- Title: Hybrid combinatorial optimization and machine learning algorithms for energyefficient water networks
Drinking water distribution is an essential industry and it is also one of the most energyintensive. In water networks equipped with pumps and storage devices (e.g., water towers),
the electricity consumption is flexible and controllable. Optimizing the operation and design
of these systems is thus a big opportunity for energy savings. However, these optimization
problems are very challenging: they combine discrete decisions and nonconvex physical
constraints, large-scale heterogeneous models and uncertain data.
The object of this PhD thesis is to develop new hybrid algorithms to solve this type of
problems by mixing Operations Research (OR) and Artificial Intelligence (AI) techniques.
Combining their respective abilities is an attractive topic in optimization that witnessed a
return of interest with the progress recently achieved with deep learning. In particular, the
domain of water networks lends itself well to the application of hybrid algorithms, because
of the problem complexity and the entanglement of the mathematical models and the
physical data. In the specific, our goal here is to achieve: optimality with integer nonlinear
programming, genericity with constraint programming, and scalability with machine
learning. From the conception of hybrid algorithms in the specific context of water network
optimization, we want to derive new generic optimization frameworks to articulate the
different techniques, mostly based on the well-known decomposition methods of
mathematical programming (price, resource and Benders decompositions) and of constraint
programming (global constraints). The main challenges are: (1) to identify the appropriate
techniques, (2) to identify the information to exchange between the different modules and
(3) to make this communication effective.
Several solution approaches will be explored. For instance, we propose to investigate a
combination of machine learning and column generation with the objective to tackle largesize instances of the deterministic day-ahead pump scheduling problem. The idea is to
populate a new extended mathematical programming formulation of the problem with
pumping configurations learned from historical data. Duality information will be
progressively communicated to the learning algorithm in order to solve implicitly the whole
program. The approach will then be extended to the stochastic variant of the problem by
considering multiple scenarios of uncertain demand. For the strategical design optimization
problem, we propose to investigate the appropriate Benders decomposition, in a hybrid variant, combining deep logic-based feasibility cuts, obtained by inference from a constraint
programming model, and duality-based optimality cuts, obtained from the solution of a
nonconvex programming model.