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Shmuel Onn - One of the best experts on this subject based on the ideXlab platform.
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Parameterized shifted Combinatorial Optimization
Journal of Computer and System Sciences, 2019Co-Authors: Jakub Gajarský, Martin Koutecký, Petr Hliněný, Shmuel OnnAbstract:Abstract Shifted Combinatorial Optimization is a new nonlinear Optimization framework broadly extending standard Combinatorial Optimization, involving the choice of several feasible solutions simultaneously. This framework captures well studied and diverse problems, from sharing and partitioning to so-called vulnerability problems. In particular, every standard Combinatorial Optimization problem has its shifted counterpart, typically harder. Already with explicitly given input set SCO may be NP -hard. Here we initiate a study of the parameterized complexity of this framework. First we show that SCO over an explicitly given set parameterized by its cardinality may be in XP , FPT or P , depending on the objective function. Second, we study SCO over sets definable in MSO logic (which includes, e.g., the well known MSO-partitioning problems). Our main results are that SCO over MSO definable sets is in XP parameterized by the MSO formula and treewidth (or clique-width) of the input graph, and W [1] -hard even under further severe restrictions.
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COCOON - Parameterized Shifted Combinatorial Optimization
Lecture Notes in Computer Science, 2017Co-Authors: Jakub Gajarský, Martin Koutecký, Petr Hliněný, Shmuel OnnAbstract:Shifted Combinatorial Optimization is a new nonlinear Optimization framework which is a broad extension of standard Combinatorial Optimization, involving the choice of several feasible solutions at a time. This framework captures well studied and diverse problems ranging from so-called vulnerability problems to sharing and partitioning problems. In particular, every standard Combinatorial Optimization problem has its shifted counterpart, which is typically much harder. Already with explicitly given input set the shifted problem may be NP-hard. In this article we initiate a study of the parameterized complexity of this framework. First we show that shifting over an explicitly given set with its cardinality as the parameter may be in XP, FPT or P, depending on the objective function. Second, we study the shifted problem over sets definable in MSO logic (which includes, e.g., the well known MSO partitioning problems). Our main results here are that shifted Combinatorial Optimization over MSO definable sets is in XP with respect to the MSO formula and the treewidth (or more generally clique-width) of the input graph, and is W[1]-hard even under further severe restrictions.
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Approximate Shifted Combinatorial Optimization.
arXiv: Optimization and Control, 2017Co-Authors: Martin Koutecký, Asaf Levin, Syed Mohammad Meesum, Shmuel OnnAbstract:Shifted Combinatorial Optimization is a new nonlinear Optimization framework, which is a broad extension of standard Combinatorial Optimization, involving the choice of several feasible solutions at a time. It captures well studied and diverse problems ranging from congestive to partitioning problems. In particular, every standard Combinatorial Optimization problem has its shifted counterpart, which is typically much harder. Here we initiate a study of approximation algorithms for this broad Optimization framework.
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Parameterized Shifted Combinatorial Optimization
arXiv: Computational Complexity, 2017Co-Authors: Jakub Gajarský, Martin Koutecký, Petr Hliněný, Shmuel OnnAbstract:Shifted Combinatorial Optimization is a new nonlinear Optimization framework which is a broad extension of standard Combinatorial Optimization, involving the choice of several feasible solutions at a time. This framework captures well studied and diverse problems ranging from so-called vulnerability problems to sharing and partitioning problems. In particular, every standard Combinatorial Optimization problem has its shifted counterpart, which is typically much harder. Already with explicitly given input set the shifted problem may be NP-hard. In this article we initiate a study of the parameterized complexity of this framework. First we show that shifting over an explicitly given set with its cardinality as the parameter may be in XP, FPT or P, depending on the objective function. Second, we study the shifted problem over sets definable in MSO logic (which includes, e.g., the well known MSO partitioning problems). Our main results here are that shifted Combinatorial Optimization over MSO definable sets is in XP with respect to the MSO formula and the treewidth (or more generally clique-width) of the input graph, and is W[1]-hard even under further severe restrictions.
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Convex Combinatorial Optimization
Discrete and Computational Geometry, 2004Co-Authors: Shmuel Onn, Uriel G. RothblumAbstract:We introduce the convex Combinatorial Optimization problem, a far-reaching generalization of the standard linear Combinatorial Optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and discuss several applications.
