Hybrid Approaches for Multi-Region Water Pipeline Extension Problems Under Multi-Period Budget Constraints

Declining tap water quality and high application fees tied to connection distance reduce user adoption. To stimulate potential users to apply for top water, authorities can address these issues by providing pipeline extensions and subsidies to applicants. This study develops a multi-period mixed-integer nonlinear programming (MINLP) model to optimize tap-water usage under budget constraints. The model incorporates user willingness based on construction distance, alternative water quality, subsidies, and extension nodes under budget limits. Two hybrid algorithms, integrating the Grey Wolf Optimizer (GWO) and Particle Swarm Optimization (PSO) with optimization techniques, are proposed to optimize construction plans and network structures. These deliver feasible solutions for large-scale network design faster than GAMS/CPLEX, which struggles with large-scale problems, achieving 8.51% better user coverage in small-scale instances. The method enhances the design of water distribution networks and supports efficient rural expansion.