Stochastic Fractal Based Multiobjective Fruit Fly Optimization

Aguirre, A.H., Rionda, S.B., Coello Coello, C.A., Lizárraga, G.L. and Montes, E.M. (2004). Handling constraints using multiobjective optimization concepts, International Journal for Numerical Methods in Engineering 59(15): 1989-2017.10.1002/nme.947Search in Google Scholar

Alcalá-Fdez, J., Sanchez, L., Garcia, S., del Jesus, M.J., Ventura, S., Garrell, J.M., Otero, J., Romero, C., Bacardit, J. and Rivas, V.M. (2009). KEEL: A software tool to assess evolutionary algorithms for data mining problems, Soft Computing 13(3): 307-318.10.1007/s00500-008-0323-ySearch in Google Scholar

Asafuddoula, M., Ray, T. and Sarker, R. (2015). A differential evolution algorithm with constraint sequencing: An efficient approach for problems with inequality constraints, Applied Soft Computing 36: 101-113.10.1016/j.asoc.2015.07.007Search in Google Scholar

Awad, N.H., Ali, M.Z., Suganthan, P.N. and Jaser, E. (2016). A decremental stochastic fractal differential evolution for global numerical optimization, Information Sciences 372: 470-491.10.1016/j.ins.2016.08.032Search in Google Scholar

Bader, J. and Zitzler, E. (2011). Hype: An algorithm for fast hypervolume-based many-objective optimization, Evolutionary computation 19(1): 45-76.10.1162/EVCO_a_0000920649424Search in Google Scholar

Ben Aicha, F., Bouani, F. and Ksouri, M. (2013). A multivariable multiobjective predictive controller, International Journal of Applied Mathematics and Computer Science 23(1): 35-45, DOI: 10.2478/amcs-2013-0004.10.2478/amcs-2013-0004Search in Google Scholar

Bilski, P. and Wojciechowski, J. (2014). Artificial intelligence methods in diagnostics of analog systems, International Journal of Applied Mathematics and Computer Science 24(2): 271-282, DOI: 10.2478/amcs-2014-0020.10.2478/amcs-2014-0020Search in Google Scholar

Bonabeau, E., Dorigo, M. and Theraulaz, G. (1999). Swarm Intelligence: From Natural to Artificial Systems, Oxford University Press, Oxford.10.1093/oso/9780195131581.001.0001Search in Google Scholar

Chen, B., Zeng, W., Lin, Y. and Zhang, D. (2015). A new local search-based multiobjective optimization algorithm, IEEE Transactions on Evolutionary Computation 19(1): 50-73.10.1109/TEVC.2014.2301794Search in Google Scholar

Chen, P.-W., Lin, W.-Y., Huang, T.-H. and Pan, W.-T. (2013). Using fruit fly optimization algorithm optimized grey model neural network to perform satisfaction analysis for e-business service, Applied Mathematics & Information Sciences 7(2L): 459-465.10.12785/amis/072L12Search in Google Scholar

Cheng, R., Jin, Y., Narukawa, K. and Sendhoff, B. (2015). A multiobjective evolutionary algorithm using Gaussian process-based inverse modeling, IEEE Transactions on Evolutionary Computation 19(6): 838-856.10.1109/TEVC.2015.2395073Search in Google Scholar

Coello, C.A.C., Pulido, G.T. and Lechuga, M.S. (2004). Handling multiple objectives with particle swarm optimization, IEEE Transactions on Evolutionary Computation 8(3): 256-279.10.1109/TEVC.2004.826067Search in Google Scholar

Coello, C.C. (2006). Evolutionary multi-objective optimization: A historical view of the field, IEEE Computational Intelligence Magazine 1(1): 28-36.10.1109/MCI.2006.1597059Search in Google Scholar

Deb, K. (2000). An efficient constraint handling method for genetic algorithms, Computer Methods in Applied Mechanics and Engineering 186(2): 311-338.10.1016/S0045-7825(99)00389-8Search in Google Scholar

Deb, K. and Jain, H. (2014). An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach. Part I: Solving problems with box constraints, IEEE Transactions on Evolutionary Computation 18(4): 577-601.Search in Google Scholar

Deb, K., Pratap, A., Agarwal, S. and Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation 6(2): 182-197.10.1109/4235.996017Search in Google Scholar

