Abstract
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.
Highlights
Accepted: 27 June 2021Optimization or mathematical programming models and tools are widely used in the strategic and tactical planning of petroleum refinery operations
Experiments decision variables with 42 nonlinear terms and 61 constraints, as summarized in Table 2, is. This as section presents our computational experimental results to investigate the perprovided Supporting formance of several representative piecewise linear relaxation methods applied to nonconvex bilinear terms in the foregoing refinery planning
We present our computational experimental results to investigate the performance of several representative piecewise linear relaxation methods applied to nonconvex bilinear terms in the foregoing refinery planning NLP model
Summary
Accepted: 27 June 2021Optimization or mathematical programming models and tools are widely used in the strategic and tactical planning of petroleum refinery operations. It is deemed inappropriate to use rigorous planning models [4] if they are not able to adequately represent the intended process details that possibly involve nonconvex nonlinearity toward obtaining globally optimal solutions [5], whose features likely vary from one plant to another [6,7]. In this regard, there is an interest in refineries developing their own planning models [8], but which necessitate customizing solution strategies rather than relying on off-the-shelf solvers, to handle the presence of nonconvexity. A chief interest is to improve the operational representation of crude distillation units (CDUs), which is the main refining process to separate crude oil mixtures into different fractions
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