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Journal articles on the topic 'Algorithmes Branch-And-Cut'

Author: Grafiati

Published: 7 September 2024

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1

Fragoso, Felipe C., Gilberto F. de Sousa Filho, and Fábio Protti. "Declawing a graph: polyhedra and Branch-and-Cut algorithms." Journal of Combinatorial Optimization 42, no. 1 (April 19, 2021): 85–124. http://dx.doi.org/10.1007/s10878-021-00736-y.

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2

Costa, Luciano, Claudio Contardo, and Guy Desaulniers. "Exact Branch-Price-and-Cut Algorithms for Vehicle Routing." Transportation Science 53, no. 4 (July 2019): 946–85. http://dx.doi.org/10.1287/trsc.2018.0878.

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3

Pereira, Dilson Lucas, Michel Gendreau, and Alexandre Salles da Cunha. "Branch-and-cut and Branch-and-cut-and-price algorithms for the adjacent only quadratic minimum spanning tree problem." Networks 65, no. 4 (February 2, 2015): 367–79. http://dx.doi.org/10.1002/net.21580.

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4

Fouilhoux, Pierre, A. Ridha Mahjoub, Alain Quilliot, and Hélène Toussaint. "Branch-and-Cut-and-Price algorithms for the preemptive RCPSP." RAIRO - Operations Research 52, no. 2 (April 2018): 513–28. http://dx.doi.org/10.1051/ro/2018031.

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In this article, we address the preemptive Resource-Constrained Precedence Scheduling Problem. We propose two mixed integer formulations containing an exponential number of variables and inequalities. An antichain is a set of pairwise incomparable elements with respect to the precedence constraints. In the first formulation, the integer variables are associated with the antichains. For the second, the integer variables are limited to a particular subset of antichains. We propose two Branch-and-Cut-and-Price algorithms for each of these formulations. We introduce some valid inequalities in order to reinforce the second formulation. Finally, we give some computational results on instances of the PSPLIB and compare the formulations.

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5

Calvete, Herminia I., Concepción Domínguez, Carmen Galé, Martine Labbé, and Alfredo Marín. "The rank pricing problem: Models and branch-and-cut algorithms." Computers & Operations Research 105 (May 2019): 12–31. http://dx.doi.org/10.1016/j.cor.2018.12.011.

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6

Li, Xiangyong, and Y. P. Aneja. "Regenerator location problem: Polyhedral study and effective branch-and-cut algorithms." European Journal of Operational Research 257, no. 1 (February 2017): 25–40. http://dx.doi.org/10.1016/j.ejor.2016.07.032.

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7

Duchenne, Éric, Gilbert Laporte, and Frédéric Semet. "Branch-and-cut algorithms for the undirected m-Peripatetic Salesman Problem." European Journal of Operational Research 162, no. 3 (May 2005): 700–712. http://dx.doi.org/10.1016/j.ejor.2003.09.024.

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8

Archetti, Claudia, Nicola Bianchessi, and M. Grazia Speranza. "Branch-and-cut algorithms for the split delivery vehicle routing problem." European Journal of Operational Research 238, no. 3 (November 2014): 685–98. http://dx.doi.org/10.1016/j.ejor.2014.04.026.

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9

Desaulniers, Guy, Diego Pecin, and Claudio Contardo. "Selective pricing in branch-price-and-cut algorithms for vehicle routing." EURO Journal on Transportation and Logistics 8, no. 2 (June 2019): 147–68. http://dx.doi.org/10.1007/s13676-017-0112-9.

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10

Di Summa, Marco, Andrea Grosso, and Marco Locatelli. "Branch and cut algorithms for detecting critical nodes in undirected graphs." Computational Optimization and Applications 53, no. 3 (February 9, 2012): 649–80. http://dx.doi.org/10.1007/s10589-012-9458-y.

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11

Bektaş, Tolga, Güneş Erdoğan, and Stefan Røpke. "Formulations and Branch-and-Cut Algorithms for the Generalized Vehicle Routing Problem." Transportation Science 45, no. 3 (August 2011): 299–316. http://dx.doi.org/10.1287/trsc.1100.0352.