Deb, K., Thiele, L., Laumanns, M. and Zitzler, E. (2005). Scalable Test Problems for Evolutionary Multiobjective Optimization, Springer, London.Search in Google Scholar

Denysiuk, R., Costa, L., Santo, I.E. and Matos, J.C. (2015). MOEA/PC: Multiobjective evolutionary algorithm based on polar coordinates, International Conference on Evolutionary Multi-Criterion Optimization, Guimar˜aes, Portugal, pp. 141-155.Search in Google Scholar

Derrac, J., García, S., Molina, D. and Herrera, F. (2011). A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms, Swarm and Evolutionary Computation 1(1): 3-18.10.1016/j.swevo.2011.02.002Search in Google Scholar

Dorigo, M., Maniezzo, V. and Colorni, A. (1996). Ant system: Optimization by a colony of cooperating agents, IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics 26(1): 29-41.10.1109/3477.48443618263004Search in Google Scholar

Eiben, A.E. and Smith, J. (2015). From evolutionary computation to the evolution of things, Nature 521(7553): 476-482.10.1038/nature1454426017447Search in Google Scholar

Falconer, K.J. (1986). Random Fractals, Cambridge University Press, Cambridge, pp. 559-582.Search in Google Scholar

Fonseca, C.M. and Fleming, P.J. (1998). Multiobjective optimization and multiple constraint handling with evolutionary algorithms. I: A unified formulation, IEEE Transactions on Systems, Man, and Cybernetics A: Systems and Humans 28(1): 26-37.Search in Google Scholar

Ishibuchi, H., Doi, T. and Nojima, Y. (2006). Incorporation of scalarizing fitness functions into evolutionary multiobjective optimization algorithms, in T.P. Runarsson et al. (Eds.), Parallel Problem Solving from Nature, PPSN IX, Springer, Berlin/Heidelberg, pp. 493-502.10.1007/11844297_50Search in Google Scholar

Karaboga, D. and Akay, B. (2009). A comparative study of artificial bee colony algorithm, Applied Mathematics and Computation 214(1): 108-132.10.1016/j.amc.2009.03.090Search in Google Scholar

Kennedy, J. (2011). Particle swarm optimization, in C. Sammut and G.I. Webb (Eds.), Encyclopedia of Machine Learning, Springer, Berlin/Heidelberg, pp. 760-766.Search in Google Scholar

Li, C., Xu, S., Li, W. and Hu, L. (2012). A novel modified fly optimization algorithm for designing the self-tuning proportional integral derivative controller, Journal of Convergence Information Technology 7(16): 69-77.10.4156/jcit.vol7.issue16.9Search in Google Scholar

Li, H.-Z., Guo, S., Li, C.-J. and Sun, J.-Q. (2013). A hybrid annual power load forecasting model based on generalized regression neural network with fruit fly optimization algorithm, Knowledge-Based Systems 37(2): 378-387.10.1016/j.knosys.2012.08.015Search in Google Scholar

Lin, S.-M. (2013). Analysis of service satisfaction in web auction logistics service using a combination of fruit fly optimization algorithm and general regression neural network, Neural Computing and Applications 22(3-4): 783-791.10.1007/s00521-011-0769-1Search in Google Scholar

Liu, H.-L., Gu, F. and Zhang, Q. (2014). Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems, IEEE Transactions on Evolutionary Computation 18(3): 450-455.10.1109/TEVC.2013.2281533Search in Google Scholar

Mandelbrot, B.B. (1983). The Fractal Geometry of Nature, Macmillan, New York, NY.10.1119/1.13295Search in Google Scholar

Mei, Y., Tang, K. and Yao, X. (2011). Decomposition-based memetic algorithm for multiobjective capacitated arc routing problem, IEEE Transactions on Evolutionary Computation 15(2): 151-165.10.1109/TEVC.2010.2051446Search in Google Scholar

Mellal, M.A. and Zio, E. (2016). A penalty guided stochastic fractal search approach for system reliability optimization, Reliability Engineering & System Safety 152: 213-227.10.1016/j.ress.2016.03.019Search in Google Scholar

Menchaca-Mendez, A. and Coello, C. A.C. (2015). GD-MOEA: A new multi-objective evolutionary algorithm based on the generational distance indicator, International Conference on Evolutionary Multi-Criterion Optimization, Guimar˜aes, Portugal, pp. 156-170.Search in Google Scholar

