This work addresses the integrated optimization of both the plant-wide material processing system and the utility system for a polyvinyl chloride (PVC) plant. In the plant-wide material processing system, vinyl chloride monomer (VCM) production process and VCM polymerization process are optimized to determine production allocation and switching operation of parallel equipment as well as raw material supply arrangement. In the utility system, power generation/supply plan is determined by combined heat and power (CHP) units and the state grid. The nonlinear electricity consuming characteristics of calcium carbide production process, CHP

This paper presents a new piecewise linear modeling method for the planning of polyvinyl chloride (PVC) plants. In our previous study (Ind. Eng. Chem. Res.2016551243012443), a multiperiod mixed-integer nonlinear programming (MINLP) model was developed to demonstrate the importance of integrating both the material processing and the utility systems. However, the optimization problem is really difficult to solve due to the process intrinsic nonlinearities, i.e., the operating cost or energy-consuming characteristics of calcium carbide furnaces, electrolytic cells, and CHP units. The present paper intends to address this challenge by using the piecewise linear modeling approach that provides good approximation of the global nonlinearity with locally linear models. Specifically, a hinging hyperplanes (HH) model is introduced to approximate the nonlinear items in the original MINLP model. HH model is a kind of continuous piecewise linear (CPWL) model, which is proven to be effective for any continuous linear functions with arbitrary dimensions on compact sets in any given precision, and is the basis for the linearization MINLP model. As a result, with the help of auxiliary variables, the original MINLP can be transformed into a mixed-integer linear program (MILP) model, which then can be solved by many established efficient and mature algorithms. Computational results show that the proposed model can reduce the solving time by up to 97% or more and the planning results are close to or even better than those obtained by the MINLP approach.

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The tripeptide Leu-Pro-Lys (LPK), derived from the Sipunculus nudus protein, was synthesized and studied to investigate its potential protective effect on bone formation. The effect and mechanism of LPK were analyzed through network pharmacology, bioinformatics, and experimental pharmacology. The study found that LPK at concentrations of 25 μg/mL and 50 μg/mL significantly increased ALP activity and mineralization in C3H10 cells. LPK also increased the expression of COL1A1 and promoted bone formation in zebrafish larvae. Network pharmacology predicted 148 interaction targets between LPK and bone development, and analysis of the protein-protein interaction network identified 13 hub genes, including ESR1, MAPK8, and EGFR, involved in bone development. Through KEGG enrichment pathways analysis, it was determined that LPK promotes bone development by regulating endocrine resistance, the relaxin signaling pathway, and the estrogen signaling pathway. Molecular docking results showed direct interactions between LPK and ESR1, MAPK8, and MAPK14. Additional verification experiments using western blot assay revealed that LPK significantly upregulated the expression of genes related to bone formation, including COL1A1, OPG, RUNX2, ESR1, phosphorylated MAPK14, and phosphorylated MAPK8 in C3H10 cells. These results suggest that LPK promotes bone formation by activating the estrogen/MAPK signaling pathway.