Spiral bacterial foraging optimization method: Algorithm, evaluation and convergence analysis

References

• Abraham, A., A. Biswas, and S. Dasgupta, 2008. “Analysis of Reproduction Operator in Bacterial Foraging Optimization Algorithm.” In IEEE World Congress on Computational Intelligence—Evolutionary Computation (CEC 2008). June 1–6, Hong Kong. New York: IEEE Press, 1476–1483.
   Google Scholar
• Angeline, P. J. 1998. “Evolutionary Optimization Versus Particle Swarm Optimization: Philosophy and Performance Differences.” In Proceedings of Evolutionary Programming VII—the 7th International Conference (EP98), March 25–27. 601–610. Berlin: Springer-Verlag.
   Google Scholar
• Arnold, D., and R. Salomon. 2007. “Evolutionary Gradient Search Revisited.” IEEE Transactions on Evolutionary Computation 11 (4): 480–495. doi: 10.1109/TEVC.2006.882427
   Web of Science ®Google Scholar
• Bertsekas, D. P., and J. N. Tsitsiklis. 1999. “Gradient Convergence in Gradient Methods with Errors.” SIAM Journal on Optimization 10 (3): 627–642. doi: 10.1137/S1052623497331063
   Web of Science ®Google Scholar
• Bharath, B., and V. S. Borkar. 1999. “Stochastic Approximation Algorithms: Overview and Recent Trends.” SĀDHANĀ—Academy Proceedings in Engineering Sciences 24 (4): 425–452.
   Google Scholar
• Biswas, A., S. Dasgupta, S. Das, and A. Abraham, 2007a. “A Synergy of Differential Evolution and Bacterial Foraging Optimization for Global Optimization.” Chap. 6 in Vol. 17 of Neural Network World. 607–626. Prague 8, 18207, Czech Republic: Institute of Computer Science.
   Google Scholar
• Biswas, A., S. Dasgupta, S. Das, and A. Abraham, 2007b. “Synergy of PSO and Bacterial Foraging Optimization—A Comparative Study on Numerical Benchmarks.” In Innovations in Hybrid Intelligent Systems, 2nd International Workshop on Hybrid Artificial Intelligence Systems. Vol. 44 of Advances in Soft Computing Series. Berlin: Springer, 255–263.
   Google Scholar
• Borkar, V. S., and S. P. Meyn. 2000. “The O.D.E. Method for Convergence of Stochastic Approximation and Reinforcement Learning.” SIAM Journal on Control and Optimization 38 (2): 447–469. doi: 10.1137/S0363012997331639
   Web of Science ®Google Scholar
• Boyd, S., and L. Vandenberghe. 2004. Convex Optimization. Cambridge: Cambridge University Press.
   Google Scholar
• Bremermann, H. 1974. “Chemotaxis and Optimization.” Journal of the Franklin Institute 297 (5): 397–404. doi: 10.1016/0016-0032(74)90041-6
   Web of Science ®Google Scholar
• Chen, H., Y. Zhu, K. Hu, X. He, and B. Niu, 2008. “Cooperative Approaches to Bacterial Foraging Optimization.” In Advanced Intelligent Computing Theories and Applications with Aspects of Artificial Intelligence—Proceedings of the 4th International Conference on Intelligent Computing (ICIC), September, Shanghai, edited by D.-S. Huang, C. D Wunsch, D. Levine and K.-H. Jo. Vol. 5227 of Lecture Notes in Computer Science. 541–548. Berlin: Springer.
   Google Scholar
• Chen, X., Y.S. Ong, M.H. Lim, and K.C. Tan, 2011. “A Multi-Facet Survey on Memetic Computation.” IEEE Transactions on Evolutionary Computation 15 (5): 591–607. doi: 10.1109/TEVC.2011.2132725
   Web of Science ®Google Scholar
• Clarke, Frank H. 1990. Optimization and Nonsmooth Analysis. Vol. 5 of Classics in Applied Mathematics. Philadelphia, PA: SIAM.
   Google Scholar
• Das, S., A. Abraham, and A. Konar, 2009. “On Stability of the Chemotactic Dynamics in Bacterial-Foraging Optimization Algorithm.” IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans 39 (3): 670–679. doi: 10.1109/TSMCA.2008.2011474
   Web of Science ®Google Scholar
• Dorigo, M., and L. M. Gambardella. 1997. “Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem.” IEEE Transactions on Evolutionary Computation 1 (1): 53–66. doi: 10.1109/4235.585892
   Google Scholar
• Ermoliev, Y. 1983. “Stochastic Quasigradient Methods and Their Application to System Optimization.” Stochastics 9 (1-2): 1–36. doi: 10.1080/17442508308833246
   Google Scholar
• Floudas, C. A. 1995. Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications. Oxford: Oxford University Press.
