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The dynamic economic dispatch problem is a high-dimensional complex constrained optimization problem that determines the optimal generation from a number of generating units by minimizing the fuel cost. Over the last few decades, a number of solution approaches, including evolutionary algorithms, have been developed to solve this problem. However, the performance of evolutionary algorithms is highly dependent on a number of factors, such as the control parameters, diversity of the population, and constraint-handling procedure used. In this paper, a self-adaptive differential evolution and a real-coded genetic algorithm are proposed to solve the dynamic dispatch problem. In the algorithm design, a new heuristic technique is introduced to guide infeasible solutions towards the feasible space. Moreover, a constraint-handling mechanism, a dynamic relaxation for equality constraints, and a diversity mechanism are applied to improve the performance of the algorithms. The effectiveness of the proposed approaches is demonstrated on a number of dynamic economic dispatch problems for a cycle of 24 h. Their simulation results are compared with each other and state-of-the-art algorithms, which reveals that the proposed method has merit in terms of solution quality and reliability. [ABSTRACT FROM AUTHOR]