Generative deep learning for decision making in gas networks

Abstract

A decision support system relies on frequent re-solving of similar problem instances. While the general structure remains the same in corresponding applications, the input parameters are updated on a regular basis. We propose a generative neural network design for learning integer decision variables of mixed-integer linear programming (MILP) formulations of these problems. We utilise a deep neural network discriminator and a MILP solver as our oracle to train our generative neural network. In this article, we present the results of our design applied to the transient gas optimisation problem. The trained generative neural network produces a feasible solution in 2.5s, and when used as a warm start solution, decreases global optimal solution time by 60.5%.

An expandable machine learning-optimization framework to sequential decision-making

“…Bertsimas and Stellato (2022) build upon that framework to solve parametric mixed-integer quadratic optimization problems without requiring a solver. Anderson et al (2022) present a generative neural network design to reduce the resolution times of repetitively solved optimization problems. The presented framework contains two neural networks: A generator to predict the values of binary decision variables and a discriminator to predict the value of the objective function when those variables are fixed.…”

“…While both studies predict the values of binary decision variables, their usages are dissimilar. Anderson et al (2022) feed predictions to a discriminator to obtain a prediction of the objective when those variables are fixed in the problem and then use them as a warm start for the optimizer. We utilize predictions of binary variables in a feasibility check loop to determine the optimal prediction level and solve the problem with fixed variables at a determined level.…”

Efficient simulation of coupled gas and power networks under uncertain demands

“…The dependencies we have are Eigen, see [29], N. Lohmanns json library, 4 googletest, 5 pcgrandom, see [43] and CLI11. 6…”

“…In addition, we also include stochastic power demands in the PF network setting. In [4], uncertainty in PF is computed relying on approaches based on neural networks. A difference to the presented approach is the restriction to linear PF problems and the absence of coupling to gas networks.…”