Michalewicz, Z. and Schoenauer, M. (1996). Evolutionary algorithms for constrained parameter optimization problems, Evolutionary Computation 4(1): 1-32.10.1162/evco.1996.4.1.1Search in Google Scholar

Mirjalili, S., Mirjalili, S.M. and Lewis, A. (2014). Grey wolf optimizer, Advances in Engineering Software 69: 46-61.10.1016/j.advengsoft.2013.12.007Search in Google Scholar

Mitić, M., Vuković, N., Petrović, M. and Miljković, Z. (2015). Chaotic fruit fly optimization algorithm, Knowledge-Based Systems 89(C): 446-458.10.1016/j.knosys.2015.08.010Search in Google Scholar

Mousavi, S.M., Alikar, N. and Niaki, S.T.A. (2016). An improved fruit fly optimization algorithm to solve the homogeneous fuzzy series-parallel redundancy allocation problem under discount-strategies, Soft Computing 20(6): 2281-2307.10.1007/s00500-015-1641-5Search in Google Scholar

Niu, J., Zhong, W., Liang, Y., Luo, N. and Qian, F. (2015). Fruit fly optimization algorithm based on differential evolution and its application on gasification process operation optimization, Knowledge-Based Systems 88(C): 253-263.10.1016/j.knosys.2015.07.027Search in Google Scholar

Pan, Q.-K., Sang, H.-Y., Duan, J.-H. and Gao, L. (2014). An improved fruit fly optimization algorithm for continuous function optimization problems, Knowledge-Based Systems 62(5): 69-83.10.1016/j.knosys.2014.02.021Search in Google Scholar

Pan, W. (2011). A new evolutionary computation approach: Fruit fly optimization algorithm, Proceedings of the Conference on Digital Technology and Innovation Management, Taipei, Taiwan.Search in Google Scholar

Pan, W.-T. (2012). A new fruit fly optimization algorithm: Taking the financial distress model as an example, Knowledge-Based Systems 26(2): 69-74.10.1016/j.knosys.2011.07.001Search in Google Scholar

Pan, W.-T. (2013). Using modified fruit fly optimisation algorithm to perform the function test and case studies, Connection Science 25(2-3): 151-160.10.1080/09540091.2013.854735Search in Google Scholar

Rafajłowicz, E. and Rafajłowicz, W. (2012). Fletcher’s filter methodology as a soft selector in evolutionary algorithms for constrained optimization, in L. Rutkowski et al. (Eds.), Swarm and Evolutionary Computation, Springer, Berlin/Heidelberg, pp. 333-341.10.1007/978-3-642-29353-5_39Search in Google Scholar

Rafajłowicz, W. (2013). Method of handling constraints in differential evolution using Fletcher’s filter, Proceedings of the 12th International Conference on Artificial Intelligence and Soft Computing (ICAICS 2013), Zakopane, Poland, pp. 46-55.Search in Google Scholar

Rajabioun, R. (2011). Cuckoo optimization algorithm, Applied Soft Computing 11(8): 5508-5518.10.1016/j.asoc.2011.05.008Search in Google Scholar

Rodríguez Villalobos, C.A. and Coello Coello, C.A. (2012). A new multi-objective evolutionary algorithm based on a performance assessment indicator, Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation, Philadelphia, PA, USA, pp. 505-512.Search in Google Scholar

Salimi, H. (2015). Stochastic fractal search: A powerful metaheuristic algorithm, Knowledge-Based Systems 75(C): 1-18.10.1016/j.knosys.2014.07.025Search in Google Scholar

Shan, D., Cao, G. and Dong, H. (2013). LGMS-FOA: An improved fruit fly optimization algorithm for solving optimization problems, Mathematical Problems in Engineering 2013(7): 1256-1271.10.1155/2013/108768Search in Google Scholar

Shen, L., Chen, H., Yu, Z., Kang, W., Zhang, B., Li, H., Yang, B. and Liu, D. (2016). Evolving support vector machines using fruit fly optimization for medical data classification, Knowledge-Based Systems 96(C): 61-75.10.1016/j.knosys.2016.01.002Search in Google Scholar

Sheng, W. and Bao, Y. (2013). Fruit fly optimization algorithm based fractional order fuzzy-PID controller for electronic throttle, Nonlinear Dynamics 73(1-2): 611-619.10.1007/s11071-013-0814-ySearch in Google Scholar

