In conventional deterministic optimization the objective is to minimize or maximize a function subject to constraints. The optimum is calculated under ideal conditions that are difficult to achieve in reality and real systems always exhibit uncertain deviations from the nominal state (scatter). Scatter is caused by variations in the design variables (control factors) and/or the noise variables (uncontrollable factors) of the real system. The aim of RDO is not only to minimize or maximize the primary objective function but also to minimize the sensitivity of the solution to scatter. This means that the RDO problem is bi-objective, requiring not only that the performance of the solution be brought towards a target but also that the variation from the target is minimized.

Based on a simulation of slit die performance that takes into account the coupling of melt flow and die body deflection due to melt pressure, a Genetic Algorithm [1,2] (GA) is used to determine choker bar profiles to give optimum (ideally uniform) melt flow distribution. The deterministic solution gained using conventional optimization alone is not necessarily a robust solution, i.e. scatter caused by slight changes in uncontrollable noise factors such as the input flow rate of the polymer may cause dramatic non-uniformity in the melt flow distribution. A GA is used to achieve a robust design by solving a bi-objective problem that minimizes both the original objective function and the variation caused by scatter.

From experience it seems that the most important sources of scatter (noise factors) in the slit die extrusion are throughput flow rate of polymer, batch-to-batch variation of the raw material, variations in the choker-bar manufacture and temperature fluctuations. In this paper robustness is assessed using these sources of scatter and RDO is carried out. Comparison is made with the optimum found without robustness considerations to those gained using the Physical Programming method [3] to generate the Pareto set for the bi-objective problem.

Acknowledgements

We gratefully acknowledge the financial support from EPSRC under the projects 'A Flexible Framework For Large Scale Optimization with Industrial Application' (Ref No. 00314975) and 'Computer Aided Optimization of Extrusion Die Design' (EPSRC GR/M 95820).

1

D.S. Langley, J.F.T. Pittman and J. Sienz, "Computerised Optimisation of Slit Die Design Taking Account of Die Body Deflection', Centre for Polymer Processing Simulation and Design, University of Wales Swansea, UK, in A.M. Habraken, (ed), in Proceedings of the 4th international ESAFORM 2001,April 2001, Liege, pp 279 - 282, 2001.

2

J.F.T. Pittman, R. Sander, W. Schuler, H. Pick, G. Martin and W. Stannek, "Mechanical Effects in Extrusion: Slit Dies, Experimental and Numerical Determination of the Die Body Deflection", Int Poly Proc, 10, 137, 1995.

3

A. Messac, "Physical Programming: Effective Optimization for Computational Design", AIAA Journal, Vol. 34, No. 1, Jan. 1996, pp. 149- 158, January 1996. doi:10.2514/3.13035

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