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On the reformulation of topology optimization problems as linear or convex quadratic mixed 0–1 programs

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Abstract

We consider equivalent reformulations of nonlinear mixed 0–1 optimization problems arising from a broad range of recent applications of topology optimization for the design of continuum structures and composite materials. We show that the considered problems can equivalently be cast as either linear or convex quadratic mixed 0–1 programs. The reformulations provide new insight into the structure of the problems and may provide a foundation for the development of new methods and heuristics for solving topology optimization problems. The applications considered are maximum stiffness design of structures subjected to static or periodic loads, design of composite materials with prescribed homogenized properties using the inverse homogenization approach, optimization of fluids in Stokes flow, design of band gap structures, and multi-physics problems involving coupled steady-state heat conduction and linear elasticity. Several numerical examples of maximum stiffness design of truss structures are presented.

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Denmark, Matematiktorvet, Building 303, 2800, Kgs. Lyngby, Denmark

    M. Stolpe

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  1. M. Stolpe
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Correspondence to M. Stolpe.

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The research is funded by the Danish Natural Science Research Council and the Danish Research Council for Technology and Production Sciences.

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Stolpe, M. On the reformulation of topology optimization problems as linear or convex quadratic mixed 0–1 programs. Optim Eng 8, 163–192 (2007). https://doi.org/10.1007/s11081-007-9005-3

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  • DOI: https://doi.org/10.1007/s11081-007-9005-3

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