模板工程設計最佳化

OPTIMAL DESIGN OF CONCRETE FORMS

傳統模板設計的作法上，主要以人工經驗求解，此法不僅缺乏效率，且常求得不佳的解。至於學術界有曾利用窮舉法求解，然此法不僅費時，且針對大型問題常因需簡化其窮舉方式，故所得的結果易失去最佳化。緣此，本研究針對木模板施工設計，以最小材料成本為目標，考量相關設計規範限制與成本參數，利用數學規劃方法建構一模式，期能幫助業者有效地設計符合安全規範之木模板。此模式在數學上可定式為一非線性整數規劃問題，屬於NP-hard 問題。本研究利用動態規劃技巧發展一求解演算法，以求解出最佳的施工間距及材料組合。最後，本研究以一工程實際資料進行範例分析，測試本研究模式及求解演算法的績效，初步結果甚佳，應可為實務界參考。

In tradition, concrete formwork was manually designed with staff experience, which is neither efficient nor effective. In literature, scholars had employed a complete enumeration method to optimally design concrete formwork, which was however time-consuming and needed simplifications for solving large-scale problems, easily losing solution optimality. Therefore, this research employs mathematical programming techniques to develop a model that considers the objective of minimizing the material cost, coupled with related design speficiations and cost parameters, in order to help construction companies optimally design concrete formwork under safety requirements. The model is formulated as a nonlinear integer program which is characterized as NP-hard. Dynamic programming techniques are employed to develop a solution algorithm. Finally, a case study with real data from a construction company is performed to evaluate the model and the solution algorithm. The preliminary results are good, showing that the model and the solution algorithm could be useful for real practice.