##
**Antioptimisation of trusses using two-level population-based incremental learning.**
*(English)*
Zbl 1266.68162

Summary: Practical optimum design of structures often involves parameters with uncertainties. There have been several ways to deal with such optimisation problems, and one of the approaches is an antioptimisation process. The task is to find the optimum solution of common design variables while simultaneously searching for the worst case scenario of those parameters with uncertainties. This paper proposed a metaheuristic based on population-based incremental learning (PBIL) for solving antioptimisation of trusses. The new algorithm is called two-level PBIL which consists of outer and inner loops. Five antioptimisation problems are posed to test the optimiser performance. The numerical results show that the concept of using PBIL probability vectors for handling the antioptimisation of truss is powerful and effective. The two-level PBIL can be considered a powerful optimiser for antioptimisation of trusses.

### MSC:

68T05 | Learning and adaptive systems in artificial intelligence |

PDF
BibTeX
XML
Cite

\textit{P. Tontragunrat} and \textit{S. Bureerat}, J. Appl. Math. 2013, Article ID 434636, 12 p. (2013; Zbl 1266.68162)

Full Text:
DOI

### References:

[1] | A. Kaveh and S. Talatahari, “Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures,” Computers and Structures, vol. 87, no. 5-6, pp. 267-283, 2009. |

[2] | P. B. Thanedar, J. S. Arora, C. H. Tseng, O. K. Lim, and G. J. Park, “Performance of some SQP algorithms on structural design problems,” International Journal for Numerical Methods in Engineering, vol. 23, no. 12, pp. 2187-2203, 1986. · Zbl 0599.73090 |

[3] | A. Kaveh and S. Talatahari, “Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures,” Computers and Structures, vol. 87, no. 5-6, pp. 267-283, 2009. |

[4] | H. M. Gomes, “Truss optimization with dynamic constraints using a particle swarm algorithm,” Expert Systems with Applications, vol. 38, no. 1, pp. 957-968, 2011. |

[5] | W. A. Bennage and A. K. Dhingra, “Single and multiobjective structural optimization in discrete-continuous variables using simulated annealing,” International Journal for Numerical Methods in Engineering, vol. 38, no. 16, pp. 2753-2773, 1995. · Zbl 0855.73052 |

[6] | N. Pholdee and S. Bureerat, “Performance enhancement of multiobjective evolutionary optimizers for truss design using an approximate gradient,” Computers and Structures, vol. 106-107, pp. 115-124, 2012. |

[7] | C. Noilublao and S. Bureerat, “Topology and sizing optimization of trusses with adaptive ground finite elements using multiobjective PBIL,” Advanced Materials Research, vol. 308-310, pp. 1116-1121, 2011. |

[8] | N. Noilublao and S. Bureerat, “Simultaneous topology, shape and sizing optimisation of a three-dimensional slender truss tower using multiobjective evolutionary algorithms,” Computers and Structures, vol. 89, pp. 2531-2538, 2011. |

[9] | B. M. Adams, M. S. Eldred, and J. W. Wittwer, “Reliability-based design optimization for shape design of compliant micro-electro-mechanical systems,” in Proceedings of the 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, pp. 1042-1056, AIAA, September 2006. |

[10] | K. Deb, S. Gupta, D. Daum, J. Branke, A. K. Mall, and D. Padmanabhan, “Reliability-based optimization using evolutionary algorithms,” IEEE Transactions on Evolutionary Computation, vol. 13, no. 5, pp. 1054-1074, 2009. |

[11] | M. Lombardi and R. T. Haftka, “Anti-optimization technique for structural design under load uncertainties,” Computer Methods in Applied Mechanics and Engineering, vol. 157, no. 1-2, pp. 19-31, 1998. · Zbl 0954.74044 |

[12] | G. Venter and R. T. Haftka, “Two-species genetic algorithm for design under worst case conditions,” Evolutionary Optimization, vol. 2, no. 1, pp. 1-19, 2000. |

[13] | N. Wang and Y. Yang, “Optimization of structures under load uncertainties based on hybrid genetic algorithm,” in Evolutionary Computation, W. P. dos Santos, Ed., pp. 321-340, I-Tech, Vienna, Austria, 2009. |

[14] | A. R. Yıldız, “A novel hybrid immune algorithm for global optimization in design and manufacturing,” Robotics and Computer-Integrated Manufacturing, vol. 25, no. 2, pp. 261-270, 2009. |

[15] | I. Durgun and A. R. Yıldız, “Structural design optimization of vehicle components using cuckoo search algorithm,” Materials Testing, vol. 54, no. 3, pp. 185-188, 2012. |

[16] | S. L. Tilahun and H. C. Ong, “Modified firefly algorithm,” Journal of Applied Mathematics, vol. 2012, Article ID 467631, 12 pages, 2012. · Zbl 1268.65082 |

[17] | X. Cai, S. Fan, and Y. Tan, “Light responsive curve selection for photosynthesis operator of APOA,” International Journal of Bio-Inspired Computation, vol. 4, no. 6, pp. 373-379, 2012. |

[18] | Z. Cui, F. Gao, Z. Cui, and J. Qu, “A second nearest-neighbor embedded atom method interatomic potential for Li-Si Alloys,” Journal of Power Sources, vol. 207, p. 150, 2012. |

[19] | S. Baluja, “Population-based incremental learning: a method for integrating genetic search based function optimization and competitive learning,” Tech. Rep. CMU_CS_95_163, Carnegie Mellon University, 1994. |

[20] | Z. Qiu and X. Wang, “Structural anti-optimization with interval design parameters,” Structural and Multidisciplinary Optimization, vol. 41, no. 3, pp. 397-406, 2010. · Zbl 1274.74243 |

[21] | F. Y. Cheng and D. Li, “Fuzzy set theory with genetic algorithm in constrained structural optimization,” in Proceedings of the 1st US-Japan Joint Seminar on Structural Optimization, pp. 55-66, Advances in Structural optimization, April 1997. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.