Optimal Distribution Feeder Reconfiguration Based on a Chu and Beasley Genetic Algorithm with an MST-Constrained Search Space to Ensure Radiality

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The optimal reconfiguration of electrical distribution feeders is a fundamental strategy for reducing active power losses and improving voltage profiles, yet it remains a challenging mixed-integer nonlinear programming (MINLP) problem due to the combinatorial explosion of radial topologies and the nonlinearities introduced by power flow equations. This paper proposes a novel master–slave methodology that integrates a Chu and Beasley genetic algorithm (CBGA) with a minimum spanning tree (MST)-based repair mechanism to address these challenges. In the master stage, the CBGA explores the binary space of switching decisions via steady-state population management, duplicate elimination, and stagnation restart policies. A key contribution lies in the MST-based repair procedure, which ensures that every individual generated by crossover and mutation is projected onto a feasible radial and connected configuration, effectively confining the search to the constrained solution space without recourse to penalty functions. A systematic weight-design rule preserves the Hamming distance between infeasible offspring and repaired solutions, minimizing the distortion of genetic information. The slave stage evaluates each candidate topology using a successive approximations power flow solver, assessing electrical feasibility and computing active power losses. The proposed methodology is validated on multiple test feeders, ranging from small 9- and 24-bus networks to large-scale benchmarks including 33-, 69-, 84-, 136-, and 415-bus systems. A comparison against the deterministic sequential switch opening method (SSOM) and a specialized tabu search demonstrates that the CBGA-MST consistently matches the best-known optima in the literature, achieving loss reductions of up to 9.63% compared to SSOM on the 415-bus system. A statistical analysis over 100 independent runs confirms the algorithm’s robustness, with zero standard deviation for networks of up to 69 buses and a standard deviation of only 2.99 kW (0.51%) for the 415-bus system. The findings confirm that the proposed approach offers superior scalability, robustness, and solution quality, positioning it as a practical and effective tool for distribution system operators seeking to enhance network efficiency under peak load conditions.

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