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12

Hintsch, Timo, Stefan Irnich, and Lone Kiilerich. "Branch-Price-and-Cut for the Soft-Clustered Capacitated Arc-Routing Problem." Transportation Science 55, no. 3 (May 2021): 687–705. http://dx.doi.org/10.1287/trsc.2020.1036.

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The soft-clustered capacitated arc-routing problem (SoftCluCARP) is a variant of the classical capacitated arc-routing problem. The only additional constraint is that the set of required edges, that is, the streets to be serviced, is partitioned into clusters, and feasible routes must respect the soft-cluster constraint, that is, all required edges of the same cluster must be served by the same vehicle. In this article, we design an effective branch-price-and-cut algorithm for the exact solution of the SoftCluCARP. Its new components are a metaheuristic and branch-and-cut-based solvers for the solution of the column-generation subproblem, which is a profitable rural clustered postman tour problem. Although postman problems with these characteristics have been studied before, there is one fundamental difference here: clusters are not necessarily vertex-disjoint, which prohibits many preprocessing and modeling approaches for clustered postman problems from the literature. We present an undirected and a windy formulation for the pricing subproblem and develop and computationally compare two corresponding branch-and-cut algorithms. Cutting is also performed at the master-program level using subset-row inequalities for subsets of size up to five. For the first time, these nonrobust cuts are incorporated into MIP-based routing subproblem solvers using two different modeling approaches. In several computational studies, we calibrate the individual algorithmic components. The final computational experiments prove that the branch-price-and-cut algorithm equipped with these problem-tailored components is effective: The largest SoftCluCARP instances solved to optimality have more than 150 required edges or more than 50 clusters.

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13

Munapo, Elias, Joshua Chukwuere, and Trust Tawanda. "Solving Linear Integer Models with Variable Bounding." Forecasting 5, no. 2 (May 5, 2023): 443–52. http://dx.doi.org/10.3390/forecast5020024.

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We present a technique to solve the linear integer model with variable bounding. By using the continuous optimal solution of the linear integer model, the variable bounds for the basic variables are approximated and then used to calculate the optimal integer solution. With the variable bounds of the basic variables known, solving a linear integer model is easier by using either the branch and bound, branch and cut, branch and price, branch cut and price, or branch cut and free algorithms. Thus, the search for large numbers of subproblems, which are unnecessary and common for NP Complete linear integer models, is avoided.

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14

Adulyasak, Yossiri, Jean-François Cordeau, and Raf Jans. "Formulations and Branch-and-Cut Algorithms for Multivehicle Production and Inventory Routing Problems." INFORMS Journal on Computing 26, no. 1 (February 2014): 103–20. http://dx.doi.org/10.1287/ijoc.2013.0550.

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15

Qiu, Yuzhuo, Liang Wang, Xuanjing Fang, Panos M. Pardalos, and Boris Goldengorin. "Formulations and branch-and-cut algorithms for production routing problems with time windows." Transportmetrica A: Transport Science 14, no. 8 (January 26, 2018): 669–90. http://dx.doi.org/10.1080/23249935.2018.1427157.

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16

Gadegaard, Sune Lauth, Lars Relund Nielsen, and Matthias Ehrgott. "Bi-objective Branch-and-Cut Algorithms Based on LP Relaxation and Bound Sets." INFORMS Journal on Computing 31, no. 4 (October 2019): 790–804. http://dx.doi.org/10.1287/ijoc.2018.0846.

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17

Andreas, April K., J. Cole Smith, and Simge Küçükyavuz. "Branch-and-price-and-cut algorithms for solving the reliable h-paths problem." Journal of Global Optimization 42, no. 4 (October 30, 2007): 443–66. http://dx.doi.org/10.1007/s10898-007-9254-x.

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18

Drexl, Michael. "Branch-and-cut algorithms for the vehicle routing problem with trailers and transshipments." Networks 63, no. 1 (September 20, 2013): 119–33. http://dx.doi.org/10.1002/net.21526.

