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A novel real-parameter optimisation algorithm called the 'real-parameter quantum evolutionary algorithm' is presented. The algorithm pieces together the ideas from evolutionary algorithms (EA) and quantum computing to provide a robust optimisation technique that can be utilised to optimise highly constrained non-linear real-parameter functions. Quantum bits have immense representational power due to their being in superposition of all the basic states at the same time. New quantum operators designed in this work enable the search to effectively handle the twin objectives of exploitation and exploration. This enables the search to be pursued with small population sizes, thereby speeding up the search process and also ensuring that there is no problem of premature convergence that often plagues pure EA implementations. The power of the proposed algorithm is demonstrated by solving the economic load dispatch (ELD) in power systems. ELD is to find the optimal loadings on the generators so as to achieve minimum operating cost while satisfying various system and unit-level constraints. The proposed method has been applied to standard load dispatch problems reported in the literature including the IEEE 30 bus system, IEEE 57 bus system and a 110-generator problem, and its performance has been compared with the results obtained by other methods. The results adequately demonstrate the enhanced search power of the proposed algorithm in terms of obtaining better solutions and provide motivation for its application to other real-parameter optimisation problems in power systems.