scholarly journals An Efficient Adaptive Sampling Approach for Mobile Robotic Sensor Networks using Proximal ADMM

2021 ◽  
Author(s):  
Viet-Anh Le ◽  
Linh Nguyen ◽  
Truong X. Nghiem
Keyword(s):  
Adaptive Sampling ◽  
Optimization Problem ◽  
Complex Function ◽  
Optimal Solution ◽  
Alternating Direction ◽  
Robotic Sensor ◽  
Sampling Problem ◽  
Sampling Optimization ◽  
Robotic Sensor Networks ◽  
Grid Based

Adaptive sampling in a resource-constrained mobile robotic sensor network for monitoring a spatial phenomenon is a fundamental but challenging problem. In applications where a Gaussian Process is employed to model a spatial field and then to predict the field at unobserved locations, the adaptive sampling problem can be formulated as minimizing the negative log determinant of a predicted covariance matrix, which is a non-convex and highly complex function. Consequently, this optimization problem is typically addressed in a grid-based discrete domain, although it is combinatorial NP-hard and only a near-optimal solution can be obtained. To overcome this challenge, we propose using a proximal alternating direction method of multipliers (Px-ADMM) technique to solve the adaptive sampling optimization problem in a continuous domain. Numerical simulations using a real-world dataset demonstrate that the proposed PxADMM- based method outperforms a commonly used grid-based greedy method in the final model accuracy.

scholarly journals An Efficient Adaptive Sampling Approach for Mobile Robotic Sensor Networks using Proximal ADMM

2021 ◽  
Author(s):  
Viet-Anh Le ◽  
Linh Nguyen ◽  
Truong X. Nghiem
Keyword(s):  
Adaptive Sampling ◽  
Optimization Problem ◽  
Complex Function ◽  
Optimal Solution ◽  
Alternating Direction ◽  
Robotic Sensor ◽  
Sampling Problem ◽  
Sampling Optimization ◽  
Robotic Sensor Networks ◽  
Grid Based

Adaptive sampling in a resource-constrained mobile robotic sensor network for monitoring a spatial phenomenon is a fundamental but challenging problem. In applications where a Gaussian Process is employed to model a spatial field and then to predict the field at unobserved locations, the adaptive sampling problem can be formulated as minimizing the negative log determinant of a predicted covariance matrix, which is a non-convex and highly complex function. Consequently, this optimization problem is typically addressed in a grid-based discrete domain, although it is combinatorial NP-hard and only a near-optimal solution can be obtained. To overcome this challenge, we propose using a proximal alternating direction method of multipliers (Px-ADMM) technique to solve the adaptive sampling optimization problem in a continuous domain. Numerical simulations using a real-world dataset demonstrate that the proposed PxADMM- based method outperforms a commonly used grid-based greedy method in the final model accuracy.

scholarly journals An Efficient Adaptive Sampling Approach for Mobile Robotic Sensor Networks using Proximal ADMM

2021 ◽  
Author(s):  
Viet-Anh Le ◽  
Linh Nguyen ◽  
Truong X. Nghiem
Keyword(s):  
Adaptive Sampling ◽  
Optimization Problem ◽  
Complex Function ◽  
Optimal Solution ◽  
Alternating Direction ◽  
Robotic Sensor ◽  
Sampling Problem ◽  
Sampling Optimization ◽  
Robotic Sensor Networks ◽  
Grid Based

Adaptive sampling in a resource-constrained mobile robotic sensor network for monitoring a spatial phenomenon is a fundamental but challenging problem. In applications where a Gaussian Process is employed to model a spatial field and then to predict the field at unobserved locations, the adaptive sampling problem can be formulated as minimizing the negative log determinant of a predicted covariance matrix, which is a non-convex and highly complex function. Consequently, this optimization problem is typically addressed in a grid-based discrete domain, although it is combinatorial NP-hard and only a near-optimal solution can be obtained. To overcome this challenge, we propose using a proximal alternating direction method of multipliers (Px-ADMM) technique to solve the adaptive sampling optimization problem in a continuous domain. Numerical simulations using a real-world dataset demonstrate that the proposed PxADMM- based method outperforms a commonly used grid-based greedy method in the final model accuracy.

scholarly journals Multi-Step Predictions for Adaptive Sampling using Proximal ADMM

