A two-stage stochastic programming approach for enhancing seismic resilience of water pipe networks

• Published in: Computers & industrial engineering Vol. 207; p. 111266
• Main Authors: Boskabadi, Azam, Kareem, Uthman Abiola, Rosenberger, Jay Michael, Shahandashti, Mohsen, Pudasaini, Binaya
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2025
• Subjects: Linear approximation; Mixed integer nonlinear programming (MINLP); Network optimization; Stochastic programming; Mixed integer nonlinear programming (MINLP); Network optimization; Linear approximation; Stochastic programming
• ISSN: 0360-8352
• DOI: 10.1016/j.cie.2025.111266

•We propose a two-stage stochastic mixed integer nonlinear program (MINLP).•We propose piecewise linear functions to approximate the nonlinearity in MINLP.•We formulate a mixed integer linear program (MILP) to approximate the MINLP.•We introduce a sequential heuristic algorithm.•We show that the sequential algorithm yields a solution within 2 % of optimality. Earthquakes are sudden and inevitable disasters that can cause enormous losses and suffering, and having accessible water is critically important for earthquake victims. To address this challenge, utility managers do preventive procedures on water pipes periodically to withstand future earthquake damage. The existing seismic vulnerability models usually consider simple methods to find the pipes to rehabilitate with highest priority. In this research, we develop an optimization approach to determine which water pipes to rehabilitate subject to a limited budget to achieve a network with highest post-disaster serviceability. We propose a two-stage stochastic mixed integer nonlinear program (MINLP). The MINLP model cannot be solved by commercial optimization software, like BARON, even for problems with a very small number of scenarios. Consequently, we propose piecewise linear functions (PLF) to approximate the nonlinearity in the MINLP. Therefore, we formulate a mixed integer linear program (MILP) to approximate the MINLP. The optimization of the MILP is still challenging to solve, so we introduce a sequential heuristic algorithm to mitigate this computational challenge and find bounds for the approximated optimal solution. We tested this method on multiple water pipe networks based on a standard network from the literature, and we show that the sequential algorithm yields a solution within 2 % of optimality.