In this paper, a recently proposed Jaya algorithm is implemented on the economic load dispatch problems (ELDPs). Different from most of the other meta-heuristics, Jaya algorithm needs no algorithm-specific parameters, and only two common parameters are required for effective execution, which makes the implementation simple and effective. Simultaneously, considering the non-convex, non-linear, and non-smooth characteristics of the ELDPs, the multi-population (MP) method is introduced to improve the population diversity. However, the introduction of the MP method adds extra parameters to the Jaya algorithm, hence a self-adaptive strategy is used to cope with the tuning problem for extra parameters. Moreover, to avoid being trapped by local optima, Levy flights distribution is incorporated into the population iteration phase. Finally, Jaya algorithm with self-adaptive multi-population and Levy flights (Jaya-SML) is proposed, it is evaluated by ELDPs with different constraints including power balance constraints, generating capacity limits, ramp rate limits, prohibited operating zones, valve-point effects, and multi-fuel options. The comparisons with state-of-the-art methods indicate that Jaya-SML can generate more competitive results for solving the ELDPs.