A non-linear branch and cut method for solving discrete minimum compliance problems to global optimality

Mathias Stolpe; Martin P. Bendsøe

A non-linear branch and cut method for solving discrete minimum compliance problems to global optimality

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Abstract

This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities) and cuts.

Original language	English
Title of host publication	7th World Congress on Structural and Multidisciplinary Optimization : Proceedings
Publication date	2007
Pages	2513-2522
Publication status	Published - 2007
Event	7th World Congress on Structural and Multidisciplinary Optimization - Seoul, Korea, Republic of Duration: 21 May 2007 → 25 May 2007 Conference number: 7 http://www.ndaportal.com/wcsmo-7.html

Conference

Conference	7th World Congress on Structural and Multidisciplinary Optimization
Number	7
Country/Territory	Korea, Republic of
City	Seoul
Period	21/05/2007 → 25/05/2007
Internet address	http://www.ndaportal.com/wcsmo-7.html

Keywords

Topology optimization
Branch and cut
Global optimality

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title = "A non-linear branch and cut method for solving discrete minimum compliance problems to global optimality",

abstract = "This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities) and cuts.",

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N2 - This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities) and cuts.

AB - This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities) and cuts.

KW - Topology optimization

KW - Branch and cut

KW - Global optimality

M3 - Article in proceedings

SP - 2513

EP - 2522

BT - 7th World Congress on Structural and Multidisciplinary Optimization

T2 - 7th World Congress on Structural and Multidisciplinary Optimization

Y2 - 21 May 2007 through 25 May 2007

ER -

A non-linear branch and cut method for solving discrete minimum compliance problems to global optimality

Abstract

Conference

Keywords

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