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Multi-objective optimal dispatching schemes with intelligent algorithms are recognized as effective measures to promote the economics and environmental friendliness of microgrid applications. However, the low accuracy and poor convergence of these algorithms have been challenging for system operators. The bird swarm algorithm (BSA), a new bioheuristic cluster intelligent algorithm, can potentially address these challenges; however, its computational iterative process may fall into a local optimum and result in premature convergence when optimizing small portions of multi-extremum functions. To analyze the impact of a multi-objective economic-environmental dispatching of a microgrid and overcome the aforementioned problems of the BSA, a self-adaptive levy flight strategy-based BSA (LF-BSA) was proposed. It can solve the dispatching problems of microgrid and enhance its dispatching convergence accuracy, stability, and speed, thereby improving its optimization performance. Six typical test functions were used to compare the LF-BSA with three commonly accepted algorithms to verify its excellence. Finally, a typical summer-time daily microgrid scenario under grid-connected operational conditions was simulated. The results proved the feasibility of the proposed LF-BSA, effectiveness of the multiobjective optimization, and necessity of using renewable energy and energy storage in microgrid dispatching optimization. [ABSTRACT FROM AUTHOR]