进化信息引导的烟花差分混合多目标算法
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摘要
烟花算法是一种有效启发式群智能算法,但基本的烟花算法只能解决单目标问题,个体间缺乏信息交流,进化过程中有用信息没有得到充分利用。为提高烟花算法的综合性能,并使其能够应用在多目标优化问题(multi-objective optimization problems,MOPs)上,提出一种基于粒子进化信息引导的自适应多目标烟花差分混合进化算法(multi-objective hybrid optimization algorithm of fireworks and differential guided by evolutioninformation,MOHFWDE)。利用Pareto前沿个体的进化信息引导种群进化,加快算法收敛速度;在烟花算法中引入差分算法的变异算子、交叉算子替换原有高斯变异算子,增强个体间的信息交流。与其他算法进行对比仿真实验,结果表明MOHFWDE具有良好的收敛性、分布性和逼近性。
Fireworks algorithm is an effective heuristic swarm intelligence algorithm proposed recently. But the basic fireworks algorithm can only solve the single objective problem, and it lacks information communication between individuals. The useful information is underutilized in the process of evolution. In order to improve the comprehensive performance of the fireworks algorithm and make it be used in solving multi-objective optimization problems(MOPs), this paper puts forward a kind of multi-objective hybrid optimization algorithm of fireworks and differential guided by evolution information(OHMFWDE). The Pareto frontier individual evolutionary information is used to guide the evolution of the population to accelerate the algorithm convergence speed. Crossover operator and mutation operator of differential algorithm are used instead of the original Gaussian mutation operator in fireworks algorithm to strengthen the exchange of information between individuals. Experimental results show that MOHFWDE is an effective multi-objective optimization algorithm which has good convergence, diversity and approximation compared with other algorithms.
Fireworks algorithm is an effective heuristic swarm intelligence algorithm proposed recently. But the basic fireworks algorithm can only solve the single objective problem, and it lacks information communication between individuals. The useful information is underutilized in the process of evolution. In order to improve the comprehensive performance of the fireworks algorithm and make it be used in solving multi-objective optimization problems(MOPs), this paper puts forward a kind of multi-objective hybrid optimization algorithm of fireworks and differential guided by evolution information(OHMFWDE). The Pareto frontier individual evolutionary information is used to guide the evolution of the population to accelerate the algorithm convergence speed. Crossover operator and mutation operator of differential algorithm are used instead of the original Gaussian mutation operator in fireworks algorithm to strengthen the exchange of information between individuals. Experimental results show that MOHFWDE is an effective multi-objective optimization algorithm which has good convergence, diversity and approximation compared with other algorithms.
引文
[1] Tan Y, Zhu Y C. Fireworks algorithm for optimization[C]//LNCS 6145:Proceedings of the 1st International Conference on Swarm Intelligence, Beijing, Jun 12-15, 2010. Berlin,Heidelberg:Springer, 2010:355-364.
[2] Tan Y, Yu C, Zheng S Q, et al. Introduction to fireworks algorithm[J]. International Journal of Swarm Intelligence Research, 2013, 4(4):39-70.
[3] Zheng S Q, Janecek A, Tan Y. Enhanced fireworks algorithm[C]//Proceedings of the IEEE Congress on Evolutionary Computation, Cancun, Jun 20-23, 2013. Piscataway:IEEE,2013:2069-2077.
[4] Li J Z, Zheng S Q, Tan Y. Adaptive fireworks algorithm[C]//Proceedings of the IEEE Congress on Evolutionary Computation, Beijing, Jul 6-11, 2014. Piscataway:IEEE, 2014:3214-3221.
[5] Zhao H T, Zhang C S, Ning J. A best firework updating information guided adaptive fireworks algorithm[J].Neural Computing and Applications, 2017, 1:1-21.
[6] Storn R, Price K V. Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces[J]. Journal of Global Optimization, 1997, 11(4):341-359.
[7] 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.
[8] Zhang Q F, Li H. MOEA/D:a multiobjective evolutionary algorithm based on decomposition[J]. IEEE Transactions on Evolutionary Computation, 2007, 11(6):712-731.
[9] Rakshit P, Konar A. Differential evolution for noisy multiobjective optimization[J]. Artificial Intelligence, 2015, 227:165-189.
[10] Abaci K, Yamacli V. Differential search algorithm for solving multi-objective optimal power flow problem[J]. International Journal of Electrical Power&Energy Systems, 2016, 79:1-10.
[11] Eckart Z, Marco L, Lothar T. SPEA2:improving the strength Pareto evolutionary algorithm:TIK-Report 103[R]. Zurich:Swiss Federal Institute of Technology, 2001.
[12] Zheng Y J, Song Q, Chen S Y. Multiobjective fireworks optimization for variable-rate fertilization in oil crop production[J]. Applied Soft Computing, 2013, 13(11):4253-4263.
[13] Deb K, Agrawal S, Pratap A, et al. A fast and elitist multiobjective genetic algorithm:NSGA-II[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2):182-197.
[14] Ye K Q, Li W, Sudjianto A. Algorithmic construction of optimal symmetric Latin hypercube designs[J]. Journal of Statistical Planning&Inference, 2000, 90(1):145-159.
