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Contrôle optimal et dimensionnement des stations de pompage dans les réseaux de distribution d'eau potable

Abstract : This thesis deal with the application of composite non-linear nonconvex mixed-integer programming techniques to solve optimization problems related to pumping stations in drinking water distribution networks (DWDNs). At the strategic level, we are examining the problem of the optimal design of pumping stations: when renewing a pumping station, which pumps should be installed to minimize costs during their life cycle? This question has led us to investigate, at the operational level, the control problem called pumping scheduling: how to operate the active elements (pumps and valves) to minimize the electrical costs associated with day-to-day pumping? One of the contributions of this work is the highlighting of the quality of the convex relaxation of nonconvex constraints arising from the pump scheduling problem that provides solutions at the limit of the achievability and optimality for the original non-convex model in the presence of the goal of minimizing energy costs. It is at the basis of two approaches to solving the scheduling problem. The first is an approximation algorithm based on the conversion of relaxed solutions into feasible solutions, which is accurate in a particular class of branched networks, typical of rural DWDNs. The second is a LP/NLP branch-and-bound global optimization algorithm adapted to this non-convex problem. This relaxation is also the basis of our contribution to the problem of the design of a pumping station in the class of branched networks. The two-level resolution approach, a stabilized Benders decomposition method exploiting a dominance concept, coordinates the generation of sizing with the evaluation of energy costs for each sizing considered. Finally, in a fourth contribution, we address the combinatorial aspect of the pumping scheduling problem by exploiting a non-compact linear programming model designed by approximation of the head at water towers level which proves remarkably competitive both in term of computational time and quality of the solutions obtained.
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Gratien Bonvin. Contrôle optimal et dimensionnement des stations de pompage dans les réseaux de distribution d'eau potable. Optimisation et contrôle [math.OC]. Université Paris sciences et lettres, 2018. Français. ⟨NNT : 2018PSLEM090⟩. ⟨tel-03283669⟩

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