Samy Bengio - One of the best experts on this subject based on the ideXlab platform.
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neural Combinatorial Optimization with reinforcement learning
International Conference on Learning Representations, 2017Co-Authors: Irwan Bello, Hieu Pham, Quoc V Le, Mohammad Norouzi, Samy BengioAbstract:This paper presents a framework to tackle Combinatorial Optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent neural network that, given a set of city coordinates, predicts a distribution over different city permutations. Using negative tour length as the reward signal, we optimize the parameters of the recurrent neural network using a policy gradient method. We compare learning the network parameters on a set of training graphs against learning them on individual test graphs. Without much engineering and heuristic designing, Neural Combinatorial Optimization achieves close to optimal results on 2D Euclidean graphs with up to 100 nodes. Applied to the KnapSack, another NP-hard problem, the same method obtains optimal solutions for instances with up to 200 items. These results, albeit still far from state-of-the-art, give insights into how neural networks can be used as a general tool for tackling Combinatorial Optimization problems.
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neural Combinatorial Optimization with reinforcement learning
arXiv: Artificial Intelligence, 2016Co-Authors: Irwan Bello, Hieu Pham, Quoc V Le, Mohammad Norouzi, Samy BengioAbstract:This paper presents a framework to tackle Combinatorial Optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city coordinates, predicts a distribution over different city permutations. Using negative tour length as the reward signal, we optimize the parameters of the recurrent network using a policy gradient method. We compare learning the network parameters on a set of training graphs against learning them on individual test graphs. Despite the computational expense, without much engineering and heuristic designing, Neural Combinatorial Optimization achieves close to optimal results on 2D Euclidean graphs with up to 100 nodes. Applied to the KnapSack, another NP-hard problem, the same method obtains optimal solutions for instances with up to 200 items.
Irwan Bello - One of the best experts on this subject based on the ideXlab platform.
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neural Combinatorial Optimization with reinforcement learning
International Conference on Learning Representations, 2017Co-Authors: Irwan Bello, Hieu Pham, Quoc V Le, Mohammad Norouzi, Samy BengioAbstract:This paper presents a framework to tackle Combinatorial Optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent neural network that, given a set of city coordinates, predicts a distribution over different city permutations. Using negative tour length as the reward signal, we optimize the parameters of the recurrent neural network using a policy gradient method. We compare learning the network parameters on a set of training graphs against learning them on individual test graphs. Without much engineering and heuristic designing, Neural Combinatorial Optimization achieves close to optimal results on 2D Euclidean graphs with up to 100 nodes. Applied to the KnapSack, another NP-hard problem, the same method obtains optimal solutions for instances with up to 200 items. These results, albeit still far from state-of-the-art, give insights into how neural networks can be used as a general tool for tackling Combinatorial Optimization problems.
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neural Combinatorial Optimization with reinforcement learning
arXiv: Artificial Intelligence, 2016Co-Authors: Irwan Bello, Hieu Pham, Quoc V Le, Mohammad Norouzi, Samy BengioAbstract:This paper presents a framework to tackle Combinatorial Optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city coordinates, predicts a distribution over different city permutations. Using negative tour length as the reward signal, we optimize the parameters of the recurrent network using a policy gradient method. We compare learning the network parameters on a set of training graphs against learning them on individual test graphs. Despite the computational expense, without much engineering and heuristic designing, Neural Combinatorial Optimization achieves close to optimal results on 2D Euclidean graphs with up to 100 nodes. Applied to the KnapSack, another NP-hard problem, the same method obtains optimal solutions for instances with up to 200 items.
Roliandrea - One of the best experts on this subject based on the ideXlab platform.
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Hybrid metaheuristics in Combinatorial Optimization
Applied Soft Computing, 2011Co-Authors: Blumchristian, Puchingerjakob, R Raidlgünther, RoliandreaAbstract:Research in metaheuristics for Combinatorial Optimization problems has lately experienced a noteworthy shift towards the hybridization of metaheuristics with other techniques for Optimization. At t...
