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Since the implementation of China's clean heating plan in 2017, the progress of natural gas replacing coal for heating is still not ideal. With the proposal of the goal of carbon neutralization and the impact of international war, the price, supply, and demand of natural gas have attracted attention. In case of gas shortage, reasonable schemes are required to be allocated to different industries and categories. Therefore, this research divides the gas field into four levels according to the social utility, and establishes the multi-objective distribution optimization model considering the social and economic benefits. The solution of the model is based on genetic algorithm and realized on MATLAB. Multi-objective optimization strategies and several constraints are used to make the algorithm's process of the search is continuously moving closer to the Pareto optimal front. Taking Beijing as an example, two scenarios are set to simulate and optimize, so as to verify the optimization effect of the model. Better quantitative results are created after reallocation of natural gas. The ideal scenario realizes 5.64% more social benefits than 2019 through additional allocation of 117.288 million cubic meters of reserve gas. The constraint scenario creates 0.67% more social benefits with only 0.07% decrease of the economic benefits. The conclusions show that allocating more gas to three main industries can improve the optimization effect and it is necessary to expand the supply of natural gas reserve volume. This paper provides a new perspective of natural gas allocation category and priority, providing theoretical and practical ideas for the planning of natural gas security emergency plan and the development of gas sales plan. [ABSTRACT FROM AUTHOR]