American Institute of Mathematical Sciences

Advanced
July  2007, 3(3): 543-552. doi: 10.3934/jimo.2007.3.543

A two-step algorithm for layout optimization of structures with discrete variables

Lianshuan Shi 1, , Enmin Feng 2, , Huanchun Sun 3, and  Zhaosheng Feng 4,

1. 

Department of Computer Science, Tianjin University of Technology and Education, Tianjin 300222, P.R., China
2. 

Department of Mathematics, Dalian University of Technology, Dalian 116023, P.R., China
3. 

Department of Mechanics, Dalian University of Technology, Dalian 116023, P.R., China
4. 

Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78541

Received  December 2006 Revised  January 2007 Published  July 2007

This paper presents a mathematical model for Layout optimization of structure with discrete variables. The optimization procedure is composed of two kinds of sub-procedures of optimization: the topological optimization and the shape optimization. In each one, a comprehensive algorithm is used to treat the problem. The two kinds of optimization procedures are used in turn until convergence appears. After the dimension of the structure is reduced, the delimiting combinatorial algorithm is used to search for the better objective value. A couple of classical examples are presented to show the efficiency of the method. Numerical results indicate that the method is efficient and the optimal results are satisfactory.
Keywords: delimiting and combinatorial algorithm, structural optimization, layout optimization, Discrete variable, relative difference quotient..
Mathematics Subject Classification: Primary: 46N10; Secondary: 49Q1.
Citation: Lianshuan Shi, Enmin Feng, Huanchun Sun, Zhaosheng Feng. A two-step algorithm for layout optimization of structures with discrete variables. Journal of Industrial & Management Optimization, 2007, 3 (3) : 543-552. doi: 10.3934/jimo.2007.3.543
[1]

Adil Bagirov, Sona Taheri, Soodabeh Asadi. A difference of convex optimization algorithm for piecewise linear regression. Journal of Industrial & Management Optimization, 2019, 15 (2) : 909-932. doi: 10.3934/jimo.2018077
[2]

Harish Garg. Solving structural engineering design optimization problems using an artificial bee colony algorithm. Journal of Industrial & Management Optimization, 2014, 10 (3) : 777-794. doi: 10.3934/jimo.2014.10.777
[3]

Sen Zhang, Guo Zhou, Yongquan Zhou, Qifang Luo. Quantum-inspired satin bowerbird algorithm with Bloch spherical search for constrained structural optimization. Journal of Industrial & Management Optimization, 2021, 17 (6) : 3509-3523. doi: 10.3934/jimo.2020130
[4]

Renato Bruni, Gianpiero Bianchi, Alessandra Reale. A combinatorial optimization approach to the selection of statistical units. Journal of Industrial & Management Optimization, 2016, 12 (2) : 515-527. doi: 10.3934/jimo.2016.12.515
[5]

David Russell. Structural parameter optimization of linear elastic systems. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1517-1536. doi: 10.3934/cpaa.2011.10.1517
[6]

Claire david@lmm.jussieu.fr David, Pierre Sagaut. Theoretical optimization of finite difference schemes. Conference Publications, 2007, 2007 (Special) : 286-293. doi: 10.3934/proc.2007.2007.286
[7]

Simone Göttlich, Oliver Kolb, Sebastian Kühn. Optimization for a special class of traffic flow models: Combinatorial and continuous approaches. Networks & Heterogeneous Media, 2014, 9 (2) : 315-334. doi: 10.3934/nhm.2014.9.315
[8]

Zhongliang Deng, Enwen Hu. Error minimization with global optimization for difference of convex functions. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1027-1033. doi: 10.3934/dcdss.2019070
[9]

Cristian Barbarosie, Anca-Maria Toader, Sérgio Lopes. A gradient-type algorithm for constrained optimization with application to microstructure optimization. Discrete & Continuous Dynamical Systems - B, 2020, 25 (5) : 1729-1755. doi: 10.3934/dcdsb.2019249
[10]

Wolfgang Riedl, Robert Baier, Matthias Gerdts. Optimization-based subdivision algorithm for reachable sets. Journal of Computational Dynamics, 2021, 8 (1) : 99-130. doi: 10.3934/jcd.2021005
[11]

Xiangyu Gao, Yong Sun. A new heuristic algorithm for laser antimissile strategy optimization. Journal of Industrial & Management Optimization, 2012, 8 (2) : 457-468. doi: 10.3934/jimo.2012.8.457
[12]

Jianjun Liu, Min Zeng, Yifan Ge, Changzhi Wu, Xiangyu Wang. Improved Cuckoo Search algorithm for numerical function optimization. Journal of Industrial & Management Optimization, 2020, 16 (1) : 103-115. doi: 10.3934/jimo.2018142
[13]

Yong Wang, Wanquan Liu, Guanglu Zhou. An efficient algorithm for non-convex sparse optimization. Journal of Industrial & Management Optimization, 2019, 15 (4) : 2009-2021. doi: 10.3934/jimo.2018134
[14]

Xueting Cui, Xiaoling Sun, Dan Sha. An empirical study on discrete optimization models for portfolio selection. Journal of Industrial & Management Optimization, 2009, 5 (1) : 33-46. doi: 10.3934/jimo.2009.5.33
[15]

Valery Y. Glizer, Vladimir Turetsky, Emil Bashkansky. Statistical process control optimization with variable sampling interval and nonlinear expected loss. Journal of Industrial & Management Optimization, 2015, 11 (1) : 105-133. doi: 10.3934/jimo.2015.11.105
[16]

Marius Durea, Elena-Andreea Florea, Radu Strugariu. Henig proper efficiency in vector optimization with variable ordering structure. Journal of Industrial & Management Optimization, 2019, 15 (2) : 791-815. doi: 10.3934/jimo.2018071
[17]

Jean-Paul Arnaout, Georges Arnaout, John El Khoury. Simulation and optimization of ant colony optimization algorithm for the stochastic uncapacitated location-allocation problem. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1215-1225. doi: 10.3934/jimo.2016.12.1215
[18]

Alireza Goli, Hasan Khademi Zare, Reza Tavakkoli-Moghaddam, Ahmad Sadeghieh. Application of robust optimization for a product portfolio problem using an invasive weed optimization algorithm. Numerical Algebra, Control & Optimization, 2019, 9 (2) : 187-209. doi: 10.3934/naco.2019014
[19]

Nguyen Van Thoai. Decomposition branch and bound algorithm for optimization problems over efficient sets. Journal of Industrial & Management Optimization, 2008, 4 (4) : 647-660. doi: 10.3934/jimo.2008.4.647
[20]

Tran Ngoc Thang, Nguyen Thi Bach Kim. Outcome space algorithm for generalized multiplicative problems and optimization over the efficient set. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1417-1433. doi: 10.3934/jimo.2016.12.1417

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (29)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy