LARGE SCALE COMPUTING/ OPTIMIZATION

[nagendra]

Hello All
As an industry affiliate this is a very interesting communication board and will enable excellent collaboration between Industry and Academia. I am really happy that this has come about.

It would be of interest to know/have a thread related with Industrial application of Optimization and large scale optimization problems (optimization using > 100+ variables). Current concepts of Grid Computing / Farm Computing etc enable the possibility of using current computers and architect them in way to handle large computing efforts for problems like an aircraft or aircraft engine at a system level much more easily than in previous years...

Any good examples of adapting new or old optimization algorithms to capture system level benefits/performance sensitivity would be of interest

Thanks
Nagendra

[BJ Fregly]

Hi Nagendra,

In response to your posting, there has been a reasonable amount of work in the biomechanics research world involving large-scale optimization of human movement. The foundation of these optimizations is typically a multi-body dynamic skeletal model possings 20 to 30 degrees of freedom actuated by joint torque actuators or individual muscles.

Below are a few relevant articles that you may find interesting that use gradient-based optimization with > 500 design variables:
F. C. Anderson and M. G. Pandy, “A dynamic optimization solution for vertical jumping in three dimensions,” Comput. Methods Biomech. Biomed. Eng., vol. 2, pp. 201-231, 1999.
F. C. Anderson and M. G. Pandy, “Dynamic optimization of human walking,” J. Biomech. Eng., vol. 123, pp. 381-390, 2001.
B. J. Fregly, J. A. Reinbolt, K. L. Rooney, K. H. Mitchell, and T. L. Chmielewski, "Design of patient-specific gait modifications
for knee osteoarthritis rehabilitation," to appear in the September 2007 issue of IEEE Trans Biomed Eng.
J. A. Reinbolt, R. T. Haftka, T. L. Chmielewski, and B. J. Fregly, "A computational framework to predict post-treatment outcome for gait-related disorders," Med. Eng. Phys. (in press).

We have tried parallel particle swarm on the same problems as in the Fregly article above and found that it did not work well at all (unpublished results), primarily because the cost function uses a penalty method, and we did not crank up the weights on the penalty terms gradually. However, without adjusting the penalty weights, we still get great solutions with a nonlinear least squares algorithm. What did help the speed of the gradient-based optimizations was use of automatic differentiation (see the Reinbolt article above, which is posted on my web site).

B.J. Fregly
Associate Professor
University of Florida
www.mae.ufl.edu/~fregly

[xueyong]

We routinely solve optimization problems with thousands or more of design variables. But they usually have a limited number of constraints, such as in structural topology optimization.

The problem to look for is problem with both large number of design variables and large number of active constraints. I recall Dr. Vanderplaats presented a paper with large number of variables and active constraints (cantilever beam or aircraft wing problem). It should be in the proceedings of 8th MAO conference at Long beach.

You may also refer to a recent paper by Prof. Fleury at the ASME DETC2007 conference.
DETC2007-34326
Structural Optimization Methods for Large Scale Problems: Status and Limitations
Claude Fleury, Université de Liège

Hope this helps.

Xueyong