<b>A Pareto-Frontier Approach to Topology Optimisation of Multi-Source Water-Distribution Networks: Comparing Looped, Minimum Spanning Tree and Hybrid Configurations under Cost, Pressure-Margin and Resilience</b>

This paper developed a multi-objective optimization framework for the topology design of a multi-source water-distribution network, comparing the Looped, Minimum-Spanning-Tree (MST) and intermediate Hybrid (MST+k) configurations on three competing criteria: construction cost, pressure margin and resilience. A greedy graph-augmentation algorithm is proposed that starts from the MST and adds k loop-closing edges, with each new edge chosen to maximally contract the tree-distance between its endpoints relative to its Euclidean length. Each added edge provably creates the largest available fundamental cycle per unit cost, and the algorithm requires only K+1 hydraulic evaluations to trace a nested, one-parameter family of feasible topologies approximating the cost resilience Pareto frontier two to three orders of magnitude fewer network simulations than population-based evolutionary methods. The framework is applied to the proposed water network of Modibbo Adama University, Yola (11 reservoirs, 71 junctions, parent graph of 411 candidate edges). Seventeen topologies were evaluated end-to-end with the EPANET 2.2 global-gradient solver: the pure MST (81 edges, NGN 17.3 million, 35 per cent single-pipe survival), 15 hybrid configurations (k = 1 to k = 60), and the fully-looped reference (411 edges, NGN 367 million). Sixteen of the seventeen are Pareto-efficient, and all sampled reliability estimates are reported with 95 per cent Wilson confidence intervals. A weighted-sum analysis under three decision-maker preference schemes (cost-focused, balanced, resilience-focused), validated by entropy weighting and by a stochastic exploration of the entire weight simplex, identifies MST+30 as the robust budget-efficient compromise design, providing 88 per cent single-pipe survival, a 16.8-m pressure margin and a Todini resilience index of 0.481 at a cost of NGN 41.8 million, or about 12 per cent of the fully-looped reference cost. The counter-intuitive decline of the Todini index with loop density is cross-validated with the structural meshedness coefficient. The framework is general purpose and transferable to any multi-source pressurised distribution network.