An improved African buffalo optimization algorithm using chaotic map and chaotic-levy flight

  • Authors

    • Chinwe Peace Igiri Amity Institute of Information Technology, Amity University Rajasthan, India
    • Yudhveer Singh Amity Institute of Information Technology, Amity University Rajasthan, India
    • Deepshikha Bhargava School of Computer Science, University of Petroleum and Energy Studies, Dehradun, India
    2018-11-15
    https://doi.org/10.14419/ijet.v7i4.22726
  • Chaotic Optimization, African Buffalo Optimization, Levy-Flight, Non-Linear Optimization, Meta-Heuristics.
  • Optimization is ever-growing research that cuts across all walks of life. Many popular metaheuristic algorithms have metamorphosed into numerous variants in search of the sophisticated kernel for optimal solution. The African Buffalo optimization (ABO) algorithm is one of the fastest metaheuristic algorithms. This algorithm is inspired by the alarm and alert calls of African buffaloes during their foraging and defending activities. The present study investigates the strengths and weaknesses of ABO and proposes two improvement strategies: Chaotic ABO (CABO) and chaotic-levy flight ABO (CLABO). The results are validated with ten benchmark optimization problems and compared with other metaheuristic algorithms in the literature. Further, the CABO and CLABO algorithms are ranked first and second, respectively. This proves the superiority of the proposed improved algorithms over others under this study. Finally, the improved chaotic ABO would be utilized for optimizing industrial scheduling for oil and gas in our future work.

     

     

     
  • References

    1. [1] A Bagheri, Mostafa Zandieh, Iraj Mahdavi, and Mehdi Yazdani. An artificial immune algorithm for the flexible job-shop scheduling problem. Future Generation Computer Systems, 26(4):533–541, 2010. https://doi.org/10.1016/j.future.2009.10.004.

      [2] EG Birgin, G Haeser, and a Ramos. Augmented lagrangians with constrained sub problems and convergence to second-order stationary points. Optimization Online, 2016.

      [3] Vahid Beiranvand, Warren Hare, and Yves Lucet. Best practices for comparing optimization algorithms. Optimization and Engineering, 18(4):815–848, 2017. https://doi.org/10.1007/s11081-017-9366-1.

      [4] Mohui Jin, Xianmin Zhang, Zhou Yang, and Benliang Zhu. Jacobian- based topology optimization method using an improved stiffness evaluation. Journal of Mechanical Design, 140(1):011402, 2018. https://doi.org/10.1115/1.4038332.

      [5] Francesco Orciuoli, Mimmo Parente, and Autilia Vitiello. Solving the shopping plan problem through bio-inspired approaches. Soft Computing, 20(5):2077–2089, 2016. https://doi.org/10.1007/s00500-015-1625-5.

      [6] Julius Beneoluchi Odili, Mohammad Nizam Kahar, and a Noraziah. Solving traveling salesman’s problem using African buffalo optimization, honey bee mating optimization & linkerninghan algorithms. World Applied Sciences Journal, 34(7):911–916, 2016.

      [7] Biao Zhang, Quan-ke Pan, Liang Gao, Xin-li Zhang, Hong-yan Sang, and Jun-qing Li. An effective modified migrating bird’s optimization for hybrid flowshop scheduling problem with lot streaming. Applied Soft Computing, 52:14–27, 2017. https://doi.org/10.1016/j.asoc.2016.12.021.

      [8] Xin-She Yang. Nature-inspired optimization algorithms. Elsevier, 2014.

      [9] Julius Beneoluchi Odili, Mohd Nizam Mohmad Kahar, and Shahid Anwar. African buffalo optimization: a swarm-intelligence technique. Procedia Computer Science, 76:443–448, 2015. https://doi.org/10.1016/j.procs.2015.12.291.

      [10] Xin-She Yang and Amir Hossein Gandomi. Bat algorithm: a novel approach for global engineering optimization. Engineering Computations, 29(5):464–483, 2012. https://doi.org/10.1108/02644401211235834.

      [11] Xin-She Yang and Suash Deb. Cuckoo search via le´vy flights. In Nature & Biologically Inspired Computing, 2009. NaBIC 2009. World Congress on, pages 210–214. IEEE, 2009.

      [12] Xin-She Yang. Firefly algorithms for multimodal optimization. In International symposium on stochastic algorithms, pages 169–178. Springer, 2009. https://doi.org/10.1007/978-3-642-04944-6_14.

      [13] Julius Beneoluchi Odili and Mohd Nizam Mohmad Kahar. Numerical function optimization solutions using the African buffalo optimization algorithm (abo). British Journal of Mathematics & Computer Science, 10(1):1–12, 2015.

