A quantum-inspired vortex search algorithm with application to function optimization

Springer Science and Business Media LLC - Tập 18 - Trang 647-674 - 2018
Panchi Li1, Ya Zhao1
1School of Computer and Information Technology, Northeast Petroleum University, DaQing, China

Tóm tắt

The vortex search is proposed as a new optimization algorithm recently. This algorithm has the advantages of simple operation and strong search capabilities. By introducing quantum computing into this algorithm, A quantum-inspired vortex search algorithm is presented in this paper. The initial population of the algorithm has only one individual called vortex center. First this individual is encoded by qubits described on the Bloch sphere, and then by repeatedly rotating all qubits on this individual about the same coordinate axis through random angles, some new individuals are generated. By choosing the best individual as a new vortex center, and rotating it again until meeting the termination conditions, the global optimal solution can be obtained. As the search in each dimension is carried out on the Bloch sphere, thus it is helpful to enhance the diversity of candidate solutions and inhibit premature convergence in the late stages of the algorithm. That the proposed algorithm is superior to the original one is demonstrated by the experimental results of some benchmark functions extreme optimization.

Tài liệu tham khảo

Ahrari A, Atai AA (2010) Grenade explosion method C a novel tool for optimization of multimodal functions. Appl Soft Comput 10(4):1132–1140 Akay B, Karaboga D (2010) A modified artificial bee colony algorithm for real-parameter optimization. Inf Sci 192(1):120–142 Akay B, Karaboga D (2011) A modified artificial bee colony (ABC) algorithm for constrained optimization problems. Appl Soft Comput 11(3):3021–3031 Amer D, Samira B, Imene B (2015) A sinusoidal differential evolution algorithm for numerical optimisation. Appl Soft Comput 27:99–126 Arpaia P, Maisto D, Manna C (2011) A quantum-inspired evolutionary algorithm with a competitive variation operator for multiple-fault diagnosis. Appl Soft Comput 11(8):4655–4666 Berat D, Tamer O (2015) A new metaheuristic for numerical function optimization: vortex Search algorithm. Inf Sci 293(1):125–145 Berat D, Tamer O (2015) Vortex search algorithm for the analog active filter componentselection problem. Int J Electron Commun (AEU) 69(9):1243–1253 Boussaïd I, Lepagnot J, Siarry P (2013) A survey on optimization metaheuristics. Inf Sci 237(10):82–117 Chakraborty P, Das S, Roy GG, Abraham A (2011) On convergence of the multi-objective particle swarm optimizers. Inf Sci 181(8):1411–1425 Chang WD (2015) A modified particle swarm optimization with multiple subpopulations for multimodal function optimization problems. Appl Soft Comput 33:170–182 Civicioglu P (2013) Backtracking search optimization algorithm for numerical optimization problems. Appl Math Comput 219(15):8121–8144 Cordon O, Damas S, Santamar J (2006) A fast and accurate approach for 3D image registration using the scatter search evolutionary algorithm. Pattern Recognit Lett 27(11):1191–1200 Dorigo M (1992) Optimization, learning and natural algorithms, Ph.D. Thesis, Politecnico di Milano, Italy Dos SCL, Ayala HVH, Zanetti FR (2013) Population’s variance-based adaptive differential evolution for real parameter optimization. In: IEEE congress on evolutionary computation, New York, USA. IEEE press, pp 1672–1677 Du W, Li B (2008) Multi-strategy ensemble particle swarm optimization for dynamic optimization. Inf Sci 178(15):3096–3109 Efren MM, Mariana EM (2010) Differential evolution in constrained numerical optimization: an empirical study. Inf Sci 180(22):4223–4262 El-Abd M (2013) Testing a particle swarm optimization and artificial bee colony hybrid algorithm on the CEC13 benchmarks. In: IEEE congress on evolutionary computation, New York, USA, pp 2215–2220. IEEE press Etemada SA, White T (2011) An ant-inspired algorithm for detection of image edge features. Appl Soft Comput 11(8):4883–4893 Eusuff M, Lansey E (2003) Optimization of water distribution network design using the shuffled frog leaping algorithm. J Water Resour Plann Manag 129(3):210–225 Farmer JD, Packard N, Perelson A (1986) The immune system, adaptation and machine learning. Physica D 22(1–3):187–204 Feynman RP (1982) Simulating physics with computings. Int J Theor Phys 21(6/7):467–488 Feynman RP (1986) Quantum mechanical computers. Found Phys 16(6):507–531 Geem ZW (2008) Novel derivative of harmony search algorithm for discrete design variables. Appl Math Comput 199(1):223–230 Goncalves JF, Mendes JJM, Resende MGC (2008) A genetic algorithm for the resource constrained multi-project scheduling problem. Eur J Oper Res 189(3):1171–1190 Hani Y, Amodeo L, Yalaoui F, Chen H (2007) Ant colony optimization for solving an industrial layout problem. Eur J Operat Res 183(2):633–642 Hansen N (1996) Ostermeier adapting arbitrary normal mutation distributions in evolution strategies: The covariance matrix adaptation. In: Proceedings of the 1996 IEEE conference on evolutionary computation piscataway. IEEE, pp 312–317 Hashemi SM, Moradi A, Rezapour M (2008) An ACO algorithm to design UMTS access network using divided and conquer techniques. Eng Appl Artif Intell 21(6):931–940 Holland J (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, p 61-6 Hossein NP (2015) A quantum-inspired gravitational search algorithm for binary encoded optimization problems. Eng Appl Artif Intell 40:62–75 Ilya L, Marc S, Michele S (2012) Alternative restart strategies for CMA-ES. In: V C. et al (ed), Parallel problem solving from