Gradient-Based Algorithm

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Christos G Cassandras - One of the best experts on this subject based on the ideXlab platform.

  • A Solution to the Optimal Lot-Sizing Problem as a Stochastic Resource Contention Game
    IEEE Transactions on Automation Science and Engineering, 2012
    Co-Authors: Chen Yao, Christos G Cassandras
    Abstract:

    We present a new way to solve the “lot-sizing” problem viewed as a stochastic noncooperative resource contention game. We develop a Stochastic Flow Model (SFM) for polling systems with non-negligible changeover times enabling us to formulate lot sizing as an optimization problem without imposing constraints on the distributional characteristics of the random processes in the system. Using Infinitesimal Perturbation Analysis (IPA) methods, we derive gradient estimators of the performance metrics of interests with respect to the lot-size parameters and prove they are unbiased. We then derive an online Gradient-Based Algorithm for obtaining optimal lot sizes from both a system-centric and user-centric perspective. Uncharacteristically for such cases, there is no gap between the two solutions in the two-class case for which we have obtained explicit numerical results. We derive a proof of this phenomenon for a deterministic version of the problem, suggesting that lot-sizing-like scheduling policies in resource contention problems have a natural property of balancing certain user-centric and system-centric performance metrics.

  • a solution of the lot sizing problem as a stochastic resource contention game
    Conference on Decision and Control, 2010
    Co-Authors: Chen Yao, Christos G Cassandras
    Abstract:

    We present a new way to solve the “lot sizing” problem viewed as a stochastic non-cooperative resource contention game. We develop a Stochastic Flow Model (SFM) for polling systems with non-negligible changeover times enabling us to formulate lot sizing as an optimization problem with no constraints on the distributional characteristics of the random processes in the system. We then use Infinitesimal Perturbation Analysis (IPA) methods and derive an on-line Gradient-Based Algorithm for obtaining optimal lot sizes from both a system-centric and user-centric perspective and observe that, uncharacteristically for such cases, there is no gap between the two solutions in the two-class case for which we have obtained explicit numerical results.

  • CDC - A solution of the lot sizing problem as a stochastic resource contention game
    49th IEEE Conference on Decision and Control (CDC), 2010
    Co-Authors: Chen Yao, Christos G Cassandras
    Abstract:

    We present a new way to solve the “lot sizing” problem viewed as a stochastic non-cooperative resource contention game. We develop a Stochastic Flow Model (SFM) for polling systems with non-negligible changeover times enabling us to formulate lot sizing as an optimization problem with no constraints on the distributional characteristics of the random processes in the system. We then use Infinitesimal Perturbation Analysis (IPA) methods and derive an on-line Gradient-Based Algorithm for obtaining optimal lot sizes from both a system-centric and user-centric perspective and observe that, uncharacteristically for such cases, there is no gap between the two solutions in the two-class case for which we have obtained explicit numerical results.

Chen Yao - One of the best experts on this subject based on the ideXlab platform.

  • A Solution to the Optimal Lot-Sizing Problem as a Stochastic Resource Contention Game
    IEEE Transactions on Automation Science and Engineering, 2012
    Co-Authors: Chen Yao, Christos G Cassandras
    Abstract:

    We present a new way to solve the “lot-sizing” problem viewed as a stochastic noncooperative resource contention game. We develop a Stochastic Flow Model (SFM) for polling systems with non-negligible changeover times enabling us to formulate lot sizing as an optimization problem without imposing constraints on the distributional characteristics of the random processes in the system. Using Infinitesimal Perturbation Analysis (IPA) methods, we derive gradient estimators of the performance metrics of interests with respect to the lot-size parameters and prove they are unbiased. We then derive an online Gradient-Based Algorithm for obtaining optimal lot sizes from both a system-centric and user-centric perspective. Uncharacteristically for such cases, there is no gap between the two solutions in the two-class case for which we have obtained explicit numerical results. We derive a proof of this phenomenon for a deterministic version of the problem, suggesting that lot-sizing-like scheduling policies in resource contention problems have a natural property of balancing certain user-centric and system-centric performance metrics.

