In power generation system, the economic dispatch (ED) is used to allocate the real power output of thermal generating units to meet required load demand so as their total operating cost is minimized while satisfying all units and system constraints. This paper proposes a novel swarm based meanvariance mapping optimization (MVMOS) for solving the ED problem with the cubic fuel cost function. The special feature of the proposed algorithm is a mapping function applied for the mutation based on the mean and variance of nbest population. This method has been tested on 3, 5 and 26 units and the obtained results are compared to those from genetic algorithm (GA), particle swarm optimization (PSO) and firefly algorithm (FA). Test results have indicated that the proposed method is efficient for solving the ED problem with cubic fuel cost function. © Springer International Publishing Switzerland 2015.