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19

Saharidis, Georgios K. D. "Review of Solution Approaches for the Symmetric Traveling Salesman Problem." International Journal of Information Systems and Supply Chain Management 7, no. 1 (January 2014): 73–87. http://dx.doi.org/10.4018/ijisscm.2014010105.

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In this paper, the main known exact and heuristic solution approaches and algorithms for the symmetric Traveling Salesman Problem (TSP), published after 1992, are surveyed. The paper categorize the most important existing algorithm to 6 main groups: i) Genetic algorithms, ii) Ant colony methods, iii) Neural Methods, iv) Local search algorithms and Tabu search, v) Lagrangian methods and vi) Branch and bound and branch & cut algorithms.

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20

Christof, T., and G. Reinelt. "Algorithmic Aspects of Using Small Instance Relaxations in Parallel Branch-and-Cut." Algorithmica 30, no. 4 (October 1, 2001): 597–629. http://dx.doi.org/10.1007/s00453-001-0029-3.

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21

Rebennack, Steffen, Gerhard Reinelt, and Panos M. Pardalos. "A tutorial on branch and cut algorithms for the maximum stable set problem." International Transactions in Operational Research 19, no. 1-2 (January 2012): 161–99. http://dx.doi.org/10.1111/j.1475-3995.2011.00805.x.

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22

Ropke, Stefan, Jean-François Cordeau, and Gilbert Laporte. "Models and branch-and-cut algorithms for pickup and delivery problems with time windows." Networks 49, no. 4 (2007): 258–72. http://dx.doi.org/10.1002/net.20177.

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23

Guimarães, Dilson Almeida, and Alexandre Salles da Cunha. "The minimum area spanning tree problem: Formulations, Benders decomposition and branch-and-cut algorithms." Computational Geometry 97 (August 2021): 101771. http://dx.doi.org/10.1016/j.comgeo.2021.101771.

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24

Bicalho, Luis Henrique, Alexandre Salles da Cunha, and Abilio Lucena. "Branch-and-cut-and-price algorithms for the Degree Constrained Minimum Spanning Tree Problem." Computational Optimization and Applications 63, no. 3 (September 14, 2015): 755–92. http://dx.doi.org/10.1007/s10589-015-9788-7.

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25

Wu, Hao, Hao Wen, and Yushan Zhu. "Branch-and-Cut Algorithmic Framework for 0−1 Mixed-Integer Convex Nonlinear Programs." Industrial & Engineering Chemistry Research 48, no. 20 (October 21, 2009): 9119–27. http://dx.doi.org/10.1021/ie9001074.

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26

Gouveia, Luis, Markus Leitner, and Mario Ruthmair. "Extended formulations and branch-and-cut algorithms for the Black-and-White Traveling Salesman Problem." European Journal of Operational Research 262, no. 3 (November 2017): 908–28. http://dx.doi.org/10.1016/j.ejor.2017.04.061.

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27

Ibrahim, Abdullahi, Jeremiah Ishaya, Rabiat Abdulaziz, and Sowole Samuel. "Solving some variants of vehicle routing problem with Branch-and-cut and Column generation algorithms." Open Journal of Mathematical Sciences 4, no. 1 (March 8, 2020): 63–73. http://dx.doi.org/10.30538/oms2020.0095.

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28

Gendron, Bernard, Abilio Lucena, Alexandre Salles da Cunha, and Luidi Simonetti. "Benders Decomposition, Branch-and-Cut, and Hybrid Algorithms for the Minimum Connected Dominating Set Problem." INFORMS Journal on Computing 26, no. 4 (November 2014): 645–57. http://dx.doi.org/10.1287/ijoc.2013.0589.

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29

Pessoa, Artur Alves, Michael Poss, Ruslan Sadykov, and François Vanderbeck. "Branch-Cut-and-Price for the Robust Capacitated Vehicle Routing Problem with Knapsack Uncertainty." Operations Research 69, no. 3 (May 2021): 739–54. http://dx.doi.org/10.1287/opre.2020.2035.

