Researchers are increasingly focusing on renewable energy due to its high reliability, energy independence, efficiency, and environmental benefits. This paper introduces a novel multi-objective framework for the short-term scheduling of microgrids (MGs), which addresses the conflicting objectives of minimizing operating expenses and reducing pollution emissions. The core contribution is the development of the Chaotic Self-Adaptive Sine Cosine Algorithm (CSASCA). This algorithm generates Pareto optimal solutions simultaneously, effectively balancing cost reduction and emission mitigation. The problem is formulated as a complex multi-objective optimization task with goals of cost reduction and environmental protection. To enhance decision-making within the algorithm, fuzzy logic is incorporated. The performance of CSASCA is evaluated across three scenarios: (1) PV and wind units operating at full power, (2) all units operating within specified limits with unrestricted utility power exchange, and (3) microgrid operation using only non-zero-emission energy sources. This third scenario highlights the algorithm's efficacy in a challenging context not covered in prior research. Simulation results from these scenarios are compared with traditional Sine Cosine Algorithm (SCA) and other recent optimization methods using three test examples. The innovation of CSASCA lies in its chaotic self-adaptive mechanisms, which significantly enhance optimization performance. The integration of these mechanisms results in superior solutions for operation cost, emissions, and execution time. Specifically, CSASCA achieves optimal values of 590.45 €ct for cost and 337.28 kg for emissions in the first scenario, 98.203 €ct for cost and 406.204 kg for emissions in the second scenario, and 95.38 €ct for cost and 982.173 kg for emissions in the third scenario. Overall, CSASCA outperforms traditional SCA by offering enhanced exploration, improved convergence, effective constraint handling, and reduced parameter sensitivity, making it a powerful tool for solving multi-objective optimization problems like microgrid scheduling.