Fairness and the set of optimal rankings for the linear ordering problem

Anderson, Paul E.; Chartier, Timothy P.; Langville, Amy N.; Pedings-Behling, Kathryn E.

doi:10.1007/s11081-021-09650-y

Cited by 7 publications

(3 citation statements)

References 14 publications

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“…Particularly, the LOP is a permutation problem that, in 1979, was proven to be NP-hard by Garey and Johnson. Since then, and due to its applicability in fields such as machine translation [35], economics [36], corruption perception [37] and rankings in sports or other tournaments [38], [39], the LOP has gained popularity and it is easy to find a wide variety of works that have dealt with it [40].…”

Section: Case Study: Linear Ordering Problemmentioning

confidence: 99%

Neural Combinatorial Optimization: a New Player in the Field

Garmendia¹,

Ceberio²,

Mendiburu³

2022

Preprint

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Neural Combinatorial Optimization attempts to learn good heuristics for solving a set of problems using Neural Network models and Reinforcement Learning. Recently, its good performance has encouraged many practitioners to develop neural architectures for a wide variety of combinatorial problems. However, the incorporation of such algorithms in the conventional optimization framework has raised many questions related to their performance and the experimental comparison with other methods such as exact algorithms, heuristics and metaheuristics. This paper presents a critical analysis on the incorporation of algorithms based on neural networks into the classical combinatorial optimization framework. Subsequently, a comprehensive study is carried out to analyse the fundamental aspects of such algorithms, including performance, transferability, computational cost and generalization to larger-sized instances. To that end, we select the Linear Ordering Problem as a case of study, an NP-hard problem, and develop a Neural Combinatorial Optimization model to optimize it. Finally, we discuss how the analysed aspects apply to a general learning framework, and suggest new directions for future work in the area of Neural Combinatorial Optimization algorithms.

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Section: Case Study: Linear Ordering Problemmentioning

confidence: 99%

Neural Combinatorial Optimization: a New Player in the Field

Garmendia¹,

Ceberio²,

Mendiburu³

2022

Preprint

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show abstract

“…Dark points within the region are most robust, i.e., least sensitive, to small changes in the weights λ i . + : λ 1 + λ 2 + λ 3 + λ 4 = 1} is a hyperplane in 4 . We can visualize the contribution of weights in 3 with a polytope.…”

Section: Theorem 33 (Bound On Cuts) At Most Nmentioning

confidence: 99%

“…Anderson et al defined the rankability of pairwise ranking data as its ability to produced a meaningful ranking of its items [2]. In subsequent papers, they link rankability to the cardinality of the set P of multiple optimal rankings [3,4,6]. Thus, this paper's set A of aggregated rankings is related to their set P .…”

Section: Introductionmentioning

confidence: 99%

Weight Set Decomposition for Weighted Rank Aggregation: An interpretable and visual decision support tool

Perini¹,

Langville²,

Kramer³

et al. 2022

Preprint

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The problem of interpreting or aggregating multiple rankings is common to many real-world applications. Perhaps the simplest and most common approach is a weighted rank aggregation, wherein a (convex) weight is applied to each input ranking and then ordered. This paper describes a new tool for visualizing and displaying ranking information for the weighted rank aggregation method. Traditionally, the aim of rank aggregation is to summarize the information from the input rankings and provide one final ranking that hopefully represents a more accurate or truthful result than any one input ranking. While such an aggregated ranking is, and clearly has been, useful to many applications, it also obscures information. In this paper, we show the wealth of information that is available for the weighted rank aggregation problem due to its structure. We apply weight set decomposition to the set of convex multipliers, study the properties useful for understanding this decomposition, and visualize the indifference regions. This methodology reveals information-that is otherwise collapsed by the aggregated ranking-into a useful, interpretable, and intuitive decision support tool. Included are multiple illustrative examples, along with heuristic and exact algorithms for computing the weight set decomposition.

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A linear ordering problem with weighted rank

Vieira

2024

J Comb Optim

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Fairness and the set of optimal rankings for the linear ordering problem

Cited by 7 publications

References 14 publications

Neural Combinatorial Optimization: a New Player in the Field

Neural Combinatorial Optimization: a New Player in the Field

Weight Set Decomposition for Weighted Rank Aggregation: An interpretable and visual decision support tool

A linear ordering problem with weighted rank

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