Bacterial foraging optimization algorithm with mutation to solve constrained problems


A simple version of a Swarm Intelligence algorithm called bacterial foraging optimization algorithm with mutation and dynamic stepsize (BFOAM-DS) is proposed. The bacterial foraging algorithm has the ability to explore and exploit the search space through its chemotactic operator. However, premature convergence is a disadvantage. This proposal uses a mutation operator in a swim, similar to evolutionary algorithms, combined with a dynamic stepsize operator to improve its performance and allows a better balance between the exploration and exploitation of the search space. BFOAM-DS was tested in three well-known engineering design optimization problems. Results were analyzed with basic statistics and common measures for nature-inspired constrained optimization problems to evaluate the behavior of the swim with a mutation operator and the dynamic stepsize operator. Results were compared against a previous version of the proposed algorithm to conclude that BFOAM-DS is competitive and better than a previous version of the algorithm.
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Arora, J. (2011). Introduction to Optimum Design (3rd. Ed.). New York, NY: McGraw-Hill.

Biswas, A., Dasgupta, S., Das, S., & Abraham A. (2007). A Synergy of Differential Evolution and Bacterial Foraging Optimization for global optimization. Neural Network World, 17, 607-626.

Calva-Yáñez, M. B., Niño-Suárez, P. A., Villarreal-Cervantes, M. G., Sepúlveda-Cervantes, G., & Portilla-Flores, E. A. (2013). Differential evolution for the control gain’s optimal tuning of a four-bar mechanism. Polibits, 47, 67-73.

Coello-Coello, C. A. (2002). Theoretical and Numerical Constraint Handling Techniques used with Evolutionary Algorithms: A Survey of the State of the Art. Computer Methods in Applied Mechanics and Engineering, 191(11-12):1245-1287. doi: 10.1016/S0045-7825(01)00323-1.

Deb, K. (2000). An Efficient Constraint Handling Method for Genetic Algorithms. Computer Methods in Applied Mechanics and Engineering, 186(2), 311-338. doi: 10.1016/S0045-7825(99)00389-8.

Dorigo, M., Maniezzo, V., & Colorni, A. (1996). The Ant System: Optimization by a Colony of Cooperating Agents. IEEE Transactions of Systems, Man and Cybernetics-Part B, 26(1), 29-41. doi: 10.1109/3477.484436.

Eiben, A., & Smith, J. E. (2003). Introduction to Evolutionary Computing (Vol. 1). Natural Computing Series. Berlin Heidelberg: Springer Verlag.

Engelbrecht, A. P. (2007). Computational Intelligence. An Introduction (2nd. Ed.). New York, NY: John Wiley & Sons.

Fogel, L. J. (1999). Intelligence Through Simulated Evolution. Forty years of Evolutionary Programming(1st. Ed.). New York, NY: John Wiley & Sons.

Hernández-Ocaña, B., Mezura-Montes, E., & Pozos-Parra, P. (2013). A review of the bacterial foraging algorithm in constrained numerical optimization. In Proccedings of the Congress on Evolutionary Computation (CEC’2013) (pp. 2695-2702). IEEE. doi: 10.1109/CEC.2013.6557895.

Hernández-Ocaña, B., Pozos-Parra, M. P., & Mezura-Montes, E. (2014). Stepsize control on the modified bacterial foraging algorithm for constrained numerical optimization. In Proceedings of the 2014 Conference on Genetic and Evolutionary Computation (GECCO ’14) (pp. 25-32). ACM. doi: 10.1145/2576768.2598379.

Hernández-Ocaña, B., Pozos-Parra, M.P., Mezura-Montes, E., Portilla-Flores, E.,

Vega-Alvarado, E., & Calva-Yáñez, M. (2016). Two swim operators in the modified bacterial foraging algorithm for the optimal synthesis of four-bar mechanisms. Computational Intelligence and Neuroscience, 2016(1), 1-18. doi: 10.1155/2016/4525294.

Hernández-Ocaña, B., Chávez-Bosquez, O., Hernández-Torruco, J., Canul-Reich, J., & Pozos-Parra, P. (2018). Bacterial foraging optimization algorithm for menu planning. IEEE Access, 6, 8619-8629. doi: 10.1109/ACCESS.2018.2794198.

Huang, H. C., Chen, Y.H., & Abraham, A. (2010). Optimized watermarking using swarm-based bacterial foraging. Information Hiding and Multimedia Signal Processing, 1(1), 51-58.

Kennedy, J., & Eberhart, R. C. (2001). Swarm Intelligence (1st. Ed.). Burlington: MA: Morgan Kaufmann.