  • a solution of the lot sizing problem as a stochastic resource contention game
    Conference on Decision and Control, 2010
    Co-Authors: Chen Yao, Christos G Cassandras
    Abstract:

    We present a new way to solve the “lot sizing” problem viewed as a stochastic non-cooperative resource contention game. We develop a Stochastic Flow Model (SFM) for polling systems with non-negligible changeover times enabling us to formulate lot sizing as an optimization problem with no constraints on the distributional characteristics of the random processes in the system. We then use Infinitesimal Perturbation Analysis (IPA) methods and derive an on-line Gradient-Based Algorithm for obtaining optimal lot sizes from both a system-centric and user-centric perspective and observe that, uncharacteristically for such cases, there is no gap between the two solutions in the two-class case for which we have obtained explicit numerical results.

  • CDC - A solution of the lot sizing problem as a stochastic resource contention game
    49th IEEE Conference on Decision and Control (CDC), 2010
    Co-Authors: Chen Yao, Christos G Cassandras
    Abstract:

    We present a new way to solve the “lot sizing” problem viewed as a stochastic non-cooperative resource contention game. We develop a Stochastic Flow Model (SFM) for polling systems with non-negligible changeover times enabling us to formulate lot sizing as an optimization problem with no constraints on the distributional characteristics of the random processes in the system. We then use Infinitesimal Perturbation Analysis (IPA) methods and derive an on-line Gradient-Based Algorithm for obtaining optimal lot sizes from both a system-centric and user-centric perspective and observe that, uncharacteristically for such cases, there is no gap between the two solutions in the two-class case for which we have obtained explicit numerical results.

Rodrigo Cabral Farias - One of the best experts on this subject based on the ideXlab platform.

  • Gradient-Based Algorithm with Spatial Regularization for Optimal Sensor Placement
    2020
    Co-Authors: Fateme Ghayem, Bertrand Rivet, Christian Jutten, Rodrigo Cabral Farias
    Abstract:

    In this paper, we are interested in optimal sensor placement for signal extraction. Recently, a new criterion based on output signal to noise ratio has been proposed for sensor placement. However, to solve the optimization problem, a greedy approach is used over a grid, which is not optimal. To improve this method, we present an optimization approach to locate all the sensors at once. We further add a constraint to the problem that controls the average distances between the sensors. To solve our problem, we use an alternating optimization penalty method. As the associated cost function is non-convex, the proposed Algorithm should be carefully initialized. We propose to initialize it with the result of the greedy method. Experimental results show the superiority of the proposed method over the greedy approach.

  • ICASSP - Gradient-Based Algorithm with Spatial Regularization for Optimal Sensor Placement
    ICASSP 2020 - 2020 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2020
    Co-Authors: Fateme Ghayem, Bertrand Rivet, Christian Jutten, Rodrigo Cabral Farias
    Abstract:

    In this paper, we are interested in optimal sensor placement for signal extraction. Recently, a new criterion based on output signal to noise ratio has been proposed for sensor placement. However, to solve the optimization problem, a greedy approach is used over a grid, which is not optimal. To improve this method, we present an optimization approach to locate all the sensors at once. We further add a constraint to the problem that controls the average distances between the sensors. To solve our problem, we use an alternating optimization penalty method. As the associated cost function is non-convex, the proposed Algorithm should be carefully initialized. We propose to initialize it with the result of the greedy method. Experimental results show the superiority of the proposed method over the greedy approach.

