Abstract
In this study a novel population based meta-heuristic, called controlled showering optimization (CSO) algorithm, for global optimization of unconstrained problems is presented. Modern irrigation systems are equipped with smart tools manufactured and controlled by human intelligence. The proposed CSO algorithm is inspired from the functioning of water distribution tools to model search agents for carrying out the optimization process. CSO imitates the mechanism of projection of water units by sprinklers and the movements of their platforms to the desired locations for scheming optimum searching procedures. The proposed method has been tested using a number of diverse natured benchmark functions with low and high dimensions. Statistical analysis of the empirical data demonstrates that CSO offers solutions of better quality in comparison with several well-practiced algorithms like genetic algorithm (GA), particle swarm optimization (PSO), differential evolution (DE), artificial bee colony (ABC), covariance matrix adaptation evolution strategy (CMA-ES), teaching and learning based optimization (TLBO) and water cycle algorithm (WCA). The experiments on high-dimensional problems reveal that CSO algorithm also outperforms significantly a number of algorithms designed specifically for high dimensional global optimization problems.
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References
Ahrari A, Atai AA (2010) Grenade explosion method—a novel tool for optimization of multimodal functions. Appl Soft Comput 10:1132–1140
Ali MZ, Salhieh A, Snanieh RTA, Reynolds RG (2012) Boosting cultural algorithms with a heterogeneous layered social fabric influence function. J Comput Math Org Theor 18:193–210
Ali J, Saeed M, Chaudhry NA, Luqman M, Tabassum MF (2015) Artificial showering algorithm: a new meta-heuristic for unconstrained optimization. Sci Int (Lahore) 27(6):4939–4942
Alihodzic A, Tuba M (2014) Improved bat algorithm applied to multilevel image thresholding. Sci World J 176718:16. https://doi.org/10.1155/2014/176718
Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In: Proceedings of IEEE Congress Evolutionary Computation, Singapore, pp. 4661–4667
Brajevic I, Tuba M (2014) Cuckoo search and firefly algorithm applied to multilevel image thresholding in Cuckoo Search and Firefly Algorithm: theory and applications. Springer Int Publ 516:115–139
Brest J, Zamuda A, Boskovic B, Maucec MS, Zumer V (2008) High-dimensional real-parameter optimization using self-adaptive differential evolution algorithm with population size reduction. In Proc IEEE Congr Evol Comput 2032–2039
Coope ID, Price CJ (2000) Frame Based Methods for Unconstrained Optimization. J Optimiz Theory App 107:261–274
Coope ID, Price CJ (2001) On the convergence of grid-based methods for unconstrained optimization. SIAM J Optim 11:859–869
Corporation RB (2018) 29JH Impact Sprinkler, http://www.rainbird.com/ag/products/impacts/29JH.htm
Davis C (1954) Theory of positive linear dependence. AM J Math 76:733–746
Derrac J, Garcia S, Hui S, Suganthan PN, Herrera F (2014) Analyzing convergence performance of evolutionary algorithms: a statistical approach. Inf Sci 289:41–58
Dog˘an B, Ölmez T (2015) A new metaheuristic for numerical function optimization: Vortex Search algorithm. Inf Sci 293:125–145
DUCAR (2017) Irricruiser ultimate travelling irrigator http://www.irrigationbox.com.au
Dymond AS, Engelbrecht AP, Kok S, Heyns PS (2015) Tuning optimization algorithms under multiple objective function evaluation budgets. IEEE Trans Evolut Comput 19(3):341–358
Engelbrecht AP (2014) Fitness function evaluations: A fair stopping condition? In Proceedings of the IEEE Swarm Intelligence Symposium 1-8
Eskandar H, Sadollah A, Bahreininejad A, Hamdi M (2012) Water Cycle Algorithm – A novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput Struct 110–111:151–166
Formato RA (2011) Central Force Optimization with variable initial probes and adaptive decision space. Appl Math Comput 217:8866–8872
García S, Fernández A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power. Inf Sci 180(10):2044–2064
