Rotational gate based quantum particle swarm optimization for benchmark suites and combined economic emission dispatch

Abstract This paper introduces a rotational quantum particle swarm optimizer (RQPSO) that updates particles via quantum rotation–gate dynamics on a compact phase representation. Real-valued amplitudes decoded from phases are mapped feasibly by construction into the decision space, removing the need for bound repair. Lightweight π -flip perturbations and brief stagnation-triggered reseeding sustain diversity, and a short local polish consolidates the incumbent near termination. RQPSO is benchmarked against Particle Swarm Optimization (PSO), Quantum Particle Swarm Optimization (QPSO), Grey Wolf Optimizer (GWO), Mayfly Algorithm (MA), self-adaptive Differential Evolution (jDE), and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) under a common protocol of 3000 function evaluations with 30 independent runs per problem. Reporting uses median [interquartile range (IQR)] as the primary statistic with Friedman/Nemenyi global tests and Holm-corrected Wilcoxon pairwise tests; effect sizes are summarized by Cliff’s δ . Experiments cover 23 classical functions and 10 CEC-2019 functions. On the classical suite, RQPSO attains the best or tied-best median on a majority of functions and achieves a leading global rank under the fixed budget. On CEC-2019, it records three best medians (including one tie) and a top mean rank; post-hoc tests show significant gains over MA and jDE and broadly comparable performance to PSO, QPSO, GWO, and CMA-ES. A combined economic–emission dispatch (CEED) study on a six-unit system with cubic cost and emission models further demonstrates budget-efficient performance. The RQPSO attains the lowest mean operating cost and the smallest dispersion at all loads versus PSO and QPSO. A percentage-recovery repair enforces generator limits and power balance without penalty functions by proportionally rescaling outputs. Together, the rotation-gate updates, feasibility-preserving decoding, and proportional repair provide a robust alternative to classical swarms for both benchmark and power-system optimization under tight evaluation budgets. The source code of RQPSO is publicly available at: (https://github.com/Naagdant/rotational-quantum-pso)