Bi-objective design-for-control of water distribution networks with global bounds

Abstract

This manuscript investigates the design-for-control (DfC) problem of minimizing pressure induced leakage and maximizing resilience in existing water distribution networks. The problem consists in simultaneously selecting locations for the installation of new valves and/or pipes, and optimizing valve control settings. This results in a challenging optimization problem belonging to the class of non-convex bi-objective mixed-integer non-linear programs (BOMINLP). In this manuscript, we propose and investigate a method to approximate the non-dominated set of the DfC problem with guarantees of global non-dominance. The BOMINLP is first scalarized using the method of $$\epsilon $$ ϵ -constraints. Feasible solutions with global optimality bounds are then computed for the resulting sequence of single-objective mixed-integer non-linear programs, using a tailored spatial branch-and-bound (sBB) method. In particular, we propose an equivalent reformulation of the non-linear resilience objective function to enable the computation of global optimality bounds. We show that our approach returns a set of potentially non-dominated solutions along with guarantees of their non-dominance in the form of a superset of the true non-dominated set of the BOMINLP. Finally, we evaluate the method on two case study networks and show that the tailored sBB method outperforms state-of-the-art global optimization solvers.

Optimization-Based Selection of Hydrants and Valves Control in Water Distribution Networks for Fire Incidents Management

“…Next, the tightened variable bounds and the relaxed constraints are used along with the method of ε-constraints ( [38]), as well as the solutions obtained with the heuristic, for the calculation of a superset of the Pareto front of OFH. The use of the ε-constraints method for the calculation of supersets of Pareto fronts for biobjective MINLPs has been previously presented by Ulusoy et al [39]. In our case, this is achieved by formulating and solving the MIP,…”

On the exactness of the ε-constraint method for biobjective nonlinear integer programming

“…This is partly due to the fact that MOIPs represent a flexible tool to model real-world applications. Such models appear in works on finance, management, transportation, design of water distribution networks, biology [15,20,21,22,23]. MOIPs are intrinsically nonconvex, implying that the design of exact and efficient solution methods is particularly challenging and requires global optimization techniques [11].…”

Heuristic-Based Approach for Near-Optimal Response to Water Distribution Network Failures in Near Real Time

“…Therefore, in this study, the results of the proposed heuristic-based method have been compared with the results of the widely used NSGA II method. Having said this, other mathematical optimization methods could have been used for the comparison instead of the NSGA II, as these methods have also proven to be effective in dealing with the issues of nonlinearity and discrete nature of decision variables present in the control and operation of water supply systems (e.g., Pecci et al 2019Pecci et al , 2021Ulusoy et al 2021). However, this is beyond the scope of present work, and a robust comparison of different mathematical and other optimization methods with the heuristic-based method proposed here is recommended for future work.…”