   Google Scholar
• Fogel, L. J., A. J. Owens, and M. J. Walsh. 1966. Artificial Intelligence Through Simulated Evolution. 159–165. New York: Wiley.
   Google Scholar
• Fort, J. C., and G. Pages. 1996. “Convergence of Stochastic Algorithms: From the Kushner–Clark Theorem to the Lyapounov Functional Method.” Journal of Advances in Applied Probability 28 (4): 1072–1094. doi: 10.2307/1428165
   Web of Science ®Google Scholar
• Goh, C., Y.S. Ong, K.C. Tan, and E.J. Teoh, 2008. “An Investigation on Evolutionary Gradient Search for Multi-Objective Optimization.” In IEEE World Congress on Computational Intelligence—Evolutionary Computation (CEC 2008), Hong Kong, June 1–6. New York: IEEE Press, 3741–3746.
   Google Scholar
• Haddad, O., A. Afshar, and M. Mariño. 2006. “Honey-Bees Mating Optimization (HBMO) Algorithm: A New Heuristic Approach for Water Resources Optimization.” Water Resources Management 20 (5): 661–680. doi: 10.1007/s11269-005-9001-3
   Web of Science ®Google Scholar
• Holland, J. H. 1975. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. 175–177. Ann Arbor: University of Michigan Press.
   Google Scholar
• Kasaiezadeh, A., A. Khajepour, and S. L. Waslander. 2010. “Spiral Bacterial Foraging Optimization Method.” In American Control Conference (ACC 2010), Baltimore, MD, USA, June 30–July 2. New York: IEEE Press, 4845–4850.
   Google Scholar
• Kennedy, J., and R. Eberhart. 1995. “Particle Swarm Optimization.” In Vol. 4 of Proceedings of the IEEE International Conference on Neural Networks, Perth, WA, USA. New York: 1942–1948.
   Google Scholar
• Korani, W. M., H. T. Dorrah, and H. M. Emara. 2009. “Bacterial Foraging Oriented by Particle Swarm Optimization Strategy for PID Tuning.” In IEEE International Symposium on Computational Intelligence in Robotics and Automation (CIRA 2009), Daejon, South Korea, December 15–18. New York: IEEE Press, 445–450.
   Google Scholar
• Li, M. X., and C. Y. Wang. 2006. “Convergence Property of Gradient-Type Methods with Non-Monotone Line Search in the Presence of Perturbations.” Applied Mathematics and Computation 174 (2): 854–868. doi: 10.1016/j.amc.2005.05.030
   Web of Science ®Google Scholar
• Li, B., Y.S. Ong, M. Nghia Le, and C.K. Goh, 2008. “Memetic Gradient Search.” In IEEE World Congress on Computational Intelligence—Evolutionary Computation (CEC 2008). Hong Kong, June 1–6. New York: IEEE Press, 2894–2901.
   Google Scholar
• Liu, Y., and K. M. Passino. 2002. “Biomimicry of Social Foraging Bacteria for Distributed Optimization: Models, Principles, and Emergent Behaviors.” Journal of Optimization Theory and Applications 115 (3): 603–628. doi: 10.1023/A:1021207331209
   Web of Science ®Google Scholar
• Müller, S. D., J. Marchetto, S. Airaghi, and P. Koumoutsakos, 2002. “Optimization Based on Bacterial Chemotaxis.” IEEE Transactions on Evolutionary Computation 6 (1): 16–29. doi: 10.1109/4235.985689
   Web of Science ®Google Scholar
• Nakonechnyi, A. N. 1995. “Stochastic Gradient Processes: A Survey of Convergence Theory Using Lyapunov Second Method.” Cybernetics and Systems Analysis 31 (1): 37–51. doi: 10.1007/BF02366794
   Google Scholar
• Nguyen, Q. H., Y. S. Ong, and M. H. Lim. 2009. “A Probabilistic Memetic Framework.” IEEE Transactions on Evolutionary Computation 13 (3): 604–623. doi: 10.1109/TEVC.2008.2009460
   Web of Science ®Google Scholar
• Niu, B., Y.L. Zhu, X.X. He, and X.P. Zeng, 2006. “An Improved Particle Swarm Optimization Based on Bacterial Chemotaxis.” In Vol. 1 of 6th World Congress on Intelligent Control and Automation (WCICA 2006), Dalian, China, June 21–23. 3193–3197.
