A Cooperation of the Multileader Fruit Fly and Probabilistic Random Walk Strategies with Adaptive Normalization for Solving the Unconstrained Optimization Problems
Abstract
A swarm-based nature-inspired optimization algorithm, namely, the fruit fly optimization algorithm (FOA), hasa simple structure and is easy to implement. However, FOA has a low success rate and a slow convergence, because FOA generates new positions around the best location, using a fixed search radius. Several improved FOAs have been proposed. However, their exploration ability is questionable. To make the search process smooth, transitioning from the exploration phase to the exploitation phase, this paper proposes a new FOA, constructed from a cooperation of the multileader and the probabilistic random walk strategies (CPFOA). This involves two population types working together. CPFOAs performance is evaluated by 18 well-known standard benchmarks. The results showed that CPFOA outperforms both the original FOA and its variants, in terms of convergence speed and performance accuracy. The results show that CPFOA can achieve a very promising accuracy, when compared with the well-known competitive algorithms. CPFOA is applied to optimize twoapplications: classifying the real datasets with multilayer perceptron and extracting the parameters of a very compact T-S fuzzy system to model the Box and Jenkins gas furnace data set. CPFOA successfully find parameters with a very high quality, compared with the best known competitive algorithms.References
Mirlekar, G.; Gebreslassie, B.; Diwekar, U.; Lima,F.V. Biomimetic model-based advanced control strategy integrated with multi-agent optimization for nonlinear chemical processes, Chemical Engineering Research and Design 2018, 140, 229-240, doi:https://doi.org/10.1016/j.cherd.2018.10.005.
Tian, W.; Zhang, G.; Liang, H. Alarm clustering analysis and ACO based multi-variable alarms thresholds optimization in chemical processes, Process Safety and Environmental Protection 2018, 113, 132-140, doi:https://doi.org/10.1016/j.psep.2017.09.020.
Chen, X.; Mei, C.; Xu, B.; Yu, K.; Huang, X. Quadratic interpolation based teaching-learning-based optimization for chemical dynamic system optimization, Knowledge-Based Systems 2018, 145, 250-263, doi:https://doi.org/10.1016/j.knosys.2018.01.021.
Ma, H.; Fei, M.; Yang, Z. Biogeography-based optimization for identifying promising compounds in chemical process, Neurocomputing 2016, 174, 494-499, doi:https://doi.org/10.1016/j.neucom.2015.05.125.
Eberhart, R.; Kennedy, J. A new optimizer using particle swarm theory, In Proceedings of Micro Machine and Human Science, 1995. MHS’95., Proceedings of the Sixth International Symposium on, 4-6 Oct 1995; pp. 39-43.
Dorigo, M.; Maniezzo, V.; Colorni, A. Ant system: optimization by a colony of cooperating agents., IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 1996, 26, 29-41, doi:10.1109/3477.484436.
Karaboga, D.; Basturk, B., A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm, Journal of Global Optimization 2007, 39, 459-471, doi:10.1007/s10898-007-9149-x.
Yang, X.S.; Suash, D. Cuckoo Search via Lévy flights, In Proceedings of 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC), 9-11 Dec. 2009; pp. 210-214.
Yang, X.-S. A New Metaheuristic Bat-Inspired Algorithm, In Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), Gonz´a lez, J.R., Pelta, D.A., Cruz, C., Terrazas, G., Krasnogor, N., Eds. Springer Berlin Heidelberg: Berlin, Heidelberg, 2010; 10.1007/978-3-642-12538-6 6pp. 65-74.
Jain, M.; Singh, V.; Rani, A. A novel nature-inspired algorithm for optimization: Squirrel search algorithm, Swarm and Evolutionary Computation 2018, https://doi.org/10.1016/j.swevo.2018.02.013, doi:https://doi.org/10.1016/j.swevo.2018.02.013.
Ma, H.; Shen, S.; Yu, M.; Yang, Z.; Fei, M.; Zhou, H. Multi-population techniques in nature inspired optimization algorithms: A comprehensive survey, Swarm and Evolutionary Computation 2018, https://doi.org/10.1016/j.swevo.2018.04.011, doi:https://doi.org/10.1016/j.swevo.2018.04.011.
Pan, W.-T. A new evolutionary computation approach: Fruit Fly Optimization Algorithm, 2011 Conference of Digital Technology and Innovation Management, Taipei 2011.
Storn, R.; Price, K. Differential Evolution - A Simple and Efficient Heuristic for global Optimization over Continuous Spaces, Journal of Global Optimization 1997, 11, 341-359, doi:10.1023/A:1008202821328.
Goldberg, D.E.; Holland, J.H. Genetic Algorithms and Machine Learning Machine Learning 1988, 3, 95-99, doi:10.1023/A:1022602019183.
