Jacek Gondzio: An efficient primal-dual interior point method for large-scale truss layout optimization problems

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