A 101-line MATLAB code for topology optimization using binary variables and integer programming

This paper presents a MATLAB code with the implementation of the Topology Optimization of Binary Structures (TOBS) method first published by Sivapuram and Picelli (Finite Elem Anal Des 139: pp. 49–61, 2018 ). The TOBS is a gradient-based topology optimization method that employs binary design variab...

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Vydané v:	Structural and multidisciplinary optimization Ročník 63; číslo 2; s. 935 - 954
Hlavní autori:	Picelli, Renato, Sivapuram, Raghavendra, Xie, Yi Min
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2021 Springer Nature B.V
Predmet:	Computational Mathematics and Numerical Analysis Design optimization Educational Paper Engineering Engineering Design Integer programming Linear programming Mathematical programming Matlab Optimization Theoretical and Applied Mechanics Topology optimization Topology optimization Integer linear programming Binary variables Educational code
ISSN:	1615-147X, 1615-1488
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Abstract	This paper presents a MATLAB code with the implementation of the Topology Optimization of Binary Structures (TOBS) method first published by Sivapuram and Picelli (Finite Elem Anal Des 139: pp. 49–61, 2018 ). The TOBS is a gradient-based topology optimization method that employs binary design variables and formal mathematical programming. Besides its educational purposes, the 101-line code is provided to show that topology optimization with integer linear programming can be efficiently carried out, contrary to the previous reports in the literature. Compliance minimization subject to a volume constraint is first solved to highlight the main features of the TOBS method. The optimization parameters are discussed. Then, volume minimization subject to a compliance constraint is solved to illustrate that the method can efficiently deal with different types of constraints. Finally, simultaneous volume and displacement constraints are investigated in order to expose the capabilities of the optimizer and to serve as a tutorial of multiple constraints. The 101-line MATLAB code and some simple enhancements are elucidated, keeping only the integer programming solver unmodified so that it can be tested and extended to other numerical examples of interest.
AbstractList	This paper presents a MATLAB code with the implementation of the Topology Optimization of Binary Structures (TOBS) method first published by Sivapuram and Picelli (Finite Elem Anal Des 139: pp. 49–61, 2018). The TOBS is a gradient-based topology optimization method that employs binary design variables and formal mathematical programming. Besides its educational purposes, the 101-line code is provided to show that topology optimization with integer linear programming can be efficiently carried out, contrary to the previous reports in the literature. Compliance minimization subject to a volume constraint is first solved to highlight the main features of the TOBS method. The optimization parameters are discussed. Then, volume minimization subject to a compliance constraint is solved to illustrate that the method can efficiently deal with different types of constraints. Finally, simultaneous volume and displacement constraints are investigated in order to expose the capabilities of the optimizer and to serve as a tutorial of multiple constraints. The 101-line MATLAB code and some simple enhancements are elucidated, keeping only the integer programming solver unmodified so that it can be tested and extended to other numerical examples of interest. This paper presents a MATLAB code with the implementation of the Topology Optimization of Binary Structures (TOBS) method first published by Sivapuram and Picelli (Finite Elem Anal Des 139: pp. 49–61, 2018 ). The TOBS is a gradient-based topology optimization method that employs binary design variables and formal mathematical programming. Besides its educational purposes, the 101-line code is provided to show that topology optimization with integer linear programming can be efficiently carried out, contrary to the previous reports in the literature. Compliance minimization subject to a volume constraint is first solved to highlight the main features of the TOBS method. The optimization parameters are discussed. Then, volume minimization subject to a compliance constraint is solved to illustrate that the method can efficiently deal with different types of constraints. Finally, simultaneous volume and displacement constraints are investigated in order to expose the capabilities of the optimizer and to serve as a tutorial of multiple constraints. The 101-line MATLAB code and some simple enhancements are elucidated, keeping only the integer programming solver unmodified so that it can be tested and extended to other numerical examples of interest.
Author	Sivapuram, Raghavendra Xie, Yi Min Picelli, Renato
Author_xml	– sequence: 1 givenname: Renato orcidid: 0000-0003-4456-0213 surname: Picelli fullname: Picelli, Renato email: rpicelli@usp.br organization: Department of Mining and Petroleum Engineering, University of São Paulo – sequence: 2 givenname: Raghavendra surname: Sivapuram fullname: Sivapuram, Raghavendra organization: Structural Engineering Department, University of California San Diego – sequence: 3 givenname: Yi Min surname: Xie fullname: Xie, Yi Min organization: Center for Innovative Structures and Materials, School of Engineering, RMIT University
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Cites_doi	10.2307/1910129 10.1108/02644409810244129 10.1002/nme.5827 10.1007/s00158-019-02396-3 10.1007/s00158-020-02598-0 10.1007/s001580050176 10.1007/978-1-4614-7630-6 10.1007/s00158-009-0430-0 10.1016/j.commatsci.2018.08.008 10.1007/1-4020-4752-5_42 10.1007/s00158-010-0594-7 10.1016/0045-7949(93)90035-C 10.1016/j.finel.2007.06.006 10.1007/s00158-018-1939-x 10.1007/BF01742754 10.1007/s00158-018-1904-8 10.1016/j.cma.2018.10.050 10.1016/S0045-7825(01)00251-1 10.1007/s00158-004-0493-x 10.1007/978-0-387-92280-5_2 10.1007/s00158-006-0087-x 10.1007/s00158-019-02339-y 10.1016/j.cma.2019.112784 10.1016/j.advengsoft.2015.02.006 10.1007/s11831-016-9203-2 10.1007/s00158-020-02549-9 10.1007/s00158-019-02443-z 10.1007/s10107-006-0086-0 10.1007/s00158-015-1372-3 10.1007/s00158-010-0527-5 10.1016/j.finel.2015.01.009 10.1007/s40324-018-00185-4 10.1016/j.finel.2017.10.006 10.1007/s00158-013-0956-z 10.1007/BF01197709 10.1002/nme.1064
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Snippet	This paper presents a MATLAB code with the implementation of the Topology Optimization of Binary Structures (TOBS) method first published by Sivapuram and...
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SubjectTerms	Computational Mathematics and Numerical Analysis Design optimization Educational Paper Engineering Engineering Design Integer programming Linear programming Mathematical programming Matlab Optimization Theoretical and Applied Mechanics Topology optimization
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Title	A 101-line MATLAB code for topology optimization using binary variables and integer programming
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