Design Water Networks through MINLP Formulation: An Algorithm to Find the Stability Region of Parameters

This paper proposes an iterative algorithm to calculate the stability region of parameters in mixed-integer non-linear programing (MINLP) problems. It is based on a previous algorithm developed for MILP problems with modifications to accelerate the search: (i) initial point is calculated; (ii) search region is bounded by context information; (iii) time limit for iterations is estimated; and (iv) the output is a stability index. The novelties of this research are the first algorithm for MINLP cases and a stability index that recognizes the critical parameters to the resilience of the solution. The proposed algorithm is applied to the water network design, and the stability region is calculated for six parameters. The modifications reduce the implementation time by 96.6% in the case study compared to the referential version. A potential direction for this work is to include a more detailed analysis of the mathematical expressions to make the algorithm faster.

Automated summary

This paper proposes an iterative algorithm to calculate the stability region of parameters in mixed-integer non-linear programing (MINLP) problems. By making several modifications, the algorithm is able to search for critical parameters of the solution more quickly, and it is applied in the context of water network design.