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A GRU-based Mixture Density Network for Data-Driven Dynamic Stochastic Programming

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Document pages: 11 pages

Abstract: The conventional deep learning approaches for solving time-series problemsuch as long-short term memory (LSTM) and gated recurrent unit (GRU) bothconsider the time-series data sequence as the input with one single unit as theoutput (predicted time-series result). Those deep learning approaches have madetremendous success in many time-series related problems, however, this cannotbe applied in data-driven stochastic programming problems since the output ofeither LSTM or GRU is a scalar rather than probability distribution which isrequired by stochastic programming model. To fill the gap, in this work, wepropose an innovative data-driven dynamic stochastic programming (DD-DSP)framework for time-series decision-making problem, which involves threecomponents: GRU, Gaussian Mixture Model (GMM) and SP. Specifically, we devisethe deep neural network that integrates GRU and GMM which is called GRU-basedMixture Density Network (MDN), where GRU is used to predict the time-seriesoutcomes based on the recent historical data, and GMM is used to extract thecorresponding probability distribution of predicted outcomes, then the resultswill be input as the parameters for SP. To validate our approach, we apply theframework on the car-sharing relocation problem. The experiment validationsshow that our framework is superior to data-driven optimization based on LSTMwith the vehicle average moving lower than LSTM.

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