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Résumé :
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The generalized pooling problem is a generic way of identifying a topology containing sources nodes, intermediate storage tanks, and sinks when monitoring specific stream qualities is imperative. One important application domain of the generalized pooling problem is wastewater treatment. Choosing among the wide array of available wastewater treatment technologies is a combinatorially complex optimization problem that requires nonconvex terms to monitor regulated stream qualities about a treatment plant. In this work, we address five instantiations of the generalized pooling problem to global optimality by introducing (i) a quadratically constrained MINLP model formulation that reduces the number of bilinear terms, (ii) novel piecewise underestimation methods for the nonconvex bilinear terms to tighten the relaxation [Gounaris et al. Ind. Eng. Chem. Res. 2009, 48, 5742−5766; Wicaksono and Karimi AIChE J. 2008, 54, 991−1008], and (iii) a branch-and-bound algorithm suited to address the combinatorial complexity of the problem. Extensive computational results are presented for small, medium, large, and two very large-scale case studies which feature 48, 300, 675, and 1260 distinct bilinear terms, respectively. We show that the small, medium, and large case studies can be solved to global optimality efficiently. The two very large case studies can be solved within 0.9% and 2.3% of the global optimum, and when the additional assumption of a limited number of plants is introduced, they can be solved to global optimality.
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