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Capacitated vehicle routing problems are widely studied combinatorial optimization problems, and branch-and-cut-and-price algorithms can solve instances harder than ever before. These models, however, neglect that demands volumes are often not known with precision when planning the vehicle routes, thus incentivizing decision makers to significantly overestimate the volumes for avoiding coping with infeasible routes. A robust formulation that models demand uncertainty through a knapsack polytope is considered. A new branch-and-cut-and-price algorithm for the problem is provided, which combines efficient algorithms for the problem with no uncertainty with profound results in robust combinatorial optimization and includes novel heuristics and new valid inequalities. The numerical results illustrate that the resulting approach is two orders of magnitude faster that the best algorithm from the literature, solving twice as many instances to optimality.

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30

He, Wei, Yiyuan Cheng, Ling Xia, and Feng Liu. "A New Particle Swarm Optimization-Based Method for Phase Unwrapping of MRI Data." Computational and Mathematical Methods in Medicine 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/475745.

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A new method based on discrete particle swarm optimization (dPSO) algorithm is proposed to solve the branch-cut phase unwrapping problem of MRI data. In this method, the optimal order of matching the positive residues with the negative residues is first identified by the dPSO algorithm, then the branch cuts are placed to join each pair of the opposite polarity residues, and in the last step phases are unwrapped by flood-fill algorithm. The performance of the proposed algorithm was tested on both simulated phase image and MRI wrapped phase data sets. The results demonstrated that, compared with conventionally used branch-cut phase unwrapping algorithms, the dPSO algorithm is rather robust and effective.

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31

J�nger, Michael, and Stefan Thienel. "The ABACUS system for branch-and-cut-and-price algorithms in integer programming and combinatorial optimization." Software: Practice and Experience 30, no. 11 (2000): 1325–52. http://dx.doi.org/10.1002/1097-024x(200009)30:11<1325::aid-spe342>3.0.co;2-t.

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32

Chwatal, Andreas M., and Günther R. Raidl. "Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques." Advances in Operations Research 2011 (2011): 1–38. http://dx.doi.org/10.1155/2011/143732.

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We present exact mixed integer programming approaches including branch-and-cut and branch-and-cut-and-price for the minimum label spanning tree problem as well as a variant of it having multiple labels assigned to each edge. We compare formulations based on network flows and directed connectivity cuts. Further, we show how to use odd-hole inequalities and additional inequalities to strengthen the formulation. Label variables can be added dynamically to the model in the pricing step. Primal heuristics are incorporated into the framework to speed up the overall solution process. After a polyhedral comparison of the involved formulations, comprehensive computational experiments are presented in order to compare and evaluate the underlying formulations and the particular algorithmic building blocks of the overall branch-and-cut- (and-price) framework.

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33

Timofeeva, A. Yu, and Yu A. Mezentsev. "Forecasting using predictor selection from a large set of highly correlated variables." Information Technology and Nanotechnology, no. 2416 (2019): 10–18. http://dx.doi.org/10.18287/1613-0073-2019-2416-10-18.

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The potential of correlation-based feature selection has been explored in selecting an optimal subset from a set of highly correlated predictors. This problem occurs, for example, in time series forecasting of economic indicators using regression models on multiple lags of a large number of candidate leading indicators. Greedy algorithms (forward selection and backward elimination) in such cases fail. To obtain the globally optimal solution, the feature selection problem is formulated as a mixed integer programming problem. To solve it, we use the binary cut-and-branch method. The results of simulation studies demonstrate the advantage of using the binary cut-and-branch method in comparison with heuristic search algorithms. The real example of the selection of leading indicators of consumer price index growth shows the acceptability of using the correlation-based feature selection method.

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34

Rostami, Borzou, Guy Desaulniers, Fausto Errico, and Andrea Lodi. "Branch-Price-and-Cut Algorithms for the Vehicle Routing Problem with Stochastic and Correlated Travel Times." Operations Research 69, no. 2 (March 2021): 436–55. http://dx.doi.org/10.1287/opre.2020.2037.

