Pyomo.GDP: an ecosystem for logic based modeling and optimization development

Chen, Qi; Johnson, Emma S.; Bernal, David E.; Valentin, Romeo; Kale, Sunjeev; Bates, J. P.; Siirola, John Daniel; Grossmann, Ignacio E.

doi:10.1007/s11081-021-09601-7

Cited by 26 publications

(24 citation statements)

References 48 publications

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“…Modeling extensions that allow for disjunctive programming are the natural place to include these automatic reformulations. Approaches have been made at the modeling language level, e.g., in GAMS [75] Pyomo [40] 4 , and Julia 5 . These could also be made at the solver level, with indicator constraints such as in CPLEX [32] and MOSEK [15].…”

Section: Conclusion Discussion and Future Workmentioning

confidence: 99%

“…Moreover, conic programming tools can be used in more advanced solution methods of GDP than the recasting of the problem into MINLP. Examples of those methods are Lagrangean decomposition based on the disjunctive structure of the problem [70] or logic-based algorithms [40]. The use of conic programming has already shown the potential speedup for mixed-integer programming solutions [24], and expanding those findings to GDP is of great interest.…”

Section: Conclusion Discussion and Future Workmentioning

confidence: 99%

“…We encounter the Logic-based Branch & Bound (LBB) and the Logic-based Outer-Approximation (LOA) among these tailored algorithms. For more information on general GDP algorithms, refer to [40].…”

Section: Generalized Disjunctive Programmingmentioning

confidence: 99%

“…In this setting, sets of constraints are activated with logical variables linked to each other by logical constraints, including disjunctions. This mathematical description of the problem can be tackled directly by logicbased optimization methods [40], which generalize mixed-integer solution methods to the logical domain. Another way of solving these problems is through reformulations into mixed-integer programs, where the logical variables are mapped to binary or indicator variables.…”

Section: Introductionmentioning

confidence: 99%

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Convex Mixed-Integer Nonlinear Programs Derived from Generalized Disjunctive Programming using Cones

Grossmann¹

2021

Preprint

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We propose the formulation of convex Generalized Disjunctive Programming (GDP) problems using conic inequalities leading to conic GDP problems. We then show the reformulation of conic GDPs into Mixed-Integer Conic Programming (MICP) problems through both the Big-M and Hull Reformulations. These reformulations have the advantage that they are representable using the same cones as the original conic GDP. In the case of HR, they require no approximation of the perspective function. Moreover, the MICP problems derived can be solved by specialized conic solvers and offer a natural extended formulation amenable to both conic and gradient-based solvers. We present the closed-form of several convex functions and their respective perspectives in conic sets, allowing users to easily formulate their conic GDP problems. We finally implement a large set of conic GDP examples and solve them via the traditional and conic mixed-integer reformulations. These examples include applications from Process Systems Engineering, Machine learning, and randomly generated instances. Our results show that the conic structure can be exploited to solve these challenging MICP problems more efficiently.

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Section: Conclusion Discussion and Future Workmentioning

confidence: 99%

Section: Conclusion Discussion and Future Workmentioning

confidence: 99%

Section: Generalized Disjunctive Programmingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Convex Mixed-Integer Nonlinear Programs Derived from Generalized Disjunctive Programming using Cones

Grossmann¹

2021

Preprint

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“…The main CPAIOR result, that P -split formulations form a hierarchy in terms of relaxation strength, was only shown for a two-term disjunction with a single constraint per disjunct [33]. The formulations for this case were recently implemented as a plugin in Pyomo.GDP [17] 1 . Here, we extend the results to general disjunctions with multiple constraints and multiple disjunctive terms.…”

Section: Introductionmentioning

confidence: 99%

P-split formulations: A class of intermediate formulations between big-M and convex hull for disjunctive constraints

Kronqvist¹,

Martin-Misener²,

Tsay³

2022

Preprint

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We develop a class of mixed-integer formulations for disjunctive constraints intermediate to the big-M and convex hull formulations in terms of relaxation strength. The main idea is to capture the best of both the big-M and convex hull formulations: a computationally light formulation with a tight relaxation. The "P -split" formulations are based on a lifted transformation that splits convex additively separable constraints into P partitions and forms the convex hull of the linearized and partitioned disjunction. We analyze the continuous relaxation of the P -split formulations and show that, under certain assumptions, the formulations form a hierarchy starting from a big-M equivalent and converging to the convex hull. The goal of the P -split formulations is to form a strong approximation of the convex hull through a computationally simpler formulation. We computationally compare the P -split formulations against big-M and convex hull formulations on 320 test instances. The test problems include K-means clustering, P_ball problems, and optimization over trained ReLU neural networks. The computational results show promising potential of the P -split formulations. For many of the test problems, P -split formulations are solved with a similar number of explored nodes as the convex hull formulation, while reducing the solution time by an order of magnitude and outperforming big-M both in time and number of explored nodes.

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Homotopy continuation enhanced branch and bound algorithms for strongly nonconvex mixed‐integer nonlinear optimization

2022

AIChE Journal

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Large‐scale strongly nonlinear and nonconvex mixed‐integer nonlinear programming (MINLP) models frequently appear in optimization‐based process synthesis, integration, intensification, and process control. However, they are usually difficult to solve by existing algorithms within acceptable time. In this study, we propose two robust homotopy continuation enhanced branch and bound (HCBB) algorithms (denoted as HCBB‐FP and HCBB‐RB) where the homotopy continuation method is employed to gradually approach the optimum of the NLP subproblem at a node from the solution at its parent node. A variable step length is adapted to effectively balance feasibility and computational efficiency. The computational results from solving four existing process synthesis problems demonstrate that the proposed HCBB algorithms can find the same optimal solution from different initial points, while the existing MINLP algorithms fail or find much worse solutions. In addition, HCBB‐RB is superior to HCBB‐FP due to much lower computational effort required for the same locally optimal solution.

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Pyomo.GDP: an ecosystem for logic based modeling and optimization development

Cited by 26 publications

References 48 publications

Convex Mixed-Integer Nonlinear Programs Derived from Generalized Disjunctive Programming using Cones

Convex Mixed-Integer Nonlinear Programs Derived from Generalized Disjunctive Programming using Cones

P-split formulations: A class of intermediate formulations between big-M and convex hull for disjunctive constraints

Homotopy continuation enhanced branch and bound algorithms for strongly nonconvex mixed‐integer nonlinear optimization

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