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An Uncertain Optimization Method Based on Adaptive Discrete Approximation Rejection Sampling for Stochastic Programming with Incomplete Knowledge of Uncertainty

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Abstract

Stochastic programming has been widely used in various application scenarios and theoretical research works. However, these excellent methods depend on specific explicit probability modeling with complete knowledge of uncertainty, which is very limited in practical problem since there is usually no way to abstract complex uncertainties into the commonly used known probability models. In this paper, a novel generative model named the Adaptive Discrete Approximation Rejection Sampling is proposed for stochastic programming with incomplete knowledge of uncertainty, which can not only simulate uncertain scenarios from a complex explicit probability model that cannot meet the constraints of existing sampling methods, but also even simulate scenarios from a sample set related to uncertainty when the specific explicit probability model of uncertainty is missing or unavailable. The method is to establish the easy-to-sample proposal distribution by approximately transforming the complex hard-to-sample target probability model, to make the proposal distribution close enough to the target distribution, so as to achieve an efficient sampling while ensuring the performance of the model. On this basis, combining the Monte Carlo method and heuristic optimization, an uncertain optimization model for stochastic programming with incomplete knowledge of uncertainty is further constructed, to solve the unavailability of the existing stochastic programming methods in the absence of explicit probability model of uncertainty. Experimental results show the advantages of the proposed method in terms of applicability, adaptability, accuracy, efficiency and model performance.

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Funding

The funding was provided by the Educational Commission of Guangdong Province, China (No.: 2020ZDZX3093).

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Authors and Affiliations

  1. Shenzhen Polytechnic, Shenzhen, 518055, China

    Bopeng Fang & Jing Wang

  2. Research Institute of New Energy Vehicle Technology, Shenzhen Polytechnic, Shenzhen, 518055, China

    Bopeng Fang, Zhurong Dong, Chen Zhao & Zhi Liu

  3. Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China

    Bopeng Fang

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  1. Bopeng Fang
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  2. Zhurong Dong
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  3. Chen Zhao
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  4. Zhi Liu
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  5. Jing Wang
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Correspondence to Zhurong Dong or Chen Zhao.

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Fang, B., Dong, Z., Zhao, C. et al. An Uncertain Optimization Method Based on Adaptive Discrete Approximation Rejection Sampling for Stochastic Programming with Incomplete Knowledge of Uncertainty. Arab J Sci Eng 48, 1399–1425 (2023). https://doi.org/10.1007/s13369-022-06835-0

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