Two-Stage Optimization Problem (TSOP) C. Acquah, et al., Ind. Eng. Chem. Res. (2006)
Using the optical fiber drawing numerical model as the basis, a deterministic TwoStage Optimization Problem (TSOP) and a Split and Bound (SB) algorithm is employed to solve the optimization under uncertainty of a fiber drawing process.
Two-Stage Optimization Problem: the two stages represent the initial design stage followed by the operational stage.
In the design stage, design variables, dk, are selected and are fixed as the process runs. During the process operation, another set of variables, zi, referred to as control variables, are varied to compensate for the effect of uncertainties.
In TSOP uncertainty, the objective function is evaluated as an expected (mean) value, whereas the constraints are treated deterministically for each realization of within the domain of the uncertain parameter. The optimization problem can be expressed as: Maximize E ( V )
Tw ,Td ,ra ,c i ,z L , V
Subject to:
g1 n d (dk ,z i , j ) n d ,crit 0
j Tw ,Td ,a, m0 E m,,D0, E dk Tw ,Td ,ra ,c 0 ,zL,,u f
g2 FT (dk ,z i , j ) Fcrit 0 g3 (dk ,z i , j ) crit 0 g4 max (dk ,z i , j ) max,crit 0
z i ucg ,uig
g5 ave (dk ,z i , j ) ave,crit 0 Advanced Materials and Technologies Laboratory • University of Connecticut