Kim, D. H., Abraham, A., & Cho, J. H. (2007). A hybrid genetic algorithm and bacterial foraging approach for global optimization. Information Sciences, 177(18), 3918-3937. doi: 10.1016/j.ins.2007.04.002.

Koza, J. R., Keane, M. A., Streeter, M. J., Mydlowec, W., Yu, J., & Lanza, G. (2003). Genetic Programming IV: Routine Human-Competitive Machine Intelligence (1st. Ed.). Hingham, MA: Kluwer Academic Publishers.

Kushwaha, N., Bisht, V. S., & Shah, G. (2012). Genetic algorithm based bacterial foraging approach for optimization. In IJCA Proceedings on National Conference on Future Aspects of Artificial intelligence in Industrial Automation ‘12, NCFAAIIA(2), 11-14.

Liang, J., Runarsson, T., Mezura-Montes, E., Clerc, M., Suganthan, P., Coello-Coello, C., & Deb, K. (2006). Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization. Technical report. School of EEE Nanyang Technological University, Singapore.

López-Ibáñez, M., Dubois-Lacoste, J., Pérez Cáceres, L., Birattari, M., & Stützle, T. (2011). The iRace package, Iterated Race for Automatic Algorithm Configuration. Operations Research Perspectives, 3, 43-58, doi: 10.1016/j.orp.2016.09.002.

Luo, Y., & Chen, Z. (2010). Optimization for PID control parameters on hydraulic servo control system based on the novel compound evolutionary algorithm. In Second International Conference on Computer Modeling and Simulation (pp. 40-43). IEEE. doi: 10.1109/ICCMS.2010.53.

Mezura-Montes, E. (2009). Constraint-Handling in Evolutionary Optimization, volume 198 of Studies in Computational Intelligence (1st. Ed.). Berlin Heidelberg: Springer-Verlag.

Mezura-Montes, E., & Coello-Coello, C. (2011). Constraint-handling in nature-inspired numerical optimization: Past, present and future. Swarm and Evolutionary Computation, 1(4), 173-194. doi: 10.1016/j.swevo.2011.10.001.

Mezura-Montes, E., & Hernández-Ocaña, B. (2009). Modified bacterial foraging optimization for engineering design. In Proceedings of the Artificial Neural Networks in Enginnering Conference (ANNIE’09), volume 19 of Intelligent Engineering Systems through Artificial Neural Networks (pp. 357-364). ASME Press. doi: 10.1115/1.802953.paper45.

Mezura-Montes, E., & López-Davila, E. A. (2012). Adaptation and local search in the modified bacterial foraging algorithm for constrained optimization. In Proccedings of the IEEE Congress on Evolutionary Computation (CEC ‘12), (pp. 497-504). IEEE. doi: 10.1109/CEC.2012.6256172.

Michalewicz, Z., & Fogel, D. B. (2004). How to Solve It: Modern Heuristics (2nd. Ed.). Berlin Heidelberg: Springer-Verlag.

Niu, B., Fan, Y., Xiao, H., & Xue, B. (2012). Bacterial foraging based approaches to portfolio optimization with liquidity risk. Neurocomputing, 98(1), 90-100. doi: 10.1016/j.neucom.2011.05.048.

Nouri, H., & Hong, T. S. (2012). A bacterial foraging algorithm based cell information considering operation time. Manufacturing Systems, 1(31), 326-336. doi: 10.1016/j.jmsy.2012.03.001.

Pandit, N., Tripathi, A., Tapaswi, S., & Pandit, M. (2012). An improved bacterial foraging algorithm for combined static/dynamic environmental economic dispatch. Applied Soft Computing, 1(12), 3500-3513. doi: 10.1016/j.asoc.2012.06.011.

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.

Praveena, P., Vaisakh, K., & Mohana Rao, S. (2010). A bacterial foraging and PSO-DE algorithm for solving dynamic economic dispatch problem with valve-point effects. In First International Conference on Integrated Intelligent Computing, (pp. 227-232). IEEE. doi: 10.1109/ICIIC.2010.26.

Price, K., Storn, R. M., & Lampinen, J. A. (2005). Differential Evolution: A Practical Approach to Global Optimization (1st. Ed.). Natural Computing Series. Berlin Heidelberg: Springer-Verlag.

Saber, A. Y. (2012). Economic dispatch using particle swarm optimization with bacterial foraging effect. Electrical Power and Energy Systems, 1(34), 38-46. doi: 10.1016/j.ijepes.2011.09.003.

Sandgren, E. (1995). Nonlinear integer and discrete programming in mechanical design optimization. ASME Journal of Mechanical Design, 112(1), 223-229, 1990. doi: 10.1115/1.2912596.

Schwefel, H. P. (1993). Evolution and Optimization Seeking (1st. Ed.). New York, NY: John Wiley & Sons.