Preprocessing algorithm and tightening constraints for multiperiod blend scheduling: cost minimization

Chen, Yifu; Maravelias, Christos T.

doi:10.1007/s10898-020-00882-3

Cited by 10 publications

(8 citation statements)

References 38 publications

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“…Similar tightening constraints were proposed by Chen and Maravelias . For each ( p , q ) ∈ P × Q , they define sets of good streams in terms of π p , q L and π p , q U as follows .25ex2ex S p , q normalL , normalg ≔ { s ∈ S : π p , q normalL ≤ π s , q } S p , q normalU , normalg ≔ { s ∈ S : π s , q ≤ π p , q normalU } and similarly, sets of bad streams are defined as .25ex2ex S p , q normalL , normalb ≔ { s ∈ S : π p , q normalL > π s , q } S…”

Section: New Tightening Constraintsmentioning

confidence: 99%

“…Constructing these constraints typically requires solving LP problems, leading to an LP-based preprocessing algorithm. Notably, the new constraints are guaranteed to dominate some previously proposed constraints . While our new tightening constraints are intended to facilitate solving MINLP via branch-and-bound algorithms, they are also useful in tightening bounding in certain decomposition-based global optimization approaches. ,,, …”

Section: Introductionmentioning

confidence: 99%

“…The multiperiod blend scheduling problem (MBSP) , is a scheduling extension of the (generalized) pooling problem and considers blending raw materials with different qualities to produce products, meeting property specifications, over a given scheduling horizon. The objective of the MBSP is to find the least cost blending plan (or maximize profit), subject to various constraints such as raw material availability, operational rules, and product demand requirements.…”

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: New Tightening Constraintsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Song,

Maravelias

2024

Ind. Eng. Chem. Res.

Self Cite

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“…28,29 To make relaxations tight, it is important to rely on preprocessing procedures that reduce the domain of the model variables. These can be suited to a specific problem, 30 or be general in nature, like with optimality-based bound tightening (OBBT). 31,32 The rest of the paper is structured as follows.…”

Section: Introductionmentioning

confidence: 99%

“…Such binary variables may be used to account for multiple periods of operation, as can be seen in the alternative formulations for the multiperiod blending problem. , To make relaxations tight, it is important to rely on preprocessing procedures that reduce the domain of the model variables. These can be suited to a specific problem, or be general in nature, like with optimality-based bound tightening (OBBT). , …”

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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Comparison of mixed-integer relaxations with linear and logarithmic partitioning schemes for quadratically constrained problems

2021

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Preprocessing algorithm and tightening constraints for multiperiod blend scheduling: cost minimization

Cited by 10 publications

References 38 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

Comparison of mixed-integer relaxations with linear and logarithmic partitioning schemes for quadratically constrained problems

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