This paper investigates Regional Integrated Energy Systems (RIES), emphasizing the connection of diverse energy supply subsystems to address varied user needs and enhance operational efficiency. A novel low-carbon economic dispatch method, utilizing the multi-objective chaotic artificial hummingbird algorithm, is introduced. The method not only optimizes economic and environmental benefits but also aligns with "carbon peak and carbon neutrality" objectives. The study begins by presenting a comprehensive low-carbon economic dispatch model, followed by the proposal of the multi-objective chaotic artificial hummingbird algorithm, crucial for deriving the Pareto frontier of the low-carbon economic dispatch model. Additionally, we introduce a TOPSIS approach based on combined subjective and objective weights, this approach harnesses the objective data from the Pareto solution set deftly, curbs the subjective biases of dispatchers effectively and facilitates the selection of an optimal system operation plan from the Pareto frontier. Finally, the simulation results highlight the outstanding performance of our method in terms of optimization outcomes, convergence efficiency, and solution diversity. Noteworthy among these results is an 8.8% decrease in system operational economic costs and a 14.2% reduction in carbon emissions.