A serious spatial inequality of educational opportunity in school enrollment persists worldwide