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Metaheuristics in Combinatorial Optimization
ACM Computing Surveys, 2003Co-Authors: Blumchristian, RoliandreaAbstract:The field of metaheuristics for the application to Combinatorial Optimization problems is a rapidly growing field of research. This is due to the importance of Combinatorial Optimization problems f...
Martin Koutecký - One of the best experts on this subject based on the ideXlab platform.
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Parameterized shifted Combinatorial Optimization
Journal of Computer and System Sciences, 2019Co-Authors: Jakub Gajarský, Martin Koutecký, Petr Hliněný, Shmuel OnnAbstract:Abstract Shifted Combinatorial Optimization is a new nonlinear Optimization framework broadly extending standard Combinatorial Optimization, involving the choice of several feasible solutions simultaneously. This framework captures well studied and diverse problems, from sharing and partitioning to so-called vulnerability problems. In particular, every standard Combinatorial Optimization problem has its shifted counterpart, typically harder. Already with explicitly given input set SCO may be NP -hard. Here we initiate a study of the parameterized complexity of this framework. First we show that SCO over an explicitly given set parameterized by its cardinality may be in XP , FPT or P , depending on the objective function. Second, we study SCO over sets definable in MSO logic (which includes, e.g., the well known MSO-partitioning problems). Our main results are that SCO over MSO definable sets is in XP parameterized by the MSO formula and treewidth (or clique-width) of the input graph, and W [1] -hard even under further severe restrictions.
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COCOON - Parameterized Shifted Combinatorial Optimization
Lecture Notes in Computer Science, 2017Co-Authors: Jakub Gajarský, Martin Koutecký, Petr Hliněný, Shmuel OnnAbstract:Shifted Combinatorial Optimization is a new nonlinear Optimization framework which is a broad extension of standard Combinatorial Optimization, involving the choice of several feasible solutions at a time. This framework captures well studied and diverse problems ranging from so-called vulnerability problems to sharing and partitioning problems. In particular, every standard Combinatorial Optimization problem has its shifted counterpart, which is typically much harder. Already with explicitly given input set the shifted problem may be NP-hard. In this article we initiate a study of the parameterized complexity of this framework. First we show that shifting over an explicitly given set with its cardinality as the parameter may be in XP, FPT or P, depending on the objective function. Second, we study the shifted problem over sets definable in MSO logic (which includes, e.g., the well known MSO partitioning problems). Our main results here are that shifted Combinatorial Optimization over MSO definable sets is in XP with respect to the MSO formula and the treewidth (or more generally clique-width) of the input graph, and is W[1]-hard even under further severe restrictions.
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Approximate Shifted Combinatorial Optimization.
arXiv: Optimization and Control, 2017Co-Authors: Martin Koutecký, Asaf Levin, Syed Mohammad Meesum, Shmuel OnnAbstract:Shifted Combinatorial Optimization is a new nonlinear Optimization framework, which is a broad extension of standard Combinatorial Optimization, involving the choice of several feasible solutions at a time. It captures well studied and diverse problems ranging from congestive to partitioning problems. In particular, every standard Combinatorial Optimization problem has its shifted counterpart, which is typically much harder. Here we initiate a study of approximation algorithms for this broad Optimization framework.
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Parameterized Shifted Combinatorial Optimization
arXiv: Computational Complexity, 2017Co-Authors: Jakub Gajarský, Martin Koutecký, Petr Hliněný, Shmuel OnnAbstract:Shifted Combinatorial Optimization is a new nonlinear Optimization framework which is a broad extension of standard Combinatorial Optimization, involving the choice of several feasible solutions at a time. This framework captures well studied and diverse problems ranging from so-called vulnerability problems to sharing and partitioning problems. In particular, every standard Combinatorial Optimization problem has its shifted counterpart, which is typically much harder. Already with explicitly given input set the shifted problem may be NP-hard. In this article we initiate a study of the parameterized complexity of this framework. First we show that shifting over an explicitly given set with its cardinality as the parameter may be in XP, FPT or P, depending on the objective function. Second, we study the shifted problem over sets definable in MSO logic (which includes, e.g., the well known MSO partitioning problems). Our main results here are that shifted Combinatorial Optimization over MSO definable sets is in XP with respect to the MSO formula and the treewidth (or more generally clique-width) of the input graph, and is W[1]-hard even under further severe restrictions.