Van Veldhuizen, D.A. and Lamont, G.B. (1998). Multiobjective evolutionary algorithm research: A history and analysis, Technical Report TR-98-03, Air Force Institute of Technology, Wright-Patterson AFB, OH.Search in Google Scholar

Vicsek, T. and Gould, H. (1989). Fractal growth phenomena, Computers in Physics 3(5): 108.10.1063/1.4822864Search in Google Scholar

Voss, R.F. (1991). Random fractals: Characterization and measurement, in R. Pynn and A. Skjeltrop (Eds.), Scaling Phenomena in Disordered Systems, Springer, New York, NY, pp. 1-11.10.1007/978-1-4757-1402-9_1Search in Google Scholar

Wang, L., Shi, Y. and Liu, S. (2015). An improved fruit fly optimization algorithm and its application to joint replenishment problems, Expert Systems with Applications 42(9): 4310-4323.10.1016/j.eswa.2015.01.048Search in Google Scholar

Wang, L., Zheng, X.-l. and Wang, S.-Y. (2013). A novel binary fruit fly optimization algorithm for solving the multidimensional knapsack problem, Knowledge-Based Systems 48(2): 17-23.10.1016/j.knosys.2013.04.003Search in Google Scholar

Wang, R., Zhang, Q. and Zhang, T. (2015). Pareto adaptive scalarising functions for decomposition based algorithms, International Conference on Evolutionary Multi-Criterion Optimization, Guimar˜aes, Portugal, pp. 248-262.Search in Google Scholar

Wang, Y.-N.,Wu, L.-H. and Yuan, X.-F. (2010). Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure, Soft Computing 14(3): 193-209.10.1007/s00500-008-0394-9Search in Google Scholar

Witten, T.A. and Sander, L.M. (1983). Diffusion-limited aggregation, Physical Review B 27(9): 5686.10.1103/PhysRevB.27.5686Search in Google Scholar

Wu, L., Zuo, C. and Zhang, H. (2015a). A cloud model based fruit fly optimization algorithm, Knowledge-Based Systems 89(C): 603-617.10.1016/j.knosys.2015.09.006Search in Google Scholar

Wu, L., Zuo, C., Zhang, H. and Liu, Z. (2015b). Bimodal fruit fly optimization algorithm based on cloud model learning, Soft Computing 21(7): 1877-1893.10.1007/s00500-015-1890-3Search in Google Scholar

Yamaguchi, M., Hata,M. and Kigami, J. (1997). Mathematics of Fractals, American Mathematical Society, New York, NY.10.1090/mmono/167Search in Google Scholar

Yang, X.-S. (2010). Firefly algorithm, stochastic test functions and design optimisation, International Journal of Bio- Inspired Computation 2(2): 78-84.10.1504/IJBIC.2010.032124Search in Google Scholar

Yuan, X., Dai, X., Zhao, J. and He, Q. (2014). On a novel multi-swarm fruit fly optimization algorithm and its application, Applied Mathematics and Computation 233(3): 260-271.10.1016/j.amc.2014.02.005Search in Google Scholar

Yuan, X., Liu, Y., Xiang, Y. and Yan, X. (2015). Parameter identification of BIPT system using chaotic-enhanced fruit fly optimization algorithm, Applied Mathematics and Computation 268(C): 1267-1281.10.1016/j.amc.2015.07.030Search in Google Scholar

Zhang, Q. and Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition, IEEE Transactions on Evolutionary Computation 11(6): 712-731.10.1109/TEVC.2007.892759Search in Google Scholar

Zhou, A., Qu, B.-Y., Li, H., Zhao, S.-Z., Suganthan, P.N. and Zhang, Q. (2011). Multiobjective evolutionary algorithms: A survey of the state of the art, Swarm and Evolutionary Computation 1(1): 32-49.10.1016/j.swevo.2011.03.001Search in Google Scholar

Zitzler, E., Deb, K. and Thiele, L. (2000). Comparison of multiobjective evolutionary algorithms: Empirical results, Evolutionary Computation 8(2): 173-195.10.1162/10636560056820210843520Search in Google Scholar

Zitzler, E. and K¨unzli, S. (2004). Indicator-based selection in multiobjective search, International Conference on Parallel Problem Solving from Nature, Birmingham, UK, pp. 832-842.Search in Google Scholar

Zitzler, E., Laumanns, M. and Thiele, L. (2001). SPEA2: Improving the strength Pareto evolutionary algorithm, Eurogen 3242: 95-100.Search in Google Scholar