New limits of treewidth-based tractability in optimization

Faenza, Yuri; Muñoz, Gonzalo; Pokutta, Sebastian

doi:10.1007/s10107-020-01563-5

Cited by 4 publications

(2 citation statements)

References 58 publications

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“…The relevance of graph representations of general optimization problems has long been recognized and, as discussed in Bienstock and Muñoz (2018) and Faenza et al (2022), polynomial optimization problems are not an exception. Our interest on these graphs is twofold: first, as a means to define new branching rules and, second, to define features that can be taken as input by the learning process.…”

Section: Graphs Associated To Polynomial Optimization Problemsmentioning

confidence: 99%

Learning for Spatial Branching: An Algorithm Selection Approach

Ghaddar¹,

Ignacio²,

González‐Díaz³

et al. 2022

Preprint

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The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To bridge this gap, we develop a learning framework for spatial branching and show its efficacy in the context of the Reformulation-Linearization Technique for polynomial optimization problems. The proposed learning is performed offline, based on instance-specific features and with no computational overhead when solving new instances. Novel graph-based features are introduced, which turn out to play an important role for the learning. Experiments on different benchmark instances from the literature show that the learning-based branching rule significantly outperforms the standard rules.

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Section: Graphs Associated To Polynomial Optimization Problemsmentioning

confidence: 99%

Learning for Spatial Branching: An Algorithm Selection Approach

Ghaddar¹,

Ignacio²,

González‐Díaz³

et al. 2022

Preprint

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“…The existence of polynomial-time algorithms for NP-hard problems given that some graph related to the problem has bounded treewidth is common in the combinatorial optimization community (e.g.,, Jagabathula and Rusmevichientong 2019, Faenza et al 2020). …”

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confidence: 99%

Traceability Technology Adoption in Supply Chain Networks

Blaettchen¹,

Calmon

Hall

2021

SSRN Journal

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Modern traceability technologies promise to improve supply chain management by simplifying recalls, increasing demand visibility, or ascertaining sustainable supplier practices. Managers in the traceability initiatives developing such technologies face a difficult question: which companies should they target as early adopters to ensure that their technology is broadly employed? To answer this question, managers must consider that supply chains are interlinked in complex networks and that a supply chain effect is inherent to traceability technologies. More specifically, the benefits obtained from traceability are conditional on technology adoption throughout a product's supply chain.We introduce a model of the dynamics of traceability technology adoption in supply chain networks to tackle the problem of selecting the smallest set of early adopters guaranteeing broad dissemination. Our model builds on extant diffusion models while incorporating that a firm's adoption decision depends on previous adoption decisions throughout its supply chains. We show that the problem is NP-hard and that no approximation within a polylogarithmic factor can be guaranteed for any polynomial-time algorithm.Nevertheless, we introduce an algorithm that identifies an exact solution in polynomial time under certain assumptions on the network structure and provide evidence that it is tractable for real-world supply chain networks. We further propose a random generative model that outputs networks consistent with real-world supply chain networks. The networks obtained display, whp, structures that allow us to find the optimal seed set in subexponential time using our algorithm. Our generative model also provides approximate seed sets when information on the network is limited.

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