A strong P-formulation for global optimization of industrial water-using and treatment networks

Xin Cheng () and Xiang Li ()
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Xin Cheng: Queen’s University
Xiang Li: Queen’s University

Journal of Global Optimization, 2024, vol. 89, issue 2, No 10, 477-507

Abstract: Abstract The problem of finding the optimal flow allocation within an industrial water-using and treatment network can be formulated into nonconvex nonlinear program or nonconvex mixed-integer nonlinear program. The efficiency of global optimization of the nonconvex program relies heavily on the strength of the problem formulation. In this paper, we propose a variant of the commonly used P-formulation, called the P $$^*$$ ∗ -formulation, for the water treatment network (WTN) and the total water network (TWN) that includes water-using and water treatment units. For either type of networks, we prove that the P $$^*$$ ∗ -formulation is at least as strong as the P-formulation under mild bound consistency conditions. We also prove for either type of networks that the P $$^*$$ ∗ -formulation is at least as strong as the split-fraction based formulation (called SF-formulation) under certain bound consistency conditions. The computational study shows that the P $$^*$$ ∗ -formulation significantly outperforms the P- and the SF-formulations. For some problem instances, the P $$^*$$ ∗ -formulation is faster than the other two formulations by several orders of magnitudes.

Keywords: Global optimization; Integrated water networks; Bilinear programming; Pooling problem; Wastewater treatment (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01363-z

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