tan, "Dynamic Search Fireworks Algorithm with Covariance Mutation for Solving the CEC 2015 Learning Based Competition Problems, " 2015 IEEE Congress on Evolutionary Computation (CEC'2015) , May 25-28, 2015, Sendai Internatonal Center, Sendai, Japan, pp.1-8 [pdf]
    [7] Chao Yu and Y. Tan, "Fireworks Algorithm with Covariance Mutation, " 2015 IEEE Congress on Evolutionary Computation (CEC'2015) , May 25-28, 2015, Sendai Internatonal Center, Sendai, Japan, pp.1-8 [pdf]
    [8] Bacanin, Nebojsa, Milan Tuba, and Marko Beko. "Hybridized Fireworks Algorithm for Global Optimization." Mathematical Methods and Systems in Science and Engineering (2015) : 108-114. [pdf]
    [9] Gao H, Li C. Opposition-based quantum firework algorithm for continuous optimisation problems[J]. International Journal of Computing Science & Mathematics, 2015, 6(3):256-265. [url]

(3) Applications

  • Initialization of Non-negative Matrix Factorization (NMF)
  • [1] Janecek, Andreas, and Ying Tan. "Using population based algorithms for initializing nonnegative matrix factorization." In Advances in Swarm Intelligence, pp. 307-316. Springer Berlin Heidelberg, 2011. [pdf]
    [2] Janecek, Andreas, and Ying Tan. "Iterative improvement of the multiplicative update nmf algorithm using nature-inspired optimization." In Natural Computation (ICNC), 2011 Seventh International Conference on, vol. 3, pp. 1668-1672. IEEE, 2011. [pdf]
    [3] Janecek, Andreas, and Ying Tan. "Swarm intelligence for non-negative matrix factorization." International Journal of Swarm Intelligence Research (IJSIR) 2, no. 4 (2011): 12-34. [pdf]
  • Digital filter design
  • [4] Gao Hongyuan, and Ming Diao. "Cultural firework algorithm and its application for digital filters design." International Journal of Modelling, Identification and Control 14, no. 4 (2011): 324-331. [pdf]
  • Parameters Optimization
  • [5] He Wenrui, Mi Guyue, and Tan Ying, "Parameter Optimization of Local-Concentration Model for Spam Detection by Using Fireworks Algorithm "The Fourth International Conference on Swarm Intelligence (ICSI 2013) , Harbin, China, June 12-15, 2013. Springer, LNCS 7928, pp. 439-450. [pdf]
    [6] Zheng Shaoqiu, Tan Ying, "A Unified Distance Measure Scheme for Orientation Coding in Identification "[pdf]
  • Selective Harmonic Elimination
  • [7] Rajaram R, Palanisamy K, Ramasamy S, et al. Selective Harmonic Elimination in PWM Inverter Using Fire Fly and Fire Works Algorithm[J]. 2014. [pdf]
  • Network Eeconfiguration
  • [8] Imran A M, Kowsalya M, Kothari D P. A novel integration technique for optimal network reconfiguration and distributed generation placement in power distribution networks[J]. International Journal of Electrical Power & Energy Systems, 2014, 63: 461-472.[pdf]
  • Mass Minimisation of Trusses
  • [9] Pholdee, Nantiwat, and Sujin Bureerat. Comparative performance of meta-heuristic algorithms for mass minimisation of trusses with dynamic constraints[J]. Advances in Engineering Software, 2014, 75: 1-13.[pdf]
  • Regional Seismic Waveform Inversion
  • [10] Ke Ding, Yanyang Chen, Yanbin Wang and Ying Tan. Regional Seismic Waveform Inversion Using Swarm Intelligence Algorithms. 2015 IEEE Congress on Evolutionary Computation (CEC'2015) , May 25-28, 2015, Sendai Internatonal Center, Sendai, Japan. [pdf]
  • Multi-satellite Control Resource Scheduling
  • [11] Zhenbao Liu, Zuren Feng, Liangjun Ke. Fireworks Algorithm for the Multi-satellite Control. 2015 IEEE Congress on Evolutionary Computation (CEC'2015) , May 25-28, 2015, Sendai Internatonal Center, Sendai, Japan. [pdf]
  • Constrained Portfolio Optimization
  • [12] Nebojsa Bacanin and Milan Tuba. Fireworks algorithm applied to constrained portfolio optimization problem. 2015 IEEE Congress on Evolutionary Computation (CEC'2015) , May 25-28, 2015, Sendai Internatonal Center, Sendai, Japan.[pdf]

(4) Survey

    [13] Tan Ying and Yu Chao, Zheng Shaoqiu, and Ding Ke, "Introduce to Fireworks Algorithm," International Journal of Swarm Intelligence Research (IJSIR), 2013, 4(4): 39-70. [pdf][supplementary file]

(5) Others

    [14] Bureerat, Sujin. "Hybrid population-based incremental learning using real codes." Learning and Intelligent Optimization. Springer Berlin Heidelberg, 2011. 379-391. [pdf]

(6) FWA Monographs

(7) Special Issues on FWA