The cost of various fuels is increasing gradually in the operation of the electric power production unit, so it is necessary to minimize the cost function to solve this kind of complex economic load dispatch problem. An improved grasshopper optimization algorithm (GOA) based on dynamic penalty factors is proposed to solve the economic load dispatch(ELD) problem and the combined economic emission dispatch(CEED) problem. In order to improve the performance of the GOA, an improved hybrid grasshopper optimization algorithm(HGOA) is proposed. The gravity search operator and pigeon landmark operator are added into the GOA to enhance the search ability of the algorithm, and balance the exploration and development of the algorithm. At the same time, in order to solve the constraints in the ELD and CEED problems, six penalty functions are proposed, including two V-shaped functions, arc tangent functions, arc sine functions, linear functions and the quadratic function, and the dynamic penalty strategy is used to replace the traditional fixed value penalty strategy. Three cases of the ELD problem and four cases of the CEED problem are presented to verify the effectiveness of the proposed method. Experimental results show that the HGOA performs better in terms of the solving quality than other meta-heuristic algorithms, and the dynamic penalty strategy performs better than the fixed value penalty strategy.