   Google Scholar
• Ong, Y. S., M.H. Lim, N. Zhu, and K.W. Wong, 2006. “Classification of Adaptive Memetic Algorithms: A Comparative Study.” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 36 (1): 141–152. doi: 10.1109/TSMCB.2005.856143
   PubMed Web of Science ®Google Scholar
• Parsopoulos, K., and M. N. Vrahatis. 2004. “On the Computation of All Global Minimizers Through Particle Swarm Optimization.” IEEE Transactions on Evolutionary Computation 8 (3): 211–224. doi: 10.1109/TEVC.2004.826076
   Web of Science ®Google Scholar
• Passino, K. M. 2002. “Biomimicry of Bacterial Foraging for Distributed Optimization and Control. IEEE Control Systems Magazine 22 (3): 52–67. doi: 10.1109/MCS.2002.1004010
   Web of Science ®Google Scholar
• Poljak, B. T. 1978. “Nonlinear Programming Methods in the Presence of Noise.” Journal of Mathematical Programming 14 (1): 87–97. doi: 10.1007/BF01588952
   Web of Science ®Google Scholar
• Rao, S. S. 1996. Engineering Optimization: Theory and Practice. 3rd ed. New York: Wiley-Interscience.
   Google Scholar
• Salomon, R. 1998. “Evolutionary Algorithms and Gradient Search: Similarities and Differences.” IEEE Transactions on Evolutionary Computation 2 (2): 45–55. doi: 10.1109/4235.728207
   Google Scholar
• Salomon, R., and D. Arnold. 2009. “The Evolutionary-Gradient-Search Procedure in Theory and Practice.” In Nature-Inspired Algorithms for Optimisation, edited by R. Chiong. Vol. 193 of Studies in Computational Intelligence. 77–101. Berlin: Springer.
   Google Scholar
• Shapiro, A., and Y. Wardi. 1996. “Convergence Analysis of Gradient Descent Stochastic Algorithms.” Journal of Optimization Theory and Applications 91 (2): 439–454. doi: 10.1007/BF02190104
   Web of Science ®Google Scholar
• Shen, H., Y. Zhu, X. Zhou, H. Guo, and C. Chang, 2009. “Bacterial Foraging Optimization Algorithm with Particle Swarm Optimization Strategy for Global Numerical Optimization.” In Proceedings of the First ACM/SIGEVO Summit on Genetic and Evolutionary Computation (GEC ’09), Shanghai. 497–504. New York: ACM.
   Google Scholar
• Shi, Z. J. 2004. “Convergence of Line Search Methods for Unconstrained Optimization.” Applied Mathematics and Computation 157 (2): 393–405. doi: 10.1016/j.amc.2003.08.058
   Web of Science ®Google Scholar
• Silva, A., A. Neves, and E. Costa. 2003. “SAPPO: A Simple, Adaptable, Predator Prey Optimiser.” In 11th Portuguese Conference on Artificial Intelligence, EPIA 2003, Beja, Portugal, December 4–7, 2003. Vol. 2902 of Lecture Notes in Computer Science. Berlin: Springer, 59–73.
   Google Scholar
• Solodov, M. V., and B. F. Svaiter. 1997. “Descent Methods with Linesearch in the Presence of Perturbations.” Journal of Computational and Applied Mathematics 80 (2): 265–275. doi: 10.1016/S0377-0427(97)00025-3
   Web of Science ®Google Scholar
• Solodov, M. V., and S. K. Zavries. 1998. “Error Stability Properties of Generalized Gradient-Type Algorithms.” Journal of Optimization Theory and Applications 98 (3): 663–680. doi: 10.1023/A:1022680114518
   Web of Science ®Google Scholar
• Song, M. P., and G. C. Gu. 2004. “Research on Particle Swarm Optimization: A Review.” In Vol. 4 of Proceedings of the Third International Conference on Machine Learning and Cybernetics, Shanghai, China. New York: IEEE Press, 2236–2241.
   Google Scholar
• Tomlin, C. J., and J. D. Axelrod. 2007. “Biology by Numbers: Mathematical Modelling in Developmental Biology.” Nature Reviews Genetics 8 (5): 331–340. doi: 10.1038/nrg2098
   PubMed Web of Science ®Google Scholar
• Tsitsiklis, J., D. Bertsekas, and M. Athans. 1986. “Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms.” IEEE Transactions on Automatic Control 31 (9): 803–812. doi: 10.1109/TAC.1986.1104412
   Web of Science ®Google Scholar
• Venkataraman, P. 2009. Applied Optimization with MATLAB Programming. 2nd ed. New York: Wiley.
   Google Scholar