Garg H (2016) A hybrid PSO-GA algorithm for constrained optimization problems. Appl Math Comput 274:292–305
Ghaheri A, Shoar S, Naderan M, Hoseini SS (2015) The applications of genetic algorithms in medicine. Oman Med J 30(6):406–416. https://doi.org/10.5001/omj.2015.82
Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Pearson publishers, India
Growing (2017) Back to Basics, http://www.growingmagazine.com/vegetables/back-to-basics/
Hajihassani M, Armaghani J, Kalatehjari D (2017) Applications of particle swarm optimization in geotechnical engineering: a comprehensive review. Geol Eng, Geotech. https://doi.org/10.1007/s10706-017-0356-z
Hakli H, Uguz H (2014) A novel particle swarm optimization with levy flight. Appl Soft Comput 23:333–345
Hansen N, Auger A, Mersmann O, Tušar T, Brockhoff D (2016) COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting. ArXiv e-prints, arXiv:1603.08785
Hieu TTA (2011) Water Flow Algorithm for Optimization Problems. PhD thesis, National University of Singapore
Holland J (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor
Hosseini HS (2007) Problem Solving By Intelligent Water Drops. In: Proceedings of IEEE Congress Evolutionary Computation. pp 3226–3231
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471
Kaveh A (2017a) Applications of metaheuristic optimization algorithms in civil engineering. Springer, Switzerland
Kaveh A (2017b) Advances in metaheuristic algorithms for optimal design of structures. Springer, Switzerland
Kennedy J, Eberhart R (1995) Particle Swarm Optimization. In: Proceedings of IEEE International Conference on Neural Networks, pp 1942–1948
Kim IK, Jung DW, Park RH (2002) Document Image Binarization Based on Topographic Analysis Using a Water Flow Model. Pattern Recog 35(1):265–277
Kirkpatrick S, Gellat CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680
Li X, Yao X (2012) Cooperatively coevolving particle swarms for large scale optimization. IEEE T. Evolut Comput 16(2):210–224
Li X, Engelbrecht A, Epitropakis M (2013) Benchmark Functions for CEC 2013 Special Session and Competition on Niching Methods for Multimodal Function Optimization. Tech Rep School of Computer Science and Information Technology RMIT University Melbourne Australia
Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive Learning particle swarm optimization for global optimization of multimodal functions. IEEE Trans Evol Comput 10:281–295
Liang JJ, Qu BY, Suganthan P, Hern´andez-D´ıaz A (2013) Problem definitions and evaluation criteria for the CEC 2013 special session and competition on real-parameter optimization. Tech Rep Computational Intelligence Laboratory Zhengzhou University Zhengzhou, China
Liang JJ, Qu BY, Suganthan PN (2014) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization. Tech Rep 201311 Computational Intelligence Laboratory Zhengzhou University, Zhengzhou, China
Majumdar DK (2010) Irrigation water management: principles and practice. New Delhi PHI learning Pvt Ltd
Mariani VC, Luvizotto LGJ, Guerra FA, Coelho LDS (2011) A hybrid shuffled complex evolution approach based on differential evolution for unconstrained optimization. Appl Math Comput 217:5822–5829
Meng KO, Pauline O, Kiong SC, Wahab HA, Jafferi N (2017) Application of modified flower pollination algorithm on mechanical engineering design problem. IOP Conference Series 165:012032
Omidvar MN, Li X (2011) A comparative study of CMA-ES on large scale global optimization. Advances in artificial intelligence. Springer, New York, pp 303–312
Ostermeier HN (2001) A Completely de-randomized self-adaptation in evolution strategies. Evol Comput 9(2):159–195
Ponsich A, Jaimes AL, Coello CAC (2013) A survey on multi-objective evolutionary algorithms for the solution of the portfolio optimization problem and other finance and economics applications. IEEE Trans Evol Comput 17(3):321–344
Price CJ, Coope ID (2003) Frame-based ray search algorithm in un-constrained optimization. J Optimiz Theor App 116(2):359–377
