<p>This paper proposes a novel physics-based metaheuristic algorithm, the quantum fluctuation optimizer (QFO), inspired by quantum mechanics. Inspired by the Heisenberg Uncertainty principle, a quantum fluctuation phase is introduced, allowing quantum search in the global space. The exploitation phase simulates the behavior of particle wave function passing through classically forbidden region and draws on the concept of Schrödinger’s cat to propose quantum tunneling and quantum superposition stages. Furthermore, based on the theory of cosmic inflation, a fluctuation factor is designed to control quantum transitions between the quantum fluctuation and quantum tunneling stages, achieving a balance between exploration and exploitation phases. To validate the effectiveness of QFO, the convergence behavior, the balance between exploration and exploitation, and parameter sensitivity of QFO are analyzed using the CEC2005, CEC2017, and CEC2020 benchmark suites. To verify the performance of QFO, it is compared with 15 metaheuristic algorithms using the CEC2017 and CEC2022 benchmark suites. The results show that QFO is an effective algorithm, outperforming most of the comparison algorithms. To validate the capability of QFO in solving constrained engineering problems, it is applied to five standard engineering problems. Lastly, QFO is used to optimize the hyperparameters of temporal convolutional neural network (TCN) for establishing photovoltaic power forecasting model. The results indicate that the TCN model based on QFO achieves high forecast accuracy, with R² = 0.9398, RMSE = 2.6798, and MAE = 1.2422. Therefore, QFO effectively addresses constrained engineering problems and practical engineering problems. The source code for QFO is publicly available on <a href="https://github.com/yylcsuft/QFO">https://github.com/yylcsuft/QFO</a>.</p>