L. Adler - One of the best experts on this subject based on the ideXlab platform.

  • SU‐FF‐J‐119: PET Tumor Segmentation: Comparison of Gradient‐Based Algorithm to Constant Threshold Algorithm
    Medical Physics, 2007
    Co-Authors: G. Shen, D. Nelson, L. Adler
    Abstract:

    Purpose: To compare the consistency and accuracy of a gradient‐based Algorithm (GRADIENT) with a constant threshold Algorithm (THRESHOLD) for delineating positron emission tomography(PET) spheres of varying size and source‐to‐background ratio (SBR). Method and Materials:PET scans were acquired for cylindrical phantoms with fillable spheres on five different scanners including GE, Phillips and Siemens, emulating clinical conditions with different contrast levels to illustrate the influence of SBR. The phantoms were segmented from the scans using the GRADIENT and 37% constant threshold Algorithm. The radii calculated from both methods were compared to the known actual radii of the phantoms in order to quantify the accuracy of each Algorithm. Results: The gradient‐based Algorithm performed consistently across different scanners and with varying SBR and phantom size while the performance of the constant threshold Algorithm deteriorated with decreases in both SBR and phantom size. For the gradient‐based Algorithm, the mean of the absolute radius percentage differences for the phantoms less than 10mm in size was 8.16% and the standard deviation was 0.1 whereas for the constant threshold Algorithm the mean of the absolute percentage differences for the same phantoms was 55.98% and the standard deviation was 0.46. The statistics for the phantoms larger than 10mm in size were 3.84%, 0.03 and 8.45%, 0.05, respectively. Similar trends in percentage difference appeared for the same scanner and phantom set when the SBR decreased from 70:1 to 2:1. GRADIENT was robust to user initialization and resulted in less than 5% difference over several measurements for the same tumor.Conclusion: The gradient‐based Algorithm is more robust resulting in consistent results across different scanners and better accuracy than the constant threshold Algorithm when evaluated in terms of varying SBR and phantom size for the in‐vitro phantom studies. Conflict of Interest: Contributing authors employed by MIMvista Corporation.

  • PET TUMOR SEGMENTATION: COMPARISON OF Gradient-Based Algorithm TO CONSTANT THRESHOLD Algorithm
    2007
    Co-Authors: G. Shen, D. Nelson, L. Adler
    Abstract:

    Introduction Accurate tumor segmentation is very important in patient diagnosis and management. Commonly used methods, such as constant threshold methods, suffer from an inability to accurately define small tumors, tumors with low source-to-background ratio (SBR), and tumors with varying levels of perfusion and metabolism. A Gradient-Based Algorithm was developed to overcome these limitations and allow for more accurate tumor segmentation.

Fateme Ghayem - One of the best experts on this subject based on the ideXlab platform.

  • Gradient-Based Algorithm with Spatial Regularization for Optimal Sensor Placement
    2020
    Co-Authors: Fateme Ghayem, Bertrand Rivet, Christian Jutten, Rodrigo Cabral Farias
    Abstract:

    In this paper, we are interested in optimal sensor placement for signal extraction. Recently, a new criterion based on output signal to noise ratio has been proposed for sensor placement. However, to solve the optimization problem, a greedy approach is used over a grid, which is not optimal. To improve this method, we present an optimization approach to locate all the sensors at once. We further add a constraint to the problem that controls the average distances between the sensors. To solve our problem, we use an alternating optimization penalty method. As the associated cost function is non-convex, the proposed Algorithm should be carefully initialized. We propose to initialize it with the result of the greedy method. Experimental results show the superiority of the proposed method over the greedy approach.

  • ICASSP - Gradient-Based Algorithm with Spatial Regularization for Optimal Sensor Placement
    ICASSP 2020 - 2020 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2020
    Co-Authors: Fateme Ghayem, Bertrand Rivet, Christian Jutten, Rodrigo Cabral Farias
    Abstract:

    In this paper, we are interested in optimal sensor placement for signal extraction. Recently, a new criterion based on output signal to noise ratio has been proposed for sensor placement. However, to solve the optimization problem, a greedy approach is used over a grid, which is not optimal. To improve this method, we present an optimization approach to locate all the sensors at once. We further add a constraint to the problem that controls the average distances between the sensors. To solve our problem, we use an alternating optimization penalty method. As the associated cost function is non-convex, the proposed Algorithm should be carefully initialized. We propose to initialize it with the result of the greedy method. Experimental results show the superiority of the proposed method over the greedy approach.