Comparative analysis of advanced constraint-handling in quantum PSO with differential mutation for optimal power flow

Optimal Power Flow (OPF) is a highly nonlinear and constrained optimization problem that seeks optimal operating conditions while ensuring secure and efficient power system operation. Although metaheuristic algorithms have demonstrated strong global search capability for OPF, their performance is often limited by ineffective constraint handling. This paper presents a systematic investigation of three advanced constraint-handling (CH) techniques, Epsilon (ε) constraint (ECO), Superiority of Feasible Solutions (SFS), and Stochastic Ranking (SRA), when integrated into a unified Quantum-behaved Particle Swarm Optimization with Differential Mutation (QPSODM) framework. The proposed approaches are evaluated on IEEE 30, 57, and 118 bus test systems under multiple OPF objectives, including fuel cost, emission, voltage deviation, and power loss, while considering practical modeling features such as valve-point loading and multi-fuel generation. Statistical significance is assessed using the Wilcoxon signed-rank test complemented by effect size analysis. Numerical results indicate that QPSODM-ECO consistently achieves superior feasibility and convergence behavior, yielding up to 3.8% cost reduction and significantly lower constraint violations compared to SFS and SRA in large-scale systems. SFS exhibits comparable performance in several cases, whereas SRA shows inferior robustness under tight constraints. These findings confirm that the ε-constraint strategy is particularly well suited to quantum-behaved swarm dynamics and highlight the critical role of constraint-handling mechanisms in advanced OPF solvers.