Rao RV, Savsani VJ, Vakharia DP (2001) Teaching–learning-based-optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des 43(3):257–268
Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a Gravitational Search Algorithm. Inform Sciences 179:2232–2248
Reynolds RG (1994) An introduction to cultural algorithms. Proc Ann Conf Evolut Comput World Sci 11(3):294–307
Saad AH, Dong Z, Karimi M (2017) A Comparative study on recently-introduced nature-based global optimization methods in complex mechanical system design. Algorithms 10(4):120. https://doi.org/10.3390/a10040120
Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2013) Mine Blast Algorithm: a new population based algorithm for solving constrained engineering optimization problems. Appl Soft Comput 13:2592–2612
Sadollah A, Eskander H, Bahreinejad A, Kim JH (2015) Water Cycle algorithm with evaporation rate for solving constrained and unconstrained optimization problems. Appl Soft Comput 30:58–71
Shang YW, Qiu YH (2006) A note on extended Rosenbrock function. Evolut Comput 14:119–126
Srinivasan D, Seow TH (2003) Evolutionary Computation (CEC’03). Congr Evol Comput 4:2292–2297
Storn R, Price K (1997) Differential evolution- a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359
Suganthan P, Hansen N, Liang J, Deb K, Chen YP, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Tech Rep Nanyang Technological University
Suganthan PN, Hansen N, Liang JJ, Deb K, Chen YP, Auger A, Tiwari S (2005b) Problem definitions and evaluation criteria for the cec 2005 special session on real parameter optimization. Technical report. Nanyang Technological University, Singapore
Sun J, Garibaldi JM, Hodgman C (2012) Parameter estimation using metaheuristics in systems biology: a comprehensive review. IEEE/ACM Trans Comput Biol Bioinform 9(1):185–202
Tang K, Yao X, Suganthan PN, MacNish C, Chen YP, Chen CM, Yang Z (2008) Benchmark functions for the CEC’2008 special session and competition on large scale global optimization, Nature Inspired Computation and Applications Laboratory, USTC. Applicat Lab Univ Sci Technol China
Tang K, Li X, Suganthan P, Yan Z, Wiese T (2010) Benchmark Functions for the CEC 2010 Special Session and Competition on Large-Scale Global Optimization. Tech Rep School of Computer Science and Technology, University of Science and Technology of China
Tseng LY, Chen C (2008) Multiple Trajectory Search for Large Scale Global Optimization. In: Proceedings of the IEEE Conference on Evolutionary Computation. pp 3052–3059
Wang Y, Li B (2008) A restart univariate estimation of distribution algorithm sampling under mixed Gaussian and Lévy probability distribution. Proc Congr Evol Comput. https://doi.org/10.1109/CEC.2008.4631330
Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82
Yang XS (2012) Free lunch or no free lunch: that is not just a question? Int J Artif Intell T 21(3):5360–5366
Yang FC, Wang YP (2007) Water flow-like algorithm for object grouping problems. J Chin Inst Ind Eng 24(6):475–488
Yang Z, Tang K, Yao X (2008) Multilevel cooperative coevolution for large scale optimization. In: Proceedings of IEEE World Congress on Computational Intelligence. pp 1663–1670
Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3(2):82–102. https://doi.org/10.1109/4235.771163
Zhang L, Liu L, Yang XS, Dai Y (2016) A novel hybrid firefly algorithm for global optimization. PLoS ONE 11(9):e0163230. https://doi.org/10.1371/journal.pone.0163230
Zhao S, Liang J, Suganthan P (2008) Dynamic multi-swarm particle swarm optimizer with local search for large scale global optimization. In: Proceedings of IEEE CEC pp 3845–3852
Zheng YJ (2015) Water wave optimization: a new nature-inspired metaheuristic. Comput Oper Res 55:1–11
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Ali, J., Saeed, M., Tabassam, M.F. et al. Controlled showering optimization algorithm: an intelligent tool for decision making in global optimization. Comput Math Organ Theory 25, 132–164 (2019). https://doi.org/10.1007/s10588-019-09293-6
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DOI: https://doi.org/10.1007/s10588-019-09293-6