Shan, D.; Cao, G.; Dong, H. LGMS-FOA: An Improved Fruit Fly Optimization Algorithm for Solving Optimization Problems, Mathematical Problems in Engineering 2013, 2013, 9, doi:10.1155/2013/108768.
Pan, Q.-K.; Sang, H.-Y.; Duan, J.-H.; Gao, L. An improved fruit fly optimization algorithm for continuous function optimization problems, Knowledge-Based Systems 2014, 62, 69-83, doi:https://doi.org/10.1016/j.knosys.2014.02.021.
Pan, W.-T. Using modified fruit fly optimisation algorithm to perform the function test and case studies, Connect. Sci 2013, 25, 151-160, doi:10.1080/09540091.2013.854735.
Yuan, X.; Dai, X.; Zhao, J.; He, Q. On a novel multi-swarm fruit fly optimization algorithm and its application, Applied Mathematics and Computation 2014, 233, 260-271, doi:https://doi.org/10.1016/j.amc.2014.02.005.
Li, H.-z.; Guo, S.; Li, C.-j.; Sun, J.-q. A hybrid annual power load forecasting model based on generalized regression neural network with fruit fly optimization algorithm, Knowledge-Based Systems 2013, 37, 378-387, doi:https://doi.org/10.1016/j.knosys.2012.08.015.
Hu, R.; Wen, S.; Zeng, Z.; Huang, T. A short-term power load forecasting model based on the generalized regression neural network with decreasing step fruit fly optimization algorithm, Neurocomputing 2017, 221, 24-31, doi:https://doi.org/10.1016/j.neucom.2016.09.027.
Niu, D.; Wang, H.; Chen, H.; Liang, Y. The General Regression Neural Network Based on the Fruit Fly Optimization Algorithm and the Data Inconsistency Rate for Transmission Line Icing Prediction, Energies 2017, 10,doi:10.3390/en10122066.
Abidin, Z.Z.; Arshad, M.R.; Ngah, U.K. A simulation based fly optimization algorithm for swarms of mini autonomous surface vehicles application, Indian Journal of Marine Sciences 2011, 40, 250-266.
Lei, X.; Ding, Y.; Fujita, H.; Zhang, A. Identification of dynamic protein complexes based on fruit fly optimization algorithm, Knowledge-Based Systems 2016, 105, 270-277, doi:https://doi.org/10.1016/j.knosys.2016.05.019.
Cao, G.; Wu, L. Support vector regression with fruit fly optimization algorithm for seasonal electricity consumption forecasting, Energy 2016, 115, 734-745, doi:https://doi.org/10.1016/j.energy.2016.09.065.
Kanarachos, S.; Griffin, J.; Fitzpatrick, M.E. Efficient truss optimization using the contrast-based fruit fly optimization algorithm, Computers & Structures 2017, 182, 137-148, doi:https://doi.org/10.1016/j.compstruc.2016.11.005.
Du, T.-S.; Ke, X.-T.; Liao, J.-G.; Shen, Y.-J. DSLC-FOA : Improved fruit fly optimization algorithm for application to structural engineering design optimization problems, Applied Mathematical Modelling 2018, 55, 314-339, doi:https://doi.org/10.1016/j.apm.2017.08.013.
Wu, L.; Liu, Q.; Tian, X.; Zhang, J.; Xiao, W. A new improved fruit fly optimization algorithm IAFOA and its application to solve engineering optimization problems, Knowledge-Based Systems 2018, 144, 153-173, doi:https://doi.org/10.1016/j.knosys.2017.12.031.
Han, S.-Z.; Pan, W.-T.; Zhou, Y.-Y.; Liu, Z.-L. Construct the prediction model for China agricultural output value based on the optimization neural network of fruit fly optimization algorithm, Future Generation Computer Systems 2018, 86, 663-669, doi:https://doi.org/10.1016/j.future.2018.04.058.
Zhang, X.; Lu, X.; Jia, S.; Li, X. A novel phase angle-encoded fruit fly optimization algorithm with mutation adaptation mechanism applied to UAV path planning, Applied Soft Computing 2018, 70, 371-388, doi:https://doi.org/10.1016/j.asoc.2018.05.030.
Zhang, Y.; Cui, G.; Wu, J.; Pan, W.-T.; He, Q. A novel multi-scale cooperative mutation Fruit Fly Optimization Algorithm, Knowledge-Based Systems 2016, 114, 24-35, doi:https://doi.org/10.1016/j.knosys.2016.09.027.
Han, X.; Liu, Q.;Wang, H.;Wang, L. Novel fruit fly optimization algorithm with trend search and co-evolution, Knowledge- Based Systems 2018, 141, 1-17, doi:https://doi.org/10.1016/j.knosys.2017.11.001.
Krishnanand, K.N.; Ghose, D. Glowworm swarm based optimization algorithm for multimodal functions with collective robotics applications, Multiagent Grid Syst. 2006, 2, 209-222.
Rajabioun, R. Cuckoo Optimization Algorithm, Applied Soft Computing 2011, 11, 5508-5518, doi:https://doi.org/10.1016/j.asoc.2011.05.008.
Chen, Z.; Tang, H. Cockroach Swarm Optimization, 10.1109/ICCET.2010.5485993.
Saremi, S.; Mirjalili, S.; Lewis, A. Grasshopper Optimisation Algorithm: Theory and application, Advances in Engineering Software 2017, 105, 30-47, doi:https://doi.org/10.1016/j.advengsoft.2017.01.004.
Mirjalili, S.; Gandomi, A.H.; Mirjalili, S.Z.; Saremi, S.; Faris, H.; Mirjalili, S.M. Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems, Advances in Engineering Software 2017, 114, 163-191, doi:https://doi.org/10.1016/j.advengsoft.2017.07.002.
Dai, H.; Zhao, G.; Lu, J.; Dai, S. Comment and improvement on ”A new Fruit Fly Optimization Algorithm: Taking the financial distress model as an example”, Knowledge-Based Systems 2014, 59, 159-160, doi:https://doi.org/10.1016/j.knosys.2014.01.010.
Niu, J.; Zhong, W.; Liang, Y.; Luo, N.; Qian, F. Fruit fly optimization algorithm based on differential evolution and its application on gasification process operation optimization, Knowledge-Based Systems 2015, 88, 253-263, doi:https://doi.org/10.1016/j.knosys.2015.07.027.
Babalık, A.;˙I s¸ can, H.; Babao˘glu,˙I.; G¨und¨uz, M. An improvement in fruit fly optimization algorithm by using sign parameters, Soft Computing 2017, 10.1007/s00500-017-2733-1, doi:10.1007/s00500-017-2733-1.
Mirjalili, S. The Ant Lion Optimizer, Advances in Engineering Software 2015, 83, 80-98, doi:https://doi.org/10.1016/j.advengsoft.2015.01.010.
Yang, X.-S. Nature-inspired Metaheuristic Algorithms, Luniver Press, 2010.
Gupta, S.; Deep, K. A novel Random Walk Grey Wolf Optimizer, Swarm and Evolutionary Computation 2018, https://doi.org/10.1016/j.swevo.2018.01.001, doi:https://doi.org/10.1016/j.swevo.2018.01.001.
Mirjalili, S.; Gandomi, A.H. Chaotic gravitational constants for the gravitational search algorithm, Applied Soft Computing 2017, 53, 407-419, doi:https://doi.org/10.1016/j.asoc.2017.01.008.
Ab. Aziz, N.A.; Ibrahim, Z.; Mubin, M.; Nawawi, S.W.; Mohamad, M.S. Improving particle swarm optimization via adaptive switching asynchronous C synchronous update, Applied Soft Computing 2018, 72, 298-311, doi:https://doi.org/10.1016/j.asoc.2018.07.047.
Pan, W.-T. A new Fruit Fly Optimization Algorithm: Taking the financial distress model as an example, Knowledge Based Systems 2012, 26, 69-74, doi:https://doi.org/10.1016/j.knosys.2011.07.001.
Rashedi, E.; Nezamabadi-pour, H.; Saryazdi, S. GSA: A Gravitational Search Algorithm, Information Sciences 2009, 179, 2232-2248, doi:https://doi.org/10.1016/j.ins.2009.03.004.
Lee, K.S.; Geem, Z.W. A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice, Computer Methods in Applied Mechanics and Engineering 2005, 194, 3902-3933, doi:https://doi.org/10.1016/j.cma.2004.09.007.
Fister, I.; Fister, I.; Yang, X.-S.; Brest, J. A comprehensive review of firefly algorithms, Swarm and Evolutionary Computation 2013, 13, 34-46, doi:https://doi.org/10.1016/j.swevo.2013.06.001.
Chen, X.; Tianfield, H.; Mei, C.; Du, W.; Liu, G. Biogeography-based learning particle swarm optimization; 2017; Vol. 21, pp. 7519C7541.
Liang, J.J.; Qin, A.K.; Suganthan, P.N.; Baskar, S. Comprehensive learning particle swarm optimizer for global optimization of multimodal functions, Trans. Evol. Comp 2006, 10, 281-295, doi:10.1109/tevc.2005.857610.
Wang, Y.; Cai, Z.; Zhang, Q. Differential Evolution With Composite Trial Vector Generation Strategies and Control Parameters IEEE Transactions on Evolutionary Computation 2011, 15, 55-66, doi:10.1109/TEVC.2010.2087271.
Zhang, J.; Sanderson, A.C. JADE: Adaptive Differential Evolution With Optional External Archive, IEEE Transactions on Evolutionary Computation 2009, 13, 945-958, doi:10.1109/TEVC.2009.2014613.
Singh, N.; Singh, S. A Modified Mean Gray Wolf Optimization Approach for Benchmark and Biomedical Problems, Evolutionary Bioinformatics 2017, 13, 1176934317729413, doi:10.1177/1176934317729413.
Nabil, E. A Modified Flower Pollination Algorithm for Global Optimization, Expert Systems with Applications 2016, 57, 192-203, doi:https://doi.org/10.1016/j.eswa.2016.03.047.
Liu, Z.; Liu, X.; Cai, X. A new hybrid aerodynamic optimization framework based on differential evolution and invasive weed optimization, Chinese Journal of Aeronautics 2018, 31, 1437-1448, doi:https://doi.org/10.1016/j.cja.2018.05.002.
Zhao, X.; Yao, Y.; Yan, L. Learning algorithm for multimodal optimization, Computers & Mathematics with Applications 2009, 57, 2016-2021, doi:https://doi.org/10.1016/j.camwa.2008.10.008.
Messikh, N.; Bousba, S.; Bougdah, N. The use of a multilayer perceptron (MLP) for modelling the phenol removal by emulsion liquid membrane, Journal of Environmental Chemical Engineering 2017, 5, 3483-3489, doi:https://doi.org/10.1016/j.jece.2017.06.053.
D´ıaz-Rodrłguez, P.; Cancilla, J.C.; Matute, G.; Chicharro, D.; Torrecilla, J.S. Inputting molecular weights into a multilayer perceptron to estimate refractive indices of dialkylimidazolium-based ionic liquidsłA purity evaluation, Applied Soft Computing 2015, 28, 394-399, doi:https://doi.org/10.1016/j.asoc.2014.12.004.
Qiao, J.; Li, W.; Han, H. Soft Computing of Biochemical Oxygen Demand Using an Improved TCS Fuzzy Neural Network, Chinese Journal of Chemical Engineering 2014, 22, 1254-1259, doi:https://doi.org/10.1016/j.cjche.2014.09.023.
Mirjalili, S. How effective is the Grey Wolf optimizer in training multi-layer perceptrons, Applied Intelligence 2015, 43, 150-161, doi:10.1007/s10489-014-0645-7.
Singh, N.; Hachimi, H. A New Hybrid Whale Optimizer Algorithm with Mean Strategy of Grey Wolf Optimizer for Global Optimization, Mathematical and Computational Applications 2018, 23, 14.
Box, G.E.P.; Jenkins, G. Time Series Analysis, Forecasting and Control; Holden-Day, Inc.: 1990; pp. 500.
Ding, X.; Xu, Z.; Cheung, N.J.; Liu, X. Parameter estimation of TakagiCSugeno fuzzy system using heterogeneous cuckoo search algorithm, Neurocomputing 2015, 151, 1332-1342, doi:https://doi.org/10.1016/j.neucom.2014.10.063.
Yinghua, L.; Cunningham, G.A. A new approach to fuzzy-neural system modeling, IEEE Transactions on Fuzzy Systems 1995, 3, 190-198, doi:10.1109/91.388173.
Euntai, K.; Minkee, P.; Seungwoo, K.; Mignon, P. A transformed input-domain approach to fuzzy modeling, IEEE Transactions on Fuzzy Systems 1998, 6, 596-604, doi:10.1109/91.728458.
Tsekouras, G.E. On the use of the weighted fuzzy c-means in fuzzy modeling, Advances in Engineering Software 2005, 36, 287-300, doi:https://doi.org/10.1016/j.advengsoft.2004.12.001.
Li, C.; Zhou, J.; Fu, B.; Kou, P.; Xiao, J. T-S Fuzzy Model Identification With a Gravitational Search-Based Hyperplane Clustering Algorithm, IEEE Transactions on Fuzzy Systems 2012, 20, 305-317, doi:10.1109/TFUZZ.2011.2173693.
Li, C.; Zhou, J.; Xiao, J.; Xiao, H. Hydraulic turbine governing system identification using T-S fuzzy model optimized by chaotic gravitational search algorithm, Engineering Applications of Artificial Intelligence 2013, 26, 2073-2082, doi:https://doi.org/10.1016/j.engappai.2013.04.002.
Cheung, N.J.; Ding, X.; Shen, H. OptiFel: A Convergent Heterogeneous Particle Swarm Optimization Algorithm for Takagi- Sugeno Fuzzy Modeling, IEEE Transactions on Fuzzy Systems 2014, 22, 919-933, doi:10.1109/TFUZZ.2013.2278972.
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