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This paper presents a novel method for solving the unit commitment (UC) problem based on quantum-inspired evolutionary algorithm (QEA). The proposed method applies QEA to handle the unit-scheduling problem and the Lambda-iteration technique to solve the economic dispatch problem. The QEA method is based on the concept and principles of quantum computing, such as quantum bits, quantum gates and superposition of states. QEA employs quantum bit representation, which has better population diversity compared with other representations used in evolutionary algorithms, and uses quantum gate to drive the population towards the best solution. The mechanism of QEA can inherently treat the balance between exploration and exploitation and also achieve better quality of solutions, even with a small population. The proposed method is applied to systems with the number of generating units in the range of 10 to 100 in a 24-hour scheduling horizon and is compared to conventional methods in the literature. Moreover, the proposed method is extended to solve a large-scale UC problem in which 100 units are scheduled over a seven-day horizon with unit ramp-rate limits considered. The application studies have demonstrated the superior performance and feasibility of the proposed algorithm.