The economic dispatch of power has evolved, shifting focus from cost optimization to prioritizing emission reduction from traditional fossil-fueled generators. Utilities now integrate renewable energy sources (RES) to mitigate emissions and address fossil fuel depletion. This paper introduces a social network search (SNS) algorithm tailored to address dynamic dispatch challenges in microgrids, with a specific focus on integrating RES such as solar and wind power. Through the analysis of four distinct test cases, the efficiency of the proposed SNS algorithm is rigorously demonstrated. Initially, the study addresses economic load dispatch (ELD), emission dispatch (EMD), and combined economic and emission dispatch (CEED) within an isolated microgrid setting, emphasizing RES integration. Subsequently, a comparative analysis of two CEED methods, penalty price factor (PPF) and fractional programming (FP), is conducted to determine optimal strategies for minimizing generation costs and emissions. Further exploration in test cases 3 and 4 examines the SNS algorithm's effectiveness in tackling complex and non-convex dynamic dispatch problems by incorporating valve point loading (VPL) effects and ramp rate constraints. The results underscore the positive impact of RES integration on microgrid management and emissions reduction. Notably, RES integration leads to a 5.25% and 5.33% reduction in generation costs for ELD and CEED, respectively, alongside a 5.62% decrease in emissions. Moreover, the results highlight the advantages of the FP method in minimizing pollutant emissions and PPF in minimizing generation costs. Additionally, the simulation and statistical analyses demonstrate that the proposed SNS algorithm consistently yields high-quality solutions, surpassing other implemented and reported algorithms.