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FOC, exact penalty algorithm converges to a local optimum after 92 trust-region iterations and 1.88 hrs of optimization CPU time. Although not so encouraging, these results and success with this case study enables us to conclude that we can indeed perform optimization using reduced-order models with the help of a systematic trust-region based adaptive strategy. We find that the reason for this high iteration count is early attainment of feasibility which further doesn’t allow infeasible moves and thus, tightens the step size. One reason for this might be the choice of high penalty for constraint violation (μ = 1000). This reflects one of the main issues with penalty functions, i.e., to find a reasonable value for μ. An updating scheme can be developed which penalizes constraint violation based on its magnitude; however, it may not be straight-forward. Instead, we develop a filter-based trust-region framework since it not only avoids such difficult decisions of choosing μ, but also allows steps which can achieve greater reduction in the objective by increasing infeasibility in a controlled manner. When applied to the PSA case study, filter trust-region algorithm converges to a local optimum within 51 trust- region iterations consuming 1.36 hrs of CPU time., which is significantly less compared to the penalty algorithm. Since trust-region subproblems with ZOC can also generate descent due to accurate ROMs, we follow a hybrid strategy for filter-based algorithm. Moreover, we also incorporate POD basis augmentation in Section I to improve ROM’s accuracy. For the PSA case study, we observe that 35 iterations out of the total 51 are indeed carried out in Section I of the algorithm, which is quite encouraging as it delays expensive gradient evaluations for FOC. Thus, we infer that a hybrid strategy and POD subspace augmentation are potentially useful tools for optimization with ROMs. Finally, success of the idea of using ROMs for computationally efficient optimization ulti- mately depends on the quality of the ROM and its ability to accurately predict the descent direction. Although we obtain promising results in this chapter, iteration count for both penalty and filter approaches can further be reduced by improving the quality of ROMs. In future, alternative methodologies can be explored to construct better and more efficient ROMs. 7.7 Conclusions Chapter 7. Trust-region Framework for ROM-based Optimization 183PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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