Unit commitment is an intractable issue aiming to reduce the overall economic cost of power system operation while maintaining the system constraints. Due to the emerging scenario of global warming, many countries are vigorously developing renewable energy to replace the traditional fossil power plant, in order to reduce the environmental and carbon emission. The increasing penetration of renewable generation significantly challenge the economic and security of power system operation. In this paper, a low carbon multi-objective objective unit commitment model considering economic cost, environmental cost and, more importantly, the carbon emission is established, integrating wind and solar power and therefore generating a multi-objective, high-dimensional, strong non-linear, multi-constraint and mixed integer optimization problem. The non-dominated sorting genetic algorithm-III is tailored and adopted for solving the proposed challenging task, where the decision-making scheme is designed according to the normalization method and weighted sum function. Numerical results show that the proposed complex many-objective low carbon unit commitment model can be successfully solved by the proposed algorithm and the carbon emission is effectively reduced by the integration of renewable generations.