Unit commitment problem (UCP) is classified as a mixed-integer, large combinatorial, high-dimensional and nonlinear optimization problem. This paper suggests solving the UCP under deterministic and stochastic load demand using a hybrid technique that includes the modified particle swarm optimization (MPSO) along with equilibrium optimizer (EO), termed as MPSO-EO. The proposed approach is tested firstly on 15 benchmark test functions, and then it is implemented to solve the UCP under two test systems. The results are basically compared to that of standard EO and previously applied optimization techniques in solving the UCP. In test system 1, the load demand is deterministic. The proposed technique is in the best three solutions for the 10-unit system with cost savings of 309.95 USD over standard EO and for the 20-unit system it shows the best results over all algorithms in comparison with cost savings of 1951.5 USD over standard EO. In test system 2, the load demand is considered stochastic, and only the 10-unit system is studied. The proposed technique outperforms the standard EO with cost savings of 40.93 USD. The simulation results demonstrate that MPSO-EO has fairly good performance for solving the UCP with significant total operating cost savings compared to standard EO compared with other reported techniques.