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A novel culture evolution learning is presented to achieve an optimal carbon-energy combined-flow (OCECF). A shared responsibility of carbon emission between electricity producers and electricity consumers is introduced in OCECF, such that a double counting of carbon emission can be eliminated. The proposed algorithm is inspired from the culture construction, culture communication, and cultural inheritance in the human society. First, a culture matrix of each country is constructed by the Q-value matrix of Q-learning, which can be simultaneously updated by its people. Second, each country can learn the superior culture from other more-advanced countries, while this so-called culture communication can improve the quality of the obtained optimal solution. Finally, the culture inheritance can be achieved by transfer learning between different optimization tasks, thus the convergence can be dramatically accelerated. The performance of CEA has been evaluated for OCECF on two IEEE benchmark systems, and a practical urban power grid of southern China, respectively. Simulation results demonstrate that CEA has a high convergence stability and fast convergence, which is around 4.02 to 51.43 times faster than that of conventional heuristic algorithms.