The Generator Maintenance Scheduling Problem (GMSP) is a problem that combines a hydropower optimization problem with a scheduling problem. Both problems are known to be hard to solve and combining them leads to an even more challenging mathematical problem. Since the hydropower production functions are nonlinear, hyperplane curve fitting is used to linearize each power production function. The goal of the GMSP is to find an optimal schedule plan to decide when to shut down generators for maintenance. Therefore, one production function needs to be formulated per generator combinations leading to a rather large number of constraints. This paper demonstrates that the complexity of the problems is linked to the number of hyperplanes selected to formulate the power production functions. To accelerate the resolution of the problem, a new heuristic based on the mean square algorithm is presented to reduce the number of hyperplanes required. This heuristic substantially reduces the number of constraints and the solving time is almost ten times faster. Numerical results show that the energy produced and the generated maintenance plannings are similar for both mathematical formulations, more precisely with one hyperplane for each generator combination versus a reduced number of hyperplanes.
Published March 2022 , 17 pages
G2208.pdf (5 MB)