Certification of an optimal TSP tour through 85,900 cities

Applegate, David; Bixby, Robert E.; Chvátal, V.; Cook, William J.; Espinoza, Daniel; Goycoolea, Marcos; Helsgaun, Keld

doi:10.1016/j.orl.2008.09.006

Cited by 137 publications

(77 citation statements)

References 13 publications

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“…Several polynomial-time heuristic methods with upper bounds on performance have been proposed since to approximately solve the TSP, including nearest neighbor, nearest insertion, furthest insertion [42], Christofides heuristic [43], and LK heuristic (see [44] for a comprehensive overview of methods). Currently, the largest TSP instance solved to optimality comprises nearly 86,000 cities [45].…”

Section: Traveling Salesman Problem (Tsp)mentioning

confidence: 99%

Efficient Visualization of Large-Scale Data Tables through Reordering and Entropy Minimization

Djuric

Vučetić

2013

2013 IEEE 13th International Conference on Data Mining

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Abstract-Visualization of data tables with n examples and m columns using heatmaps provides a holistic view of the original data. As there are n! ways to order rows and m! ways to order columns, and data tables are typically ordered without regard to visual inspection, heatmaps of the original data tables often appear as noisy images. However, if rows and columns of a data table are ordered such that similar rows and similar columns are grouped together, a heatmap may provide a deep insight into the underlying data distribution. We propose an informationtheoretic approach to produce a well-ordered data table. In particular, we search for ordering that minimizes entropy of residuals of predictive coding applied on the ordered data table. This formalization leads to a novel ordering procedure, EMordering, that can be applied separately on rows and columns. For ordering of rows, EM-ordering repeats until convergence the steps of (1) rescaling columns and (2) solving a Traveling Salesman Problem (TSP) where rows are treated as cities. To allow fast ordering of large data tables, we propose an efficient TSP heuristic with modest O n log(n) time complexity. When compared to the existing state-of-the-art reordering approaches, we show that the method often provides heatmaps of higher visual quality, while being significantly more scalable. Moreover, analysis of real-world traffic and financial data sets using the proposed method, which allowed us to readily gain deeper insights about the data, further confirmed that EM-ordering can be a valuable tool for visual exploration of large-scale data sets.

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Section: Traveling Salesman Problem (Tsp)mentioning

confidence: 99%

Efficient Visualization of Large-Scale Data Tables through Reordering and Entropy Minimization

Djuric

Vučetić

2013

2013 IEEE 13th International Conference on Data Mining

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“…Helsgaun (Helsgaun 2009 andApplegate et al 2009) has developed extremely effective approaches for solving the traveling salesman problem with as many as 10,000,000 nodes and has demonstrated that his computationally efficient procedure has found a solution to these very large traveling saleman problems that is within .02% of the optimal solution.…”

Section: Traveling Salesman Problemmentioning

confidence: 99%

Vacation Model

2013

Encyclopedia of Operations Research and Management Science

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“…Despite important work in this problem, cutting plane techniques to date are still limited in terms of the instance sizes that can effectively be tackled computationally. This is a problem, because if there is any hope of being able to solve large integer programming formulations of PCKP generalizations, such as those that appear in the context of open pit mining, cutting planes are likely to play an important role as they have in solving other large combinatorial optimization problems [2,3].…”

Section: Introductionmentioning

confidence: 99%

The precedence constrained knapsack problem: Separating maximally violated inequalities

Espinoza

Goycoolea

Moreno

2015

Discrete Applied Mathematics

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We consider the problem of separating maximally violated inequalities for the precedence constrained knapsack problem. Though we consider maximally violated constraints in general, special emphasis is placed on induced cover inequalities and induced clique inequalities. Our contributions include a new partial characterization of maximally violated inequalities, a new safe shrinking technique, and new insights on strengthening and lifting. This work follows on the work of Boyd (1993), Park and Park (1997), van de Leesel et al (1999) and Boland et al (2011).

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Certification of an optimal TSP tour through 85,900 cities

Abstract: a b s t r a c tWe describe a computer code and data that together certify the optimality of a solution to the 85,900-city traveling salesman problem pla85900, the largest instance in the TSPLIB collection of challenge problems.

Cited by 137 publications

References 13 publications

Efficient Visualization of Large-Scale Data Tables through Reordering and Entropy Minimization

Efficient Visualization of Large-Scale Data Tables through Reordering and Entropy Minimization

Vacation Model

The precedence constrained knapsack problem: Separating maximally violated inequalities

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