2021 ◽  
Author(s):  
Viet-Anh Le ◽  
Linh Nguyen ◽  
Truong X. Nghiem
Keyword(s):  
Adaptive Sampling ◽  
Optimization Problem ◽  
Conditional Entropy ◽  
Mobile Sensors ◽  
Mixed Integer ◽  
Sampling Step ◽  
Multiple Sampling ◽  
Novel Approach ◽  
Sampling Problem ◽  
Gp Model

<p>The paper presents a novel approach by using multi- step predictions to address the adaptive sampling problem in a resources and obstacles constrained mobile robotic sensor network to efficiently monitor environmental spatial phenomena. It is first proposed to employ the Gaussian process (GP) to represent the spatial field, which can then be used to predict the field at unmeasured locations. The adaptive sampling problem aims to drive the mobile sensors to optimally navigate the environment where the sensors adaptively take measurements of the spatial phenomena at each sampling step. To this end, a conditional entropy based optimality criterion is proposed, which aims to minimize prediction uncertainty of the GP model. By predicting possible measurements the mobile sensors potentially take in a horizon of multiple sampling steps ahead and exploiting the chain rule of the conditional entropy, a multi-step predictions based adaptive sampling optimization problem is formulated. The objective of the optimization problem is to find the optimal sampling paths for the mobile sensors in multiple sampling steps ahead, which then provides their benefits in terms of better navigation, deployment and data collection with more informative sensor readings. However, the optimization problem is nonconvex, complex, constrained and mixed-integer. Therefore, it is proposed to employ the proximal alternating direction method of multipliers algorithm to efficiently solve the problem. More importantly, the solution obtained by the proposed approach is theoretically guaranteed to be converged to a stationary value. Effectiveness of the proposed algorithm was extensively validated by the real- world dataset, where the obtained results are highly promising.</p>

scholarly journals Multi-Step Predictions for Adaptive Sampling using Proximal ADMM

2021 ◽  
Author(s):  
Viet-Anh Le ◽  
Linh Nguyen ◽  
Truong X. Nghiem
Keyword(s):  
Adaptive Sampling ◽  
Optimization Problem ◽  
Conditional Entropy ◽  
Mobile Sensors ◽  
Mixed Integer ◽  
Sampling Step ◽  
Multiple Sampling ◽  
Novel Approach ◽  
Sampling Problem ◽  
Gp Model

<p>The paper presents a novel approach by using multi- step predictions to address the adaptive sampling problem in a resources and obstacles constrained mobile robotic sensor network to efficiently monitor environmental spatial phenomena. It is first proposed to employ the Gaussian process (GP) to represent the spatial field, which can then be used to predict the field at unmeasured locations. The adaptive sampling problem aims to drive the mobile sensors to optimally navigate the environment where the sensors adaptively take measurements of the spatial phenomena at each sampling step. To this end, a conditional entropy based optimality criterion is proposed, which aims to minimize prediction uncertainty of the GP model. By predicting possible measurements the mobile sensors potentially take in a horizon of multiple sampling steps ahead and exploiting the chain rule of the conditional entropy, a multi-step predictions based adaptive sampling optimization problem is formulated. The objective of the optimization problem is to find the optimal sampling paths for the mobile sensors in multiple sampling steps ahead, which then provides their benefits in terms of better navigation, deployment and data collection with more informative sensor readings. However, the optimization problem is nonconvex, complex, constrained and mixed-integer. Therefore, it is proposed to employ the proximal alternating direction method of multipliers algorithm to efficiently solve the problem. More importantly, the solution obtained by the proposed approach is theoretically guaranteed to be converged to a stationary value. Effectiveness of the proposed algorithm was extensively validated by the real- world dataset, where the obtained results are highly promising.</p>

scholarly journals Multi-Step Predictions for Adaptive Sampling using Proximal ADMM

2021 ◽  
Author(s):  
Viet-Anh Le ◽  
Linh Nguyen ◽  
Truong X. Nghiem
Keyword(s):  
Adaptive Sampling ◽  
Optimization Problem ◽  
Conditional Entropy ◽  
Mobile Sensors ◽  
Mixed Integer ◽  
Sampling Step ◽  
Multiple Sampling ◽  
Novel Approach ◽  
Sampling Problem ◽  
Gp Model

