As the global climate change problem is getting more and more serious, carbon emission quota allocation is more and more emphasized by countries all over the world, while the traditional carbon quota allocation program has the problem of single objective. In order to improve the scientificity and acceptability of the carbon quota allocation scheme, this paper constructs indicators and forms multiobjective functions to formulate the carbon quota allocation scheme from the three perspectives of efficiency, fairness and sustainability, and builds a multi-objective optimization model for carbon quota allocation and decision support. Aiming at the solution problem of the carbon quota allocation model, an improved hybrid swarm algorithm based on Gaussian perturbation, tournament selection strategy and proposed Newtonian local optimization search operator (L-BFGS) is proposed. The model is used to explore the quota allocation scheme for cities in the Bohai Economic Rim in 2030. In the three single-target pre-allocation schemes based on the principles of efficiency, fairness, and sustainability, the difference between the cities with the largest and smallest quotas is 319 Mt, 289 Mt, and 256 Mt, respectively, which lacks scientificity and rationality. In contrast, the allocation results of the multi-objective pre-allocation scheme proposed by the carbon quota allocation model in this paper are relatively balanced and the difference is small, which can eliminate the conflict between multiple principles.