Topological Sort

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Qing Zhou - One of the best experts on this subject based on the ideXlab platform.

  • Optimizing Regularized Cholesky Score for Order-Based Learning of Bayesian Networks
    IEEE Transactions on Pattern Analysis and Machine Intelligence, 1
    Co-Authors: Qiaoling Ye, Arash Amini, Qing Zhou
    Abstract:

    Bayesian networks are a class of popular graphical models that encode causal and conditional independence relations among variables by directed acyclic graphs (DAGs). We propose a novel structure learning method, annealing on regularized Cholesky score (ARCS), to search over Topological Sorts, or permutations of nodes, for a high-scoring Bayesian network. Our scoring function is derived from regularizing Gaussian DAG likelihood, and its optimization gives an alternative formulation of the sparse Cholesky factorization problem from a statistical viewpoint. We combine simulated annealing over permutation space with a fast proximal gradient algorithm, operating on triangular matrices of edge coefficients, to compute the score of any permutation. Combined, the two approaches allow us to quickly and effectively search over the space of DAGs without the need to verify the acyclicity constraint or to enumerate possible parent sets given a candidate Topological Sort. Through extensive numerical comparisons, we show that ARCS outperformed existing methods by a substantial margin, demonstrating its great advantage in structure learning of Bayesian networks from both observational and experimental data. We also establish the consistency of our scoring function in estimating Topological Sorts and DAG structures in the large-sample limit. Source code of ARCS is available at https://github.com/yeqiaoling/arcs_bn.

Chiung Moon - One of the best experts on this subject based on the ideXlab platform.

  • integrated process planning and scheduling in a supply chain
    Computers & Industrial Engineering, 2008
    Co-Authors: Chiung Moon, Young Hae Lee, Chan Seok Jeong, Youngsu Yun
    Abstract:

    This paper deals with the integration of process planning and scheduling, which is one of the most important functions in a supply chain to achieve high quality products at lower cost, lower inventory, and high level of performance. Solving the problem is essential for the generation of flexible process sequences with resource selection and for the decision of the operation schedules that can minimize makespan. We formulate a mixed integer programming model to solve this problem of integration. This model considers alternative resources: sequences and precedence constraints. To solve the model, we develop a new evolutionary search approach based on a Topological Sort. We use the Topological Sort to generate a set of feasible sequences in the model within a reasonable computing time. Since precedence constraints between operations are handled by the Topological Sort, the developed evolutionary search approach produces only feasible solutions. The experimental results using various sizes of problems provide a way to demonstrate the efficiency of the developed evolutionary search approach.

  • evolutionary algorithm based on Topological Sort for precedence constrained sequencing
    Congress on Evolutionary Computation, 2007
    Co-Authors: Chiung Moon, Youngsu Yun, Choonseong Leem
    Abstract:

    In this paper we suggest an efficient evolutionary approach based on Topological Sort techniques for precedence constrained sequencing. The determination of optimal sequence has much to offer to downstream project management and opens up new opportunities for supply chains and logistics. Experimental results show that the suggested approach is a good alternative to locate optimal solution for complicated precedence constrained sequencing as in optimization method for instance.

  • IEEE Congress on Evolutionary Computation - Evolutionary algorithm based on Topological Sort for precedence constrained sequencing
    2007 IEEE Congress on Evolutionary Computation, 2007
    Co-Authors: Chiung Moon, Youngsu Yun, Choonseong Leem
    Abstract:

    In this paper we suggest an efficient evolutionary approach based on Topological Sort techniques for precedence constrained sequencing. The determination of optimal sequence has much to offer to downstream project management and opens up new opportunities for supply chains and logistics. Experimental results show that the suggested approach is a good alternative to locate optimal solution for complicated precedence constrained sequencing as in optimization method for instance.

  • an efficient genetic algorithm for the traveling salesman problem with precedence constraints
    European Journal of Operational Research, 2002
    Co-Authors: Chiung Moon, Jongsoo Kim, Gyunghyun Choi, Yoonho Seo
    Abstract:

    Abstract The traveling salesman problem with precedence constraints (TSPPC) is one of the most difficult combinatorial optimization problems. In this paper, an efficient genetic algorithm (GA) to solve the TSPPC is presented. The key concept of the proposed GA is a Topological Sort (TS), which is defined as an ordering of vertices in a directed graph. Also, a new crossover operation is developed for the proposed GA. The results of numerical experiments show that the proposed GA produces an optimal solution and shows superior performance compared to the traditional algorithms.

