Deep Learning solves the NP-Hard mathematical optimization problem for the application scenario of water networks. :

This is a binary classification problem addressed by deep learning. In this work, the objective is to design a data-driven controller, which could estimate the pump scheduling of a given water distribution network in real-time. The data-driven controller is designed from a feed-forward deep neural network, and the necessary dataset is obtained from the state-of-the-art mixed-integer solver. One may question the necessity to design a data-driven controller even though there exists mixed-integer solvers (such as Gurobi). The primary reason is that computing an optimal pump scheduling of a large-scale water distribution network is an NP-Hard problem. Solving such problems using traditional optimization solvers is a computationally inefficient approach. Therefore, we presented a data-driven controller using deep learning, which can potentially estimate the time-ahead pump scheduling given the estimated nodal water demand. This controler is tested for various time horizons such as T = 10 hrs, T=15 Hrs, T= 20 Hrs, and T=24 Hrs). The results demonstrates that this controller can potentially estimate the time ahead pump scheduling with error < 0.01. Kindly **refer** the paper (link) .

*An example of a Water Distribution Network [a. Diagram] [b. Training Loss] [c. Computation Time]:

Using conda, tensorflow can be installed as follows (for beginners):

$ conda create -n tf tensorflow
$ conda activate tf

Requirements:

• TensorFlow
• Keras
• numpy
• Gurobi
• matplotlib
• pandas
• jupyter

Installation

This framework is suitable for Python >= 3.7 environment. In addition, to generate relevant dataset, kindly use functionalities of Gurobi Solver (https://www.gurobi.com/resource/modeling-examples-using-the-gurobi-python-api-in-jupyter-notebook/)

License

The project is licensed under the GNU General Public License v3.0.

BibTeX Citation

If you refer this data-driven controller/approach in a scientific publication, we would appreciate using the following citations:

@inproceedings{bhardwaj2021data,
  title={Data-Driven Pump Scheduling for Cost Minimization in Water Networks},
  author={Bhardwaj, Jyotirmoy and Krishnan, Joshin and Beferull-Lozano, Baltasar},
  booktitle={2021 IEEE International Conference on Autonomous Systems (ICAS)},
  pages={1--5},
  year={2021},
  organization={IEEE}
}

Citing Work

• Dimitris Bertsimas and Bartolomeo Stellato. Online Mixed-Integer Optimization in Milliseconds. arXiv (2021). https://arxiv.org/pdf/1907.02206.pdf.

Funding

This work was funded by:

Wisenet Research Center (UiA) Data-Driven Pump Scheduling for Cost Minimization in Water Networks

Norsk institutt for vannforskning (https://www.niva.no/)