Investigating a Hybrid Approach for Global Optimization of Pump Scheduling Problem
Résumé
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 pressure-flow relations throughout the network results in non-convex Mixed Integer Non-Linear programs (MINLP) that could be particularly hard to solve. The branch-and-check algorithm [1] implemented on top of a commercial linear solver to guarantee the global optimization paradigm for solving such non-convex MINLPs is viable due to convexification of malign constraints. The looseness of convexifications (relaxations) exacerbates the convergence of the optimization process. In response to these caveats, we propose bound tightening and generation of valid inequalities (i.e., cutting planes) at preprocessing stage. This may mitigate the effect of relaxations in form of continuous or nonlinearity, yet potentially too costly. We have proposed a surrogate model to efficiently lower estimate some bounds and a heuristic to control the generation of such cuts.
Domaines
Optimisation et contrôle [math.OC]
Origine : Fichiers produits par l'(les) auteur(s)