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Approximation of non-linear cost functions in p-graph structures

Abstract
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.
Type
Journal Article
Type of thesis
Series
Citation
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
Date
2016
Publisher
AIDIC
Degree
Supervisors
Rights
Copyright © 2016, AIDIC Servizi S.r.l.. Used with permission.