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This study addresses the problem of cost-optimal expansion planning for rural radial distribution networks via a mixed-integer nonlinear programming (MINLP) formulation that jointly determines feeder routing and conductor type selection. The developed method was evaluated using standard 9-node and 25-node test networks, with performance benchmarked against minimum spanning tree (MST)-based procedures and two metaheuristic techniques (sine-cosine algorithm and tabu search). The application of the MINLP approach led to significant reductions in overall expenditure. In the 9-node test case, the total cost was reduced from USD 131,819.33 (obtained via MST-TSA) to USD 77,129.34, resulting in savings of USD 54,689.99, equivalent to 41.48%. Energy loss costs alone decreased from USD 111,746.73 to USD 63,764.12, a drop of USD 47,982.61 or 42.94%. In the 25-node network, overall costs fell by more than 65%, from USD 371,516.59 to USD 128,974.72, while energy loss expenses decreased by USD 210,057.16 (61.06%). Although conductor-related capital expenditure increased under the MINLP solution, the strategy generated significant long-run economic benefits by markedly reducing operating expenses. In contrast to conventional strategies that address topology definition and conductor sizing in separate stages, the proposed framework integrates these decisions, thereby ensuring globally optimal configurations. These outcomes highlight the method’s ability to scale and its practical value for strategic, long-horizon planning in sophisticated distribution grids. All numerical experiments were conducted in Julia (v1.10.2), leveraging JuMP (v1.21.1) together with the BONMIN solver.

This research proposes a novel, low-power routing protocol tailored for IoT networks that merges intelligent data-aggregation clustering with optimized path selection to overcome critical data-handling challenges in smart urban environments. The protocol relies on a layered architecture that includes Data Fusion Heads (DFH), intermediate relay DFHs, and the marine predators algorithm—an effective nature-inspired optimizer equipped with a purpose-built fitness function. This function simultaneously refines multiple criteria: the geographic clustering density of Sensor Nodes (SNs) inside each data fusion group (DFG), the total hop distance toward the sink, intra-group node proximity, residual battery level (RE), Average Scale of Building Occlusions (ASBO), and the rotation interval of the Primary DFH (PDFH). One of the protocol’s core advancements is the systematic application of in-network data fusion, which drastically reduces duplicate packet forwarding and markedly improves the accuracy and usefulness of collected information across all DFGs. By aggregating readings from multiple sensors, the volume of outbound traffic is greatly reduced, yielding substantial improvements in energy efficiency. Two complementary forwarding strategies are supported: single-hop forwarding, where already fused payloads travel directly to the sink, and multi-hop forwarding, in which an appropriate PDF relay is dynamically elected using a weighted relay selection metric that incorporates remaining energy (RE), sink distance, and ASBO. By integrating robust fault-tolerance procedures, intelligent redundancy elimination, and efficient fusion mechanisms, the protocol achieves markedly greater dependability and sustains strong operation under adverse or unpredictable network conditions. Detailed simulation experiments, along with side-by-side benchmarking against contemporary methods, confirm the protocol’s clear advantage across essential performance indicators—namely, network longevity, total energy expenditure, data throughput, and mean end-to-end latency. Compared with leading recent approaches such as the Particle Swarm Optimization-based energy-efficient clustering protocol (PSO-EEC), linearly decreasing inertia weight PSO (LDIWPSO), Optimized Fuzzy Clustering Algorithm (OFCA), and Novel PSO-based Protocol (NPSOP), the presented solution delivers outstanding gains. Concretely, network lifetime is prolonged by 299% versus PSO-EEC, 264% versus LDIWPSO, 306% versus OFCA, and 249% versus NPSOP. Energy usage drops by 254% relative to PSO-EEC, 264% relative to LDIWPSO, 247% relative to OFCA, and 253% relative to NPSOP. Throughput rises by 67% over PSO-EEC, 59% over LDIWPSO, 53% over OFCA, and 50% over NPSOP. By skillfully combining data aggregation with carefully tuned routing decisions, this protocol establishes a new benchmark for power-efficient organization and communication within IoT-based data fusion groups, delivering a dependable and adaptable framework suitable for diverse smart-city and IoT scenarios.