Pre-trained solution methods for unit commitment

Abstract

This thesis aims to improve the solution methods for the unit commitment problem, a short-term planning problem in the energy industry. In particular, we focus on Dantzig-Wolfe decomposition with a column generation procedure. Special emphasis is placed on approaches based on machine learning, which is of interest when one needs to solve the unit commitment problem repeatedly.

Firstly, an initialisation method of the column generation procedure based on a neural network is studied. After offline training, for each unit commitment problem, the method outputs dual values which can be used to warmstart the solution method, leading to a significant saving of computational time. The training is done efficiently by exploiting the decomposable structure of the problem.

Secondly, primal heuristics are discussed. Two novel primal heuristics are proposed: one based on the decomposition and another based on machine learning. Both of them fix a subset of the binary variable to reduce the problem size. The remaining variable is optimised quickly by an optimisation solver, which gives primal feasible solutions with small suboptimality in a short time.

Finally, the column generation procedure is extended to handle incremental generation of columns. Instead of generating columns for all the components (power plants in the unit commitment problem) in each iteration, our method generates a subset of them and update the dual variable using the partially updated restricted master problem. Convergence analysis of the method is given under various conditions as well as numerical experiments to show the performance of the method.

By combining the above enhancements, we obtain a fast solution method to solve the unit commitment problem to small tolerances down to 0.1%.