Refinery planning optimization is a challenging problem as regards handling the nonconvex bilinearity, mainly due to pooling operations in processes such as crude oil distillation and product blending. This work investigated the performance of several representative piecewise linear (or piecewise affine) relaxation schemes (referred to as McCormick, bm, nf5, and nf6t) and de (which is a new approach proposed based on eigenvector decomposition) that mainly give rise to mixed-integer optimization programs to convexify a bilinear term using predetermined univariate partitioning for instances of uniform and non-uniform partition sizes. The computational results showed that applying these schemes improves the relaxation tightness compared to only applying convex and concave envelopes as estimators. Uniform partition sizes typically perform better in terms of relaxation solution quality and convergence behavior. It was also seen that there is a limit on the number of partitions that contribute to relaxation tightness, which does not necessarily correspond to a larger number of partitions, while a direct relationship between relaxation size and tightness does not always hold for non-uniform partition sizes.

Refrigeration systems are complex, non-linear, multi-modal, and multi-dimensional. However, traditional methods are based on a trial and error process to optimize these systems, and a global optimum operating point cannot be guaranteed. Therefore, this work aims to study a two-stage vapor compression refrigeration system (VCRS) through a novel and robust hybrid multi-objective grey wolf optimizer (HMOGWO) algorithm. The system is modeled using response surface methods (RSM) to investigate the impacts of design variables on the set responses. Firstly, the interaction between the system components and their cycle behavior is analyzed by building four surrogate models using RSM. The model fit statistics indicate that they are statistically significant and agree with the design data. Three conflicting scenarios in bi-objective optimization are built focusing on the overall system following the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) decision-making methods. The optimal solutions indicate that for the first to third scenarios, the exergetic efficiency (EE) and capital expenditure (CAPEX) are optimized by 33.4% and 7.5%, and the EE and operational expenditure (OPEX) are improved by 27.4% and 19.0%. The EE and global warming potential (GWP) are also optimized by 27.2% and 19.1%, where the proposed HMOGWO outperforms the MOGWO and NSGA-II. Finally, the K-means clustering technique is applied for Pareto characterization. Based on the research outcomes, the combined RSM and HMOGWO techniques have proved an excellent solution to simulate and optimize two-stage VCRS.

Refinery planning optimization is a challenging problem as regards handling the nonconvex bilinearity mainly due to pooling operations in processes such as crude oil distillation and product blending. This work investigates the performance of several representative piecewise-linear (or piecewise-affine) relaxation schemes (referred to as McCormick, bm, nf5, nf6t, and de (which is a new approach proposed based on eigenvector decomposition) that mainly give rise to mixed-integer optimization programs to convexify a bilinear term using predetermined univariate partitioning for instances of uniform and non-uniform partition sizes. Computational results show that applying these schemes give improved relaxation tightness than only applying convex and concave envelopes as estimators. Uniform partition sizes typically perform better in terms of relaxation solution quality and convergence behavior. It is also seen that there is a limit on the number of partitions that contributes to relaxation tightness, which does not necessarily correspond to a larger number of partitions, while a direct relation between relaxation size and tightness does not always hold for non-uniform partition sizes.