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35

Kobeaga, Gorka, María Merino, and Jose A. Lozano. "On solving cycle problems with Branch-and-Cut: extending shrinking and exact subcycle elimination separation algorithms." Annals of Operations Research 305, no. 1-2 (August 3, 2021): 107–36. http://dx.doi.org/10.1007/s10479-021-04210-0.

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36

Armbruster, Michael, Marzena Fügenschuh, Christoph Helmberg, and Alexander Martin. "LP and SDP branch-and-cut algorithms for the minimum graph bisection problem: a computational comparison." Mathematical Programming Computation 4, no. 3 (April 15, 2012): 275–306. http://dx.doi.org/10.1007/s12532-012-0040-5.

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37

Cherkesly, Marilène, Guy Desaulniers, Stefan Irnich, and Gilbert Laporte. "Branch-price-and-cut algorithms for the pickup and delivery problem with time windows and multiple stacks." European Journal of Operational Research 250, no. 3 (May 2016): 782–93. http://dx.doi.org/10.1016/j.ejor.2015.10.046.

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38

Costa, Alysson M., Jean-François Cordeau, and Gilbert Laporte. "Models and branch-and-cut algorithms for the Steiner tree problem with revenues, budget and hop constraints." Networks 53, no. 2 (December 17, 2008): 141–59. http://dx.doi.org/10.1002/net.20274.

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39

Desaulniers, Guy, Timo Gschwind, and Stefan Irnich. "Variable Fixing for Two-Arc Sequences in Branch-Price-and-Cut Algorithms on Path-Based Models." Transportation Science 54, no. 5 (September 2020): 1170–88. http://dx.doi.org/10.1287/trsc.2020.0988.

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Variable fixing by reduced costs is a popular technique for accelerating the solution process of mixed-integer linear programs. For vehicle-routing problems solved by branch-price-and-cut algorithms, it is possible to fix to zero the variables associated with all routes containing at least one arc from a subset of arcs determined according to the dual solution of a linear relaxation. This is equivalent to removing these arcs from the network used to generate the routes. In this paper, we extend this technique to routes containing sequences of two arcs. Such sequences or their arcs cannot be removed directly from the network because routes traversing only one arc of a sequence might still be allowed. For some of the most common vehicle-routing problems, we show how this issue can be overcome by modifying the route-generation labeling algorithm in order to remove indirectly these sequences from the network. The proposed acceleration strategy is tested on benchmark instances of the vehicle-routing problem with time windows (VRPTW) and four variants of the electric VRPTW. The computational results show that it yields a significant speedup, especially for the most difficult instances.

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40

Ishida, Yusuke, Yuki Kato, Liang Zhao, Hiroshi Nagamochi, and Tatsuya Akutsu. "Branch-and-Bound Algorithms for Enumerating Treelike Chemical Graphs with Given Path Frequency Using Detachment-Cut." Journal of Chemical Information and Modeling 50, no. 5 (April 26, 2010): 934–46. http://dx.doi.org/10.1021/ci900447z.

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41

Rahmani, Arsalan, and Majid Yousefikhoshbakht. "An Effective Branch-and-cut algorithm in Order to Solve the Mixed Integer Bi-level Programming." International Journal of Production Management and Engineering 5, no. 1 (January 31, 2017): 1. http://dx.doi.org/10.4995/ijpme.2017.6512.

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<p>In this paper, a new branch-and-cut algorithm for mixed integer bi-level programming is proposed. For achieving this purpose, a historical perspective of the development of enumeration methods in the field of bi-level linear programming is considered. Then, we present some obstacles for using branch and bound method based on them, and an algorithm is developed to solve for mixed integer bi-level problem. Finally, we use a preference function to determine the choice of branching and specialized cuts in a branch and cut tree. Computational results are reported and compared favorably to those of previous methods and then implications discussed. The results show that not only the proposed algorithm can find high quality solutions for solving a number of the problems, but also it is competitive with other famous published algorithms.</p>

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42

De Oliveira, Willy Alves, and Maristela Oliveira dos Santos. "A New Branching Rule to Solve the Capacitated Lot Sizing and Scheduling Problem with Sequence Dependent Setups." TEMA (São Carlos) 18, no. 3 (January 10, 2018): 515. http://dx.doi.org/10.5540/tema.2017.018.03.515.