Yoonho Seo - One of the best experts on this subject based on the ideXlab platform.

  • an efficient genetic algorithm for the traveling salesman problem with precedence constraints
    European Journal of Operational Research, 2002
    Co-Authors: Chiung Moon, Jongsoo Kim, Gyunghyun Choi, Yoonho Seo
    Abstract:

    Abstract The traveling salesman problem with precedence constraints (TSPPC) is one of the most difficult combinatorial optimization problems. In this paper, an efficient genetic algorithm (GA) to solve the TSPPC is presented. The key concept of the proposed GA is a Topological Sort (TS), which is defined as an ordering of vertices in a directed graph. Also, a new crossover operation is developed for the proposed GA. The results of numerical experiments show that the proposed GA produces an optimal solution and shows superior performance compared to the traditional algorithms.

Csaba Szepesvári - One of the best experts on this subject based on the ideXlab platform.

  • NeurIPS - TopRank: A practical algorithm for online stochastic ranking.
    2018
    Co-Authors: Tor Lattimore, Branislav Kveton, Csaba Szepesvári
    Abstract:

    Online learning to rank is a sequential decision-making problem where in each round the learning agent chooses a list of items and receives feedback in the form of clicks from the user. Many sample-efficient algorithms have been proposed for this problem that assume a specific click model connecting rankings and user behavior. We propose a generalized click model that encompasses many existing models, including the position-based and cascade models. Our generalization motivates a novel online learning algorithm based on Topological Sort, which we call TopRank. TopRank is (a) more natural than existing algorithms, (b) has stronger regret guarantees than existing algorithms with comparable generality, (c) has a more insightful proof that leaves the door open to many generalizations, (d) outperforms existing algorithms empirically.

  • TopRank: A practical algorithm for online stochastic ranking
    arXiv: Machine Learning, 2018
    Co-Authors: Tor Lattimore, Branislav Kveton, Csaba Szepesvári
    Abstract:

    Online learning to rank is a sequential decision-making problem where in each round the learning agent chooses a list of items and receives feedback in the form of clicks from the user. Many sample-efficient algorithms have been proposed for this problem that assume a specific click model connecting rankings and user behavior. We propose a generalized click model that encompasses many existing models, including the position-based and cascade models. Our generalization motivates a novel online learning algorithm based on Topological Sort, which we call TopRank. TopRank is (a) more natural than existing algorithms, (b) has stronger regret guarantees than existing algorithms with comparable generality, (c) has a more insightful proof that leaves the door open to many generalizations, (d) outperforms existing algorithms empirically.

Qiaoling Ye - One of the best experts on this subject based on the ideXlab platform.

  • Optimizing Regularized Cholesky Score for Order-Based Learning of Bayesian Networks
    IEEE Transactions on Pattern Analysis and Machine Intelligence, 1
    Co-Authors: Qiaoling Ye, Arash Amini, Qing Zhou
    Abstract:

    Bayesian networks are a class of popular graphical models that encode causal and conditional independence relations among variables by directed acyclic graphs (DAGs). We propose a novel structure learning method, annealing on regularized Cholesky score (ARCS), to search over Topological Sorts, or permutations of nodes, for a high-scoring Bayesian network. Our scoring function is derived from regularizing Gaussian DAG likelihood, and its optimization gives an alternative formulation of the sparse Cholesky factorization problem from a statistical viewpoint. We combine simulated annealing over permutation space with a fast proximal gradient algorithm, operating on triangular matrices of edge coefficients, to compute the score of any permutation. Combined, the two approaches allow us to quickly and effectively search over the space of DAGs without the need to verify the acyclicity constraint or to enumerate possible parent sets given a candidate Topological Sort. Through extensive numerical comparisons, we show that ARCS outperformed existing methods by a substantial margin, demonstrating its great advantage in structure learning of Bayesian networks from both observational and experimental data. We also establish the consistency of our scoring function in estimating Topological Sorts and DAG structures in the large-sample limit. Source code of ARCS is available at https://github.com/yeqiaoling/arcs_bn.