Mathematical Methods of Operations Research

, Volume 68, Issue 2, pp 313–331

# Integer linear programming models for topology optimization in sheet metal design

• Armin Fügenschuh
• Marzena Fügenschuh
Original Article

## Abstract

The process of designing new industrial products is in many cases solely based on the intuition and experience of the responsible design engineer. The aid of computers is restricted to visualization and manual manipulation tools. We demonstrate that the design process for conduits, which are made out of sheet metal plates, can be supported by mathematical optimization models and solution techniques, leading to challenging optimization problems. The design goal is to find a topology that consists of several channels with a given cross section area using a minimum amount of sheet metal and, at the same time, maximizing its stiffness. We consider a mixed integer linear programming model to describe the topology of two dimensional slices of a three dimensional sheet metal product. We give different model formulations, based on cuts and on multicommodity flows. Numerical results for various test instances are presented.

## Keywords

Integer programming Topology optimization Discretization Multicommodity flow Separation Sheet metal products

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