Dipartimento di Matematica e Applicazioni "Renato Caccioppoli"
# Jacek Gondzio: An efficient primal-dual interior point method for large-scale truss layout optimization problems

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Sala riunioni II livello del Dipartimento di Matematica e Applicazioni "Renato Caccioppoli"
#### Sala riunioni II livello del Dipartimento di Matematica e Applicazioni "Renato Caccioppoli"

MS Angelo

Description

il Prof. Jacek Gondzio,

School of Mathematics, University of Edinburgh terra' un seminario dal

titolo

**An efficient primal-dual interior point method for large-scale truss layout
optimization problems**

Abstract:

Truss layout optimization problems are often formulated by using a ground

structure approach where a set of nodes is distributed in the design domain

and all the possible interconnecting bars are generated. The main goal is

then to determine the optimal cross-sectional areas of these bars and obtain

the minimum weight structure that is able to sustain a given set of applied

loads.

However, such consideration of the full connectivity of the nodes results in

a large number of bars making the optimization problems computationally

challenging for solution techniques. We solve the problems using a

primal-dual interior point method where we employ several novel techniques

to deal with the large size of the problems.

The first step is to use a column generation procedure where the optimal

solution of the large original problem is obtained by solving a sequence of

smaller restricted master problems.

However, after performing a few column generation iterations, the size of

the restricted master problems grows and the problems still challenge

standard interior point solvers.

Therefore, we additionally exploit the algebraic structure of the problems

and reduce the normal equations originating from the interior point

algorithm to much smaller linear equation systems. We apply the

preconditioned conjugate gradient method to solve these reduced linear

systems. A special purpose preconditioner based on the mathematical

properties of the problem is designed. The efficiency and robustness of the

method is supported with several numerical experiments.

This is a joint work with Alemseged Weldeyesus.

References:

A.G. Weldeyesus and J. Gondzio,

A specialized primal-dual interior point method for the plastic truss layout

optimization, Computational Optimization and Applications (2018) 71:613--640

https://doi.org/10.1007/s10589-018-0028-9

A. G. Weldeyesus, J. Gondzio, L. He, M. Gilbert, P. Shepherd and A. Tyas,

Using member adding technique to solve truss layout optimization problems

with constraints on global stability, Structural Modelling and Optimization

(submitted).

http://www.maths.ed.ac.uk/~gondzio/reports/loptGlobStab.html

J. Gondzio and P. Gonzalez-Brevis,

A new warmstarting strategy for the primal-dual column generation method

Mathematical Programming, Ser. A (2015) 152:113--146 DOI

10.1007/s10107-014-0779-8

Organised by

Prof. Gerardo Toraldo