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In this paper, we deal with the Capacitated Lot Sizing and Scheduling Problem with sequencedependent setup times and costs - CLSD model. More specifically, we propose a simple reformulation for the CLSD model that enables us to define a new branching rule to be used in Branch-and-Bound (or Branch-and-Cut) algorithms to solve this NP-hard problem. Our branching rule can be easily implemented in commercial solvers. Computational tests performed in 240 test instances from the literature show that our approach can significantly reduce the running time to solve this problem using a Branch-and-Cut algorithm of a commercial MIP solver.Therefore, our approach can also improve the performance of other approaches that need to solve partial sub problems of the CLSD model in each iteration, such as Lagrangian approaches and heuristics based on the mathematical formulation of the problem.

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43

Qiu, Yuzhuo, Liang Wang, Xiaoling Xu, Xuanjing Fang, and Panos M. Pardalos. "Formulations and branch-and-cut algorithms for multi-product multi-vehicle production routing problems with startup cost." Expert Systems with Applications 98 (May 2018): 1–10. http://dx.doi.org/10.1016/j.eswa.2018.01.006.

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44

Pereira, Dilson Lucas, and Alexandre Salles da Cunha. "Polyhedral results, branch-and-cut and Lagrangian relaxation algorithms for the adjacent only quadratic minimum spanning tree problem." Networks 71, no. 1 (October 31, 2017): 31–50. http://dx.doi.org/10.1002/net.21787.

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45

Vakhania, Nodari, and Frank Werner. "Branch Less, Cut More and Schedule Jobs with Release and Delivery Times on Uniform Machines." Mathematics 9, no. 6 (March 16, 2021): 633. http://dx.doi.org/10.3390/math9060633.

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We consider the problem of scheduling n jobs with identical processing times and given release as well as delivery times on m uniform machines. The goal is to minimize the makespan, i.e., the maximum full completion time of any job. This problem is well-known to have an open complexity status even if the number of jobs is fixed. We present a polynomial-time algorithm for the problem which is based on the earlier introduced algorithmic framework blesscmore (“branch less and cut more”). We extend the analysis of the so-called behavior alternatives developed earlier for the version of the problem with identical parallel machines and show how the earlier used technique for identical machines can be extended to the uniform machine environment if a special condition on the job parameters is imposed. The time complexity of the proposed algorithm is O(γm2nlogn), where γ can be either n or the maximum job delivery time qmax. This complexity can even be reduced further by using a smaller number κ<n in the estimation describing the number of jobs of particular types. However, this number κ becomes only known when the algorithm has terminated.

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46

Hashemi Doulabi, Hossein, Gilles Pesant, and Louis-Martin Rousseau. "Vehicle Routing Problems with Synchronized Visits and Stochastic Travel and Service Times: Applications in Healthcare." Transportation Science 54, no. 4 (July 2020): 1053–72. http://dx.doi.org/10.1287/trsc.2019.0956.

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This paper, for the first time, studies vehicle routing problems with synchronized visits (VRPS) and stochastic travel and service times. In addition to considering a home healthcare scheduling problem, we introduce an operating room scheduling problem with stochastic durations as a novel application of VRPS. We formulate VRPS with stochastic times as a two-stage stochastic integer programming model that, unlike the deterministic models in the VRPS literature, does not have any big-M constraints. This advantage comes at the cost of a large number of second-stage integer variables. We prove that the integrality constraints on second-stage variables can be relaxed, and therefore, we can apply the L-shaped algorithm and its branch-and-cut implementation to solve the problem. We enhance the model by developing valid inequalities and a lower bounding functional. We analyze the subproblems of the L-shaped algorithm and devise a specialized algorithm for them that is significantly faster than standard linear programming algorithms. Computational results show that the branch-and-cut algorithm optimally solves stochastic home healthcare scheduling instances with 15 patients and 10%–30% of synchronized visits. It also finds solutions with an average optimality gap of 3.57% for instances with 20 patients. Furthermore, the branch-and-cut algorithm optimally solves stochastic operating room scheduling problems with 20 surgeries.

