Column generation for the discrete Unit Commitment problem with min-stop ramping constraints

TL;DR

This paper evaluates whether Dantzig-Wolfe reformulation enhances solving the discrete Unit Commitment problem with min-stop ramping constraints, concluding that it does not improve the linear relaxation quality of existing compact ILP formulations.

Contribution

The study introduces an extended ILP formulation with column generation for the problem and demonstrates its limitations compared to existing methods.

Findings

Dantzig-Wolfe reformulation does not improve linear relaxation quality.

The compact ILP formulation of min-stop ramping constraints is likely tight.

Existing exact methods and heuristics are validated by these results.

Abstract

The discrete unit commitment problem with min-stop ramping constraints optimizes the daily production of thermal power plants (coal, gas, fuel units). For this problem, compact Integer Linear Programming (ILP) formulations have been designed to solve exactly small instances and heuristically real-size instances. This paper investigates whether Dantzig-Wolfe reformulation allows to improve the previous exact method and matheuristics. The extended ILP formulation is presented with the column generation algorithm to solve its linear relaxation. The experimental results show that the Dantzig-Wolfe reformulation does not improve the quality of the linear relaxation of the tightest compact ILP formulations. Computational experiments suggest also a conjecture which would explain such result: the compact ILP formulation of min-stop ramping constraints would be tight. Such results validate the quality of the exact methods and matheuristics based on compact ILP formulations previously designed.