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Ong, B. H. Y., Walmsley, T. G., Atkins, M. J., Walmsley, M. R. W., & Neale, J. R. (2016). Approximation of non-linear cost functions in p-graph structures. Chemical Engineering Transactions, 52, 1093–1098. https://doi.org/10.3303/CET1652183
Permanent Research Commons link: https://hdl.handle.net/10289/10851
P-graph employs combinatorial and optimisation algorithms to solve process network synthesis (PNS) problem. However, the P-graph framework requires linear cost functions when optimising PNS problems. As a result, a high error between the user-input linear cost function and the actual non-linear cost function is likely to occur. This paper presents a new method to incorporate multiple linear cost functions in parallel for raw materials, operating units and products in P-graph problems to accurately approximate the non-linear functional form of most cost estimation functions. This was achieved by dividing the original cost functions into multiple equal segments that then could be individually represented by linear sub-functions. Application of the new method to a simple wood-to-fuel processing example influences the optimal P-graph process structure such that a previously uneconomic side-product route (pyrolysis) becomes economic and increases the overall profit. The results also demonstrate that the linear approximation error decreases with increasing numbers of segments and linear cost sub-functions. The time increase to solve the new problem structure, which has over threefold more operating units, is negligible for this simple case, but may be significant for more complex problems.
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