Approximate Uncertain Program

Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address chance constrained program. Firstly, a single layer neural-n...

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Veröffentlicht in:IEEE access Jg. 7; S. 182357 - 182365
Hauptverfasser: Shen, Xun, Zhuang, Jiancang, Zhang, Xingguo
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Piscataway IEEE 2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Approximation algorithms
Artificial neural networks
Chance constrained program
Constraints
Domains
extreme learning machine
Indexes
Machine learning
Mathematical models
Neural networks
Optimization
Probabilistic logic
Probability
randomized optimization
Statistical analysis
ISSN:2169-3536, 2169-3536
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Abstract Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address chance constrained program. Firstly, a single layer neural-network is used to approximate the function from decision domain to violation probability domain. The algorithm for updating parameters in single layer neural-network adopts sequential extreme learning machine. Based on the neural violation probability approximate model, a randomized algorithm is then proposed to approach the optimizer in the probabilistic feasible domain of decision. In the randomized algorithm, samples are extracted from decision domain uniformly at first. Then, violation probabilities of all samples are calculated according to neural violation probability approximate model. The ones with violation probability higher than the required level are discarded. The minimizer in the remained feasible decision samples is used to update sampling policy. The policy converges to the optimal feasible decision. Numerical simulations are implemented to validate the proposed method for non-convex problems comparing with scenario approach and parallel randomized algorithm. The results show that proposed method have improved performance.
AbstractList Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address chance constrained program. Firstly, a single layer neural-network is used to approximate the function from decision domain to violation probability domain. The algorithm for updating parameters in single layer neural-network adopts sequential extreme learning machine. Based on the neural violation probability approximate model, a randomized algorithm is then proposed to approach the optimizer in the probabilistic feasible domain of decision. In the randomized algorithm, samples are extracted from decision domain uniformly at first. Then, violation probabilities of all samples are calculated according to neural violation probability approximate model. The ones with violation probability higher than the required level are discarded. The minimizer in the remained feasible decision samples is used to update sampling policy. The policy converges to the optimal feasible decision. Numerical simulations are implemented to validate the proposed method for non-convex problems comparing with scenario approach and parallel randomized algorithm. The results show that proposed method have improved performance.
Author Zhuang, Jiancang
Zhang, Xingguo
Shen, Xun
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StartPage 182357
SubjectTerms Algorithms
Approximation algorithms
Artificial neural networks
Chance constrained program
Constraints
Domains
extreme learning machine
Indexes
Machine learning
Mathematical models
Neural networks
Optimization
Probabilistic logic
Probability
randomized optimization
Statistical analysis
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Title Approximate Uncertain Program
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