Improved quadratic cuts for convex mixed-integer nonlinear programs

Su, Lijie; Tang, Lixin; Bernal, David E.; Grossmann, Ignacio E.

doi:10.1016/j.compchemeng.2017.10.011

Cited by 17 publications

(4 citation statements)

References 26 publications

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“…In B&B methods (Dakin, 1965; Quesada and Grossmann, 1992; Leyffer, 2001), integer relaxed convex subproblems are solved in each node of a B&B tree. The decomposition methods ECP (Westerlund and Pettersson, 1995), ESH (Kronqvist et al., 2016), and OA (Duran and Grossmann, 1986; Su et al., 2018; Coey et al., 2020; Muts et al., 2020; De Mauri et al., 2020) exploit the properties of convex MINLPs to derive linearizations of nonlinear constraints based on their gradients. These linearizations are equivalent to first‐order Taylor expansions of nonlinear inequalities.…”

Section: Related Literaturementioning

confidence: 99%

Fill‐rate service level constrained distribution network design

Escalona

Angulo

Brotcorne

et al. 2023

Int Trans Operational Res

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The design of distribution networks that simultaneously consider location and inventory decisions seeks to balance costs and product availability. The most commonly observed measure of product availability in practical settings is the fill‐rate service level. However, the optimal design of a distribution network that considers the fill rate to control shortages of fast‐moving consumer goods (FMCG) is considered intractable and has only been addressed by heuristic methods. This paper addresses the optimal design of a distribution network for FMCG able to provide high fill‐rate service level under a continuous review policy. Considering the exact formulation for the provided fill rate, we formulated a joint location–inventory model with fill‐rate service level constraints as a convex mixed integer nonlinear problem for which a novel decomposition‐based outer approximation algorithm is proposed. Numerical experiments have shown that our solution approach provides good‐quality solutions that are on average 0.15% and, at worst, 2.2% from the optimal solution.

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Section: Related Literaturementioning

confidence: 99%

Fill‐rate service level constrained distribution network design

Escalona

Angulo

Brotcorne

et al. 2023

Int Trans Operational Res

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“…L-OA algorithm could be viewed as an extension of normal outer approximation algorithm which is one of the most common methods of MINLP problems. More details of OA algorithm could be found in (Duran and Grossmann, 1986) and (Su et al, 2018).…”

Section: Logic-based Outer Approximation Algorithmmentioning

confidence: 99%

Optimal plate design problem in steel production

Zhao

Meng

et al. 2022

International Journal of Production Research

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In this paper, we address a new optimal plate design problem in steel production, in which slab selection is jointly considered. On the basis of the underlying features, the problem is formulated as a mixed integer nonlinear programming (MINLP) model with generalized disjunctive programming (GDP) constraints. A logic-based outer approximation (L-OA) algorithm is proposed to solve the problem. Specifically, a two-stage heuristic method is designed to initialize the L-OA algorithm. Numerical results are presented to demonstrate that the proposed L-OA algorithm and the heuristic method are effective and computationally efficient.

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“…The OA algorithm also uses a similar approach of iteratively solving problem (3) and generating new linearization points by solving an NLP subproblem [16,20]. Techniques for utilizing quadratic approximations within an OA framework have also been presented in [35,65]. If a polyhedral approximation technique is combined with convexification procedures and spatial branch and bound, then it can also be employed as a deterministic global optimization technique [69].…”

Section: Polyhedral Approximationmentioning

confidence: 99%

Polyhedral approximation strategies for nonconvex mixed-integer nonlinear programming in SHOT

Lundell

Kronqvist

2021

J Glob Optim

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Different versions of polyhedral outer approximation are used by many algorithms for mixed-integer nonlinear programming (MINLP). While it has been demonstrated that such methods work well for convex MINLP, extending them to solve nonconvex problems has traditionally been challenging. The Supporting Hyperplane Optimization Toolkit (SHOT) is a solver based on polyhedral approximations of the nonlinear feasible set of MINLP problems. SHOT is an open source COIN-OR project, and is currently one of the most efficient global solvers for convex MINLP. In this paper, we discuss some extensions to SHOT that significantly extend its applicability to nonconvex problems. The functionality include utilizing convexity detection for selecting the nonlinearities to linearize, lifting reformulations for special classes of functions, feasibility relaxations for infeasible subproblems and adding objective cuts to force the search for better feasible solutions. This functionality is not unique to SHOT, but can be implemented in other similar methods as well. In addition to discussing the new nonconvex functionality of SHOT, an extensive benchmark of deterministic solvers for nonconvex MINLP is performed that provides a snapshot of the current state of nonconvex MINLP.

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Improved quadratic cuts for convex mixed-integer nonlinear programs

Cited by 17 publications

References 26 publications

Fill‐rate service level constrained distribution network design

Fill‐rate service level constrained distribution network design

Optimal plate design problem in steel production

Polyhedral approximation strategies for nonconvex mixed-integer nonlinear programming in SHOT

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