<p>The paper presents a novel approach by using multi- step predictions to address the adaptive sampling problem in a resources and obstacles constrained mobile robotic sensor network to efficiently monitor environmental spatial phenomena. It is first proposed to employ the Gaussian process (GP) to represent the spatial field, which can then be used to predict the field at unmeasured locations. The adaptive sampling problem aims to drive the mobile sensors to optimally navigate the environment where the sensors adaptively take measurements of the spatial phenomena at each sampling step. To this end, a conditional entropy based optimality criterion is proposed, which aims to minimize prediction uncertainty of the GP model. By predicting possible measurements the mobile sensors potentially take in a horizon of multiple sampling steps ahead and exploiting the chain rule of the conditional entropy, a multi-step predictions based adaptive sampling optimization problem is formulated. The objective of the optimization problem is to find the optimal sampling paths for the mobile sensors in multiple sampling steps ahead, which then provides their benefits in terms of better navigation, deployment and data collection with more informative sensor readings. However, the optimization problem is nonconvex, complex, constrained and mixed-integer. Therefore, it is proposed to employ the proximal alternating direction method of multipliers algorithm to efficiently solve the problem. More importantly, the solution obtained by the proposed approach is theoretically guaranteed to be converged to a stationary value. Effectiveness of the proposed algorithm was extensively validated by the real- world dataset, where the obtained results are highly promising.</p>

A new algorithm for finding CRM-model coefficients

2019 ◽  
Vol 5 (3) ◽  
pp. 164-185 ◽  
Author(s):  
Alexander D. Bekman ◽  
Sergey V. Stepanov ◽  
Alexander A. Ruchkin ◽  
Dmitry V. Zelenin
Keyword(s):  
Approximate Solution ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Complex Form ◽  
Approximate Solutions ◽  
The Other ◽  
Programming Algorithm ◽  
Stochastic Algorithms ◽  
Large Set ◽  
Flow Rates

The quantitative evaluation of producer and injector well interference based on well operation data (profiles of flow rates/injectivities and bottomhole/reservoir pressures) with the help of CRM (Capacitance-Resistive Models) is an optimization problem with large set of variables and constraints. The analytical solution cannot be found because of the complex form of the objective function for this problem. Attempts to find the solution with stochastic algorithms take unacceptable time and the result may be far from the optimal solution. Besides, the use of universal (commercial) optimizers hides the details of step by step solution from the user, for example&nbsp;— the ambiguity of the solution as the result of data inaccuracy.<br> The present article concerns two variants of CRM problem. The authors present a new algorithm of solving the problems with the help of “General Quadratic Programming Algorithm”. The main advantage of the new algorithm is the greater performance in comparison with the other known algorithms. Its other advantage is the possibility of an ambiguity analysis. This article studies the conditions which guarantee that the first variant of problem has a unique solution, which can be found with the presented algorithm. Another algorithm for finding the approximate solution for the second variant of the problem is also considered. The method of visualization of approximate solutions set is presented. The results of experiments comparing the new algorithm with some previously known are given.

scholarly journals Algebraic Solution to Constrained Bi-Criteria Decision Problem of Rating Alternatives through Pairwise Comparisons

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 303
Author(s):  
Nikolai Krivulin
Keyword(s):  
Decision Problem ◽  
Optimization Problem ◽  
Pareto Frontier ◽  
Sufficient Conditions ◽  
Approximation Error ◽  
Optimal Solution ◽  
Algebraic Solution ◽  
Pairwise Comparisons ◽  
Logarithmic Scale ◽  
Idempotent Algebra

We consider a decision-making problem to evaluate absolute ratings of alternatives from the results of their pairwise comparisons according to two criteria, subject to constraints on the ratings. We formulate the problem as a bi-objective optimization problem of constrained matrix approximation in the Chebyshev sense in logarithmic scale. The problem is to approximate the pairwise comparison matrices for each criterion simultaneously by a common consistent matrix of unit rank, which determines the vector of ratings. We represent and solve the optimization problem in the framework of tropical (idempotent) algebra, which deals with the theory and applications of idempotent semirings and semifields. The solution involves the introduction of two parameters that represent the minimum values of approximation error for each matrix and thereby describe the Pareto frontier for the bi-objective problem. The optimization problem then reduces to a parametrized vector inequality. The necessary and sufficient conditions for solutions of the inequality serve to derive the Pareto frontier for the problem. All solutions of the inequality, which correspond to the Pareto frontier, are taken as a complete Pareto-optimal solution to the problem. We apply these results to the decision problem of interest and present illustrative examples.

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