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47

Bouzarth, Elizabeth L., Richard J. Forrester, Kevin R. Hutson, Rahul Isaac, James Midkiff, Danny Rivers, and Leonard J. Testa. "A Comparison of Algorithms for Finding an Efficient Theme Park Tour." Journal of Applied Mathematics 2018 (October 16, 2018): 1–14. http://dx.doi.org/10.1155/2018/2453185.

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The problem of efficiently touring a theme park so as to minimize the amount of time spent in queues is an instance of the Traveling Salesman Problem with Time-Dependent Service Times (TSP-TS). In this paper, we present a mixed-integer linear programming formulation of the TSP-TS and describe a branch-and-cut algorithm based on this model. In addition, we develop a lower bound for the TSP-TS and describe two metaheuristic approaches for obtaining good quality solutions: a genetic algorithm and a tabu search algorithm. Using test instances motivated by actual theme park data, we conduct a computational study to compare the effectiveness of our algorithms.

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48

Cherkesly, Marilène, Guy Desaulniers, and Gilbert Laporte. "Branch-Price-and-Cut Algorithms for the Pickup and Delivery Problem with Time Windows and Last-in-First-Out Loading." Transportation Science 49, no. 4 (November 2015): 752–66. http://dx.doi.org/10.1287/trsc.2014.0535.

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49

Przybylski, Maciej. "AD*-Cut: A Search-Tree Cutting Anytime Dynamic A* Algorithm." Proceedings of the International Conference on Automated Planning and Scheduling 28 (June 15, 2018): 494–99. http://dx.doi.org/10.1609/icaps.v28i1.13925.

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This paper presents a new anytime incremental search algorithm, AD*-Cut. AD*-Cut is based on two algorithms, namely, Anytime Repairing A* (ARA*) and the novel incremental search algorithm, D* Extra Lite. D* Extra Lite reinitializes (cuts) entire search-tree branches that have been affected by changes in an environment, and D* Extra Lite appears to be quicker than the reinitialization during the search utilized by the popular incremental search algorithm, D* Lite. The search-tree branch cutting is a simple and robust technique that can be easily applied to ARA*. Consequently, AD*-Cut extends D* Extra Lite in the same manner, as the state-of-the-art Anytime D* (AD*) algorithm extends D* Lite. The benchmark results suggest that AD*-Cut is quicker and achieves shorter paths than AD* when used for path planning on 3D state-lattices (a 2D position with rotation).

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Jin, Mingming, Jiongzhi Zheng, and Kun He. "KD-Club: An Efficient Exact Algorithm with New Coloring-Based Upper Bound for the Maximum k-Defective Clique Problem." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 18 (March 24, 2024): 20735–42. http://dx.doi.org/10.1609/aaai.v38i18.30061.

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Abstract:

The Maximum k-Defective Clique Problem (MDCP) aims to find a maximum k-defective clique in a given graph, where a k-defective clique is a relaxation clique missing at most k edges. MDCP is NP-hard and finds many real-world applications in analyzing dense but not necessarily complete subgraphs. Exact algorithms for MDCP mainly follow the Branch-and-bound (BnB) framework, whose performance heavily depends on the quality of the upper bound on the cardinality of a maximum k-defective clique. The state-of-the-art BnB MDCP algorithms calculate the upper bound quickly but conservatively as they ignore many possible missing edges. In this paper, we propose a novel CoLoring-based Upper Bound (CLUB) that uses graph coloring techniques to detect independent sets so as to detect missing edges ignored by the previous methods. We then develop a new BnB algorithm for MDCP, called KD-Club, using CLUB in both the preprocessing stage for graph reduction and the BnB searching process for branch pruning. Extensive experiments show that KD-Club significantly outperforms state-of-the-art BnB MDCP algorithms on the number of solved instances within the cut-off time, having much smaller search tree and shorter solving time on various benchmarks.

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