The power system with high penetration of wind power is gradually formed, and it would be difficult to determine the optimal economic dispatch (ED) solution in such an environment with significant uncertainties. This paper proposes a multi-objective ED (MuOED) model, in which the expected generation cost (EGC), upside potential (USP), and downside risk (DSR) are simultaneously considered. The heterogeneous indices of upside potential and downside risk mean the potential economic gains and losses brought by high penetration of wind power, respectively. Then, the MuOED model is formulated as a tri-objective optimization problem, which is related to uncertain multi-criteria decision-making against uncertainties. Afterwards, the tri-objective optimization problem is solved by an extreme learning machine (ELM) assisted group search optimizer with multiple producers (GSOMP). Pareto solutions are obtained to reflect the trade-off among the expected generation cost, the upside potential, and the downside risk. And a fuzzy decision-making method is used to choose the final ED solution. Case studies based on the Midwestern US power system verify the effectiveness of the proposed MuOED model and the developed optimization algorithm.