[15] Neri F, Cotta C. Memetic algorithms and memetic computing optimization:a literature review[J]. Swarm&Evolutionary Computation, 2012, 2:1-14.
[16] Schott J R. Fault tolerant design using single and multicriteria genetic algorithm optimization[J]. Cellular Immunology, 1995,37(1):1-13.
[17] Zitzler E, Deb K, Thiele L. Comparison of multiobjective evolutionary algorithms:empirical results[J]. Evolutionary Computation, 2000, 8(2):173-195.
[18] Deb K, Thiele L, Laumanns M, et al. Scalable multiobjective optimization test problems[C]//Proceedings of the World on Congress on Computational Intelligence, Honolulu,May 12-17, 2002. Washington:IEEE Computer Society, 2002:825-830.
[19] Huband S, Hingston P, Barone L, et al. A review of multiobjective test problems and a scalable test problem toolkit[J]. IEEE Transactions on Evolutionary Computation,2006, 10(5):477-506.
[20] Chen X, Du W L, Qian F. Multi-objective differential evolution with ranking-based mutation operator and its application in chemical process optimization[J]. Chemometrics&Intelligent Laboratory Systems, 2014, 136(16):85-96.
[21] Martínez S Z, Coello C A C. A multi-objective particle swarm optimizer based on decomposition[C]//Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, Dublin, Jul 12-16, 2011. New York:ACM, 2011:69-76.
[2] Tan Y, Yu C, Zheng S Q, et al. Introduction to fireworks algorithm[J]. International Journal of Swarm Intelligence Research, 2013, 4(4):39-70.
[3] Zheng S Q, Janecek A, Tan Y. Enhanced fireworks algorithm[C]//Proceedings of the IEEE Congress on Evolutionary Computation, Cancun, Jun 20-23, 2013. Piscataway:IEEE,2013:2069-2077.
[4] Li J Z, Zheng S Q, Tan Y. Adaptive fireworks algorithm[C]//Proceedings of the IEEE Congress on Evolutionary Computation, Beijing, Jul 6-11, 2014. Piscataway:IEEE, 2014:3214-3221.
[5] Zhao H T, Zhang C S, Ning J. A best firework updating information guided adaptive fireworks algorithm[J].Neural Computing and Applications, 2017, 1:1-21.
[6] Storn R, Price K V. Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces[J]. Journal of Global Optimization, 1997, 11(4):341-359.
[7] 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.
[8] Zhang Q F, Li H. MOEA/D:a multiobjective evolutionary algorithm based on decomposition[J]. IEEE Transactions on Evolutionary Computation, 2007, 11(6):712-731.
[9] Rakshit P, Konar A. Differential evolution for noisy multiobjective optimization[J]. Artificial Intelligence, 2015, 227:165-189.
[10] Abaci K, Yamacli V. Differential search algorithm for solving multi-objective optimal power flow problem[J]. International Journal of Electrical Power&Energy Systems, 2016, 79:1-10.
[11] Eckart Z, Marco L, Lothar T. SPEA2:improving the strength Pareto evolutionary algorithm:TIK-Report 103[R]. Zurich:Swiss Federal Institute of Technology, 2001.
[12] Zheng Y J, Song Q, Chen S Y. Multiobjective fireworks optimization for variable-rate fertilization in oil crop production[J]. Applied Soft Computing, 2013, 13(11):4253-4263.
[13] Deb K, Agrawal S, Pratap A, et al. A fast and elitist multiobjective genetic algorithm:NSGA-II[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2):182-197.
[14] Ye K Q, Li W, Sudjianto A. Algorithmic construction of optimal symmetric Latin hypercube designs[J]. Journal of Statistical Planning&Inference, 2000, 90(1):145-159.
[15] Neri F, Cotta C. Memetic algorithms and memetic computing optimization:a literature review[J]. Swarm&Evolutionary Computation, 2012, 2:1-14.
[16] Schott J R. Fault tolerant design using single and multicriteria genetic algorithm optimization[J]. Cellular Immunology, 1995,37(1):1-13.
[17] Zitzler E, Deb K, Thiele L. Comparison of multiobjective evolutionary algorithms:empirical results[J]. Evolutionary Computation, 2000, 8(2):173-195.
[18] Deb K, Thiele L, Laumanns M, et al. Scalable multiobjective optimization test problems[C]//Proceedings of the World on Congress on Computational Intelligence, Honolulu,May 12-17, 2002. Washington:IEEE Computer Society, 2002:825-830.
[19] Huband S, Hingston P, Barone L, et al. A review of multiobjective test problems and a scalable test problem toolkit[J]. IEEE Transactions on Evolutionary Computation,2006, 10(5):477-506.
[20] Chen X, Du W L, Qian F. Multi-objective differential evolution with ranking-based mutation operator and its application in chemical process optimization[J]. Chemometrics&Intelligent Laboratory Systems, 2014, 136(16):85-96.
[21] Martínez S Z, Coello C A C. A multi-objective particle swarm optimizer based on decomposition[C]//Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, Dublin, Jul 12-16, 2011. New York:ACM, 2011:69-76.