nature (PPSN XII), LNCS, pp 296–305. Springer Jiaquan G, Jun W (2011) A hybrid quantum-inspired immune algorithm for multiobjective optimization. Appl Math Comput 217(9):4754–4770 Juang YT, Tung SL, Chiu HC (2011) Adaptive fuzzy particle swarm optimization for global optimization of multimodal functions. Inf Sci 181(20):4539–4549 Kalinlia A, Karabogab N (2005) Artificial immune algorithm for IIR filter design. Eng Appl Artif Intell 18(8):919–929 Kang SL, Zong WG (2005) A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194(36–38):3902–3933 Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39:459–471 Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8(1):687–697 Kashan AH (2012) A new metaheuristic for optimization: optics inspired optimization (OIO). Technical paper, Department of Industrial Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran, pp 1–69 Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, New York, USA, pp 1942–1948. IEEE press Kim TH, Maruta I, Sugie T (2008) Robust PID controller tuning based on the constrained particle swarm optimization. Automatica 44(4):1104–1110 Li PC (2014) A quantum-behaved evolutionary algorithm based on the Bloch spherical search. Commun Nonlinear Sci Numer Simul 19(4):763–771 Li PC, Xiao H (2014) An improved quantum-behaved particle swarm optimization algorithm. Appl Intell 40(3):479–496 Li X, Luo J, Chen MR, Wang N (2012) An improved shuffled frog-leaping algorithm with external optimization for continuous optimization. Inf Sci 192(1):143–151 Li GQ, Niu PF, Xiao XJ (2012) Development and investigation of efficient artificial bee colony algorithm for numerical function optimization. Appl Soft Comput 12(1):320–332 Liang JJ, Qu BY, Suganthan PN, et al (2013) Problem definitions and evaluation criteria for the CEC2013 special session on real-parameter optimization. Technical Report 201212, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore Liang Y, Leung KS (2011) Genetic algorithm with adaptive elitist-population strategies for multimodal function optimization. Appl Soft Comput 11(2):2017–2034 Liao WH, Kao Y, Fan CM (2008) Data aggregation in wireless sensor networks using ant colony algorithm. J Netw Comput Appl 31(4):387–401 Lin YL, Chang WD, Hsieh JG (2008) A particle swarm optimization approach to nonlinear rational filter modeling. Expert Syst Appl 34(2):1194–1199 Liu J, Tang L (1999) A modified genetic algorithm for single machine scheduling. Comput Ind Eng 37(1–2):43–46 Liu Y, Yi Z, Wu H, Ye M, Chen K (2008) A tabu search approach for the minimum sum-of-squares clustering problem. Inf Sci 178(12):2680–2704 Liu L, Yang S, Wang D (2011) Force-imitated particle swarm optimization using the near-neighbor effect for locating multiple optima. Inf Sci 182(1):139–155 Manoj T (2014) A new genetic algorithm for global optimization of multimodal continuous functions. J Comput Sci 5(2):298–311 Mohamed AW (2015) An improved differential evolution algorithm with triangular mutation for global numerical optimization. Comput Ind Eng 85:359–375 Nazmul S, Hojjat A (2014) Spiral dynamics algorithm. Int J Artif Intell Tools 23(6):1430001(24 pages) Nielsen MA, Chuang IL (2000) Quantum computation and quantum information. Cambridge University Press, Cambridge, pp 96–103 Ombach J (2008) Stability of evolutionary algorithms. J Math Anal 342(1):326–333 Passino KM (2002) Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst Mag 22(3):52–67 Perez RE, Behdinan K (2007) Particle swarm approach for structural design optimization. Comput Struct 85(29–30):1579–1588 Rashedi E, Pour HN, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248 Serap US, Yunus E, Merve E, TUrkay D (2013) Ant colony optimization for continuous functions by using novel pheromone updating. Appl Math Comput 219(9):4163–4175 Shi W, Shen Q, Kong W, Ye B (2007) QSAR analysis of tyrosine kinase inhibitor using modified ant colony optimization and multiple linear regression. Eur J Med Chem 42(1):81–86 Simon D (2008) Biogeography-based optimization. IEEE Trans Evolut Comput 12(6):702–713 Storn R, Price K (1997) Differential evolution C a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359 Sun CL, Zeng JC, Pan JS (2011) An improved vector particle swarm optimization for constrained optimization problems. Inf Sci 181(6):1153–1163 Sun J, Wu XJ, Fang W, Ding YG, Long HX, Xu WB (2012) Multiple sequence alignment using the hidden Markov model trained by an improved quantum-behaved particle swarm optimization. Inf Sci 182(1):93–114 Suresh S, Sujit PB, Rao AK (2007) Particle swarm optimization approach for multiobjective composite-beam design. Compos Struct 81(4):598–605 Tan X, Bhanu B (2006) Fingerprint matching by genetic algorithms. Pattern Recognit 39(3):465–477 Wang Y, Yang Y (2009) Particle swarm optimization with preference order ranking for multi-objective optimization. Inf Sci 179(12):1944–1959 Wu Z, Ding G, Wang K, Fukaya M (2008) Application of a genetic algorithm to optimize the refrigerant circuit of fin-and-tube heat exchangers for maximum heat transfer or shortest tube. Int J Thermal Sci 47(8):985–997 Yildiz AR (2009) A novel hybrid immune algorithm for global optimization in design and manufacturing. Robot Comput Integr Manuf 25(2):261–270 Zamuda A, Brest J, Mezura-Montes E (2013) Structured population size reduction differential evolution with multiple mutation strategies on CEC 2013 real parameter optimization. In: IEEE congress on evolutionary computation, New York, USA,pp.1925–1931. IEEE press Zhu gp, Sam K (2010) Gbest-guided artificial bee colony algorithm for numerical function optimization. Appl Math Comput 217(7):3166–3173