Solving Large Scale Optimization Problems in the Transportation Industry and Beyond Through Column Generation

Xu, Yanqi

doi:10.1007/978-3-030-28565-4_23

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…While the worst-case number of rules can be huge with high-dimensional data, we show that our problem can be solved efficiently via column generation (CG). CG has been successful in solving large-scale discrete optimization models in many domains including vehicle routing (Chen and Xu 2006), crew scheduling (Subramanian and Sherali 2008;Bront, Méndez-Díaz, and Vulcano 2009), and supply chain management, among others (Xu 2019). Utilizing large-scale optimization techniques for MIP-based ODTs has been attempted previously.…”

Section: Related Literaturementioning

confidence: 99%

Scalable Optimal Multiway-Split Decision Trees with Constraints

Subramanian¹,

Sun²

2023

AAAI

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There has been a surge of interest in learning optimal decision trees using mixed-integer programs (MIP) in recent years, as heuristic-based methods do not guarantee optimality and find it challenging to incorporate constraints that are critical for many practical applications. However, existing MIP methods that build on an arc-based formulation do not scale well as the number of binary variables is in the order of 2 to the power of the depth of the tree and the size of the dataset. Moreover, they can only handle sample-level constraints and linear metrics. In this paper, we propose a novel path-based MIP formulation where the number of decision variables is independent of dataset size. We present a scalable column generation framework to solve the MIP. Our framework produces a multiway-split tree which is more interpretable than the typical binary-split trees due to its shorter rules. Our framework is more general as it can handle nonlinear metrics such as F1 score, and incorporate a broader class of constraints. We demonstrate its efficacy with extensive experiments. We present results on datasets containing up to 1,008,372 samples while existing MIP-based decision tree models do not scale well on data beyond a few thousand points. We report superior or competitive results compared to the state-of-art MIP-based methods with up to a 24X reduction in runtime.

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Section: Related Literaturementioning

confidence: 99%

Scalable Optimal Multiway-Split Decision Trees with Constraints

Subramanian¹,

Sun²

2023

AAAI

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“…2) Instead of an arc-based formulation, we present a path-based MIP formulation to construct the tree, which allows us to model constraints naturally and solve the problem efficiently via column generation (CG). CG has been successfully adopted by the AI community (e.g., Bach 2008; Jawanpuria, Nath, and Ramakrishnan 2011) and in practice to solve complex discrete optimization models including airline scheduling (Klabjan et al 2002;Subramanian and Sherali 2008;Bront, Méndez-Díaz, and Vulcano 2009), vehicle routing (Chen and Xu 2006), and inventory planning for supply chain, among others (Desaulniers, Desrosiers, and Solomon 2006;Xu 2019).…”

Section: Related Literaturementioning

confidence: 99%

Constrained Prescriptive Trees via Column Generation

Subramanian¹,

Sun²,

Drissi³

et al. 2022

AAAI

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With the abundance of available data, many enterprises seek to implement data-driven prescriptive analytics to help them make informed decisions. These prescriptive policies need to satisfy operational constraints, and proactively eliminate rule conflicts, both of which are ubiquitous in practice. It is also desirable for them to be simple and interpretable, so they can be easily verified and implemented. Existing approaches from the literature center around constructing variants of prescriptive decision trees to generate interpretable policies. However, none of the existing methods is able to handle constraints. In this paper, we propose a scalable method that solves the constrained prescriptive policy generation problem. We introduce a novel path-based mixed-integer program (MIP) formulation which identifies a (near) optimal policy efficiently via column generation. The policy generated can be represented as a multiway-split tree which is more interpretable and informative than binary-split trees due to its shorter rules. We demonstrate the efficacy of our method with extensive computational experiments on both synthetic and real datasets.

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Solving Large Scale Optimization Problems in the Transportation Industry and Beyond Through Column Generation

Cited by 2 publications

References 15 publications

Scalable Optimal Multiway-Split Decision Trees with Constraints

Scalable Optimal Multiway-Split Decision Trees with Constraints

Constrained Prescriptive Trees via Column Generation

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