On the P-formulation and the split-fraction-formulation for the generalized pooling problem

Cheng, Xin; Li, Xiang

doi:10.1016/j.compchemeng.2022.107893

Cited by 4 publications

(3 citation statements)

References 25 publications

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“…36,38,47 However, there is no known theoretical result comparing the relaxations of P-and S-formulations, and no formulation is clearly faster than another. For pooling problems, Cheng and Li 48 established conditions under which the S-formulation's relaxation is not tighter than the P-formulation's relaxation. Whether their conclusions can be extended to the MBSP requires further investigation.…”

Section: Introductionmentioning

confidence: 99%

“…Compared to their property-tracking counterparts, the P- and S-formulations with certain established tightening constraints have at least as tight relaxations and are in general superior in practice. ,, However, there is no known theoretical result comparing the relaxations of P- and S-formulations, and no formulation is clearly faster than another. For pooling problems, Cheng and Li established conditions under which the S-formulation’s relaxation is not tighter than the P-formulation’s relaxation. Whether their conclusions can be extended to the MBSP requires further investigation.…”

Section: Introductionmentioning

confidence: 99%

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Linear Programming-Based Preprocessing Algorithm and Tightening Constraints for Multiperiod Blend Scheduling Problems

Song,

Maravelias

2024

Ind. Eng. Chem. Res.

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The multiperiod blend scheduling problem has a wide variety of engineering applications and is typically formulated as a nonconvex mixed-integer nonlinear program (MINLP). Such an MINLP is challenging to solve due to a large number of bilinear terms and binary variables. One prevalent solution method is branch and bound, whose efficiency heavily relies on the tightness of the convex relaxation of the MINLP. In this article, we propose new constraints that can be used for tightening such convex relaxation. These constraints are derived from the physical information lost due to relaxation and require solving linear programs during preprocessing. Extensive numerical tests are executed to examine the effectiveness of the proposed methods. The results show that even though hundreds of linear programs may be solved during preprocessing, our new methods can significantly reduce the overall computational time, including both the preprocessing and MINLP solver solution time. Further implications are discussed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Linear Programming-Based Preprocessing Algorithm and Tightening Constraints for Multiperiod Blend Scheduling Problems

Song,

Maravelias

2024

Ind. Eng. Chem. Res.

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“…In water networks, we observe the opposite behavior, , with the formulation with total flows and concentrations, closely related to the p-formulation of the pooling problem, performing better than the one using split fractions . Recently, stronger, multicommodity flow formulations − have been proposed for the generalized pooling problem and wastewater treatment networks . The tightening procedure often involves adding linear constraints that are redundant in the original space, including the well-known McCormick envelopes, and is known as reformulation linearization technique (RLT) …”

Section: Introductionmentioning

confidence: 99%

Global Optimization of QCPs Using MIP Relaxations with a Base-2 Logarithmic Partitioning Scheme

Castro

2023

Ind. Eng. Chem. Res.

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Several problems of interest to Process Systems Engineering can be formulated as nonconvex quadratically constrained programs (QCPs). These are challenging to solve to global optimality due to the existence of many local optimal solutions and the difficulty of computing a tight dual bound. Although recent research has shown that mixed-integer programming (MIP) relaxations of the bilinear terms in the constraints can play an important role addressing this challenge, because they take considerably more time to solve than their linear programming counterparts, state-of-the art commercial solvers have found limited use for them. We now propose a global optimization algorithm relying extensively on MIP relaxations, for reducing the variable domain through optimality-based bound tightening and improving the dual bound. MIP relaxations are derived from the multiparametric disaggregation technique, using a logarithmic partitioning scheme to ensure tractability and base-2 to minimize the jump in complexity when increasing the number of intervals in the partition for a subset of the bilinear variables. Major improvements are achieved doing this sequentially, with refinements occurring within a spatial branch and bound procedure. Using a set of 54 benchmark instances from the literature, we show that the new algorithm significantly outperforms GUROBI 9.5.2 and BARON 22.7.23, in terms of optimality gap at termination (reduction up to four orders of magnitude), and number of problems solved.

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A strong P-formulation for global optimization of industrial water-using and treatment networks

Cheng,

2024

J Glob Optim

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On the P-formulation and the split-fraction-formulation for the generalized pooling problem

Cited by 4 publications

References 25 publications

Linear Programming-Based Preprocessing Algorithm and Tightening Constraints for Multiperiod Blend Scheduling Problems

Linear Programming-Based Preprocessing Algorithm and Tightening Constraints for Multiperiod Blend Scheduling Problems

Global Optimization of QCPs Using MIP Relaxations with a Base-2 Logarithmic Partitioning Scheme

A strong P-formulation for global optimization of industrial water-using and treatment networks

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