Strengthening Mathematical Formulation for Global Optimization of the Operational Water Network Distribution
Abstract
Pump scheduling is a decision-making problem in water distribution networks. The aim is to plan the pumping operations to minimize the energy cost over the day ahead. Modelling the binary status of the pumps and the nonconvex head-flow relations throughout the network results in nonconvex Mixed Integer Nonlinear programs (MINLP) that could be particularly hard to solve. The branch-and-check algorithm implemented on top of a commercial linear solver to guarantee the global optimization paradigm is viable due to convexification of malign constraints. The looseness of convexifications exacerbates the convergence of the optimization process. In response to these caveats, we propose a tailored bound tightening and generation of valid inequalities at the preprocessing stage. The promising computational results over a set of benchmarks indicate the effectiveness of our approach.
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