      [14] Julius Beneoluchi Odili, Mohd Nizam Mohmad Kahar, Shahid An- war, and Mohammed Adam Kunna Azrag. A comparative study of African buffalo optimization and randomized insertion algorithm for asymmetric travelling sales clerk’s problem. In Software Engineering and Computer Systems (ICSECS), 2015 4th International Conference on, pages 90–95. IEEE, 2015.

      [15] Julius Beneoluchi Odili, Mohd Nizam Mohmad Kahar, and A Noraziah. African buffalo optimization algorithm for tuning parameters of a PID controller in automatic voltage regulators.

      [16] Boris Almonacid, Juan Reyes-Hagemann, Juan Campos-Nazer, and Jorge Ramos-Aguilar. Selecting a biodiversity conservation area with a limited budget using the binary African buffalo optimization algorithm. IET Software, 2017.

      [17] Yunqing Rao, Dezhong Qi, and Jinling Li. An improved hierarchical genetic algorithm for sheet cutting scheduling with process constraints. The Scientific World Journal, 2013, 2013.

      [18] Lin Wang, Hui Qu, Tao Chen, and Fang-Ping Yan. An effective hybrid self-adapting differential evolution algorithm for the joint replenishment and location-inventory problem in a three-level supply chain. The Scientific World Journal, 2013, 2013.

      [19] Yanhui Li, Hao Guo, Lin Wang, and Jing Fu. A hybrid genetic- simulated annealing algorithm for the location-inventory-routing problem considering returns under e-supply chain environment. The Scientific World Journal, 2013, 2013.

      [20] Xiaobing Yu, Jie Cao, Haiyan Shan, Li Zhu, and Jun Guo. An adaptive hybrid algorithm based on particle swarm optimization and differential evolution for global optimization. The Scientific World Journal, 2014, 2014.

      [21] Qian-Qian Duan, Gen-Ke Yang, and Chang-Chun Pan. A novel algorithm combining finite state method and genetic algorithm for solving crude oil scheduling problem. The Scientific World Journal, 2014, 2014.

      [22] David Sloan Wilson. Altruism and organism: Disentangling the themes of multilevel selection theory. The American Naturalist, 2015.

      [23] Henrieta Palubova´. Chaotic sequences in MC-CDMA systems.

      [24] Dixiong Yang, Zhenjun Liu, and Jilei Zhou. Chaos optimization algorithms based on chaotic maps with different probability distribution and search speed for global optimization. Communications in Nonlinear Science and Numerical Simulation, 19(4):1229–1246, 2014. https://doi.org/10.1016/j.cnsns.2013.08.017.

      [25] S Talatahari, B Farahmand Azar, R Sheikholeslami, and AH Gandomi. Imperialist competitive algorithm combined with chaos for global optimization. Communications in Nonlinear Science and Numerical Simulation, 17(3):1312–1319, 2012. https://doi.org/10.1016/j.cnsns.2011.08.021.

      [26] A Rezaee Jordehi. Chaotic bat swarm optimization (CBSO). Applied Soft Computing, 26:523–530, 2015. https://doi.org/10.1016/j.asoc.2014.10.010.

      [27] Amir H Gandomi and Xin-She Yang. Chaotic bat algorithm. Journal of Computational Science, 5(2):224–232, 2014. https://doi.org/10.1016/j.jocs.2013.10.002.

      [28] Robert M May. Simple mathematical models with very complicated dynamics. Nature, 261(5560):459–467, 1976. https://doi.org/10.1038/261459a0.

      [29] Andy Reynolds. Liberating le´vy walk research from the shackles of optimal foraging. Physics of life reviews, 14:59–83, 2015. https://doi.org/10.1016/j.plrev.2015.03.002.

      [30] Arild O Gautestad and Atle Mysterud. The le´vy flight foraging hypothesis: forgetting about memory may lead to false verification of Brownian motion. Movement ecology, 1(1):9, 2013. https://doi.org/10.1186/2051-3933-1-9.

      [31] Nasif Shawkat, Shariba Islam Tusiy, and Md Arman Ahmed. Advanced cuckoo search algorithm for optimization problem. International Journal of Computer Applications, 132(2), 2015.

      [32] Ling Ai Wong, Hussain Shareef, Azah Mohamed, and Ahmad Asrul Ibrahim. Optimal battery sizing in photovoltaic based distributed generation using enhanced opposition-based firefly algorithm for voltage rise mitigation. The Scientific World Journal, 2014, 2014.

  • Downloads

  • How to Cite

    Peace Igiri, C., Singh, Y., & Bhargava, D. (2018). An improved African buffalo optimization algorithm using chaotic map and chaotic-levy flight. International Journal of Engineering & Technology, 7(4), 4570-4576. https://doi.org/10.14419/ijet.v7i4.22726