In order to produce electricity, EDF operates many physical facilities such as nuclear or
hydroelectric power plants, wind turbines, solar panels and so on. EDF seeks to optimize the
exploitation of these physical assets in order to improve their reliability as well as their
economic and technical performance. Maintenance optimization is one of the main levers of action
towards this goal.
We study systems of components that are at the heart of the electricity production process and
sharing a common stock of spare parts. Over time, the components experience random failures that
occur according to known failure distributions. If a failed component cannot be replaced -
because the stock is empty for example - the system is in forced outage which causes a heavy
loss of production. An efficient maintenance policy is then needed to increase the availability
of the equipments and hence the electricity production, which can lead to important gains.
The industrial problem of optimal maintenance scheduling is a stochastic optimization problem. In
our problem, randomness comes from the failures of the component. Some mathematical challenges
must be addressed:
- We consider systems with up to 80 components coupled with a common stock. This is a
difficult large-scale optimization problem for which the goal is to improve the solution
given by heuristic methods rather than to find the true optimum.
- The objective we aim at minimizing is the expectation of a cost, which is computed using
Monte-Carlo simulations. Hence, we only have access to an estimation of the expected cost
and not to the true value of the objective. The evaluations are said to be noisy.
- The objective function is computed with a simulation model which is considered to be a
blackbox: for a given maintenance strategy, we only know the value of the objective
function. We have no information on the gradient, which may not even be defined.
Two approaches are investigated for the optimization of maintenance scheduling:
- Currently, the evaluation of the objective function is done with a simulation-based model
that is seen as a blackbox. A natural idea is then to investigate blackbox optimization
methods that can be easily plugged to simulation software. These methods may be efficient
for small systems or when the set of admissible maintenance strategies is small, but they
are known to be subject to the curse of dimensionality. This is why, if we aim at tackling
problems involving exceptional maintenance for large-scale systems, another approach is
needed.
- To tackle high-dimensional maintenance optimization problems, we get out of the blackbox
context. We develop an analytical model of the dynamics of the system. Then, we set up a
decomposition methodology that uses information on the structure of the system to perform
the optimization efficiently. The decomposition method is designed to be parallelized and
can then tackle large-scale optimization problems.