Multi-strategy quantum-enhanced RIME algorithm for underdetermined system of equations solution in grounding network corrosion diagnosis

Grounding network corrosion diagnosis is one of the most important safeguards for the security of modern power systems, and establishing corrosion diagnostic equations based on the electrical network theory can support engineers and researchers in analyzing the status of the grounding network. However, solving this complex mathematical model may cause an underdetermined system of equations that is challenging for traditional mathematical methodologies. To address this problem, this paper proposes a Multi-Strategy Quantum-Enhanced RIME Algorithm (Q-ENRIME) to solve the underdetermined system of equations efficiently. Firstly, an adaptive Latin hypercube sampling is utilized to initialize the population to ensure that individuals are uniformly distributed within the search space. Secondly, an adaptive acceptance mechanism based on the Manhattan distance and fitness difference is designed to improve the population diversity and avoid premature convergence during optimization. Finally, a quantum-enhanced local search operator is integrated into Q-ENRIME to fine-tune the exploitation phase and improve the convergence accuracy. To confirm the competitiveness of Q-ENRIME, we conduct numerical experiments in CEC2017, CEC2022, and seven classic engineering problems against eleven representative optimizers. Experimental results and statistical analysis confirm the advantages of Q-ENRIME in convergence accuracy and robustness. Furthermore, Q-ENRIME is successfully applied to solve the underdetermined system of equations in the corrosion diagnosis of the grounding network, which demonstrates its applicability and scalability. The source code of Q-ENRIME can be downloaded at https://github.com/RuiZhong961230/Q-ENRIME.