Heat and power have become the most indispensable resources. However, the traditional ways of generating power and heat are inefficient and cause high pollution; a CHP (Combined Heat and Power) unit can solve these problems well. In recent years, more attention has been paid to energy conservation and environmental protection, and Combined Heat and Power Economic Emission Dispatch (CHPEED) has become an important multi-objective optimization problem. In this paper, an Indicator & crowding Distance-based Evolutionary Algorithm (IDBEA) is put forward for handling this non-convex and non-linear problem. With consideration of the valve-point effects and power transmission loss, IDBEA is tested on three standard test systems with different types, including four units, five units and seven units. In the experiment, IDBEA is compared with several evolutionary algorithms, the simulation results demonstrate that IDBEA has strong stability and superiority, while the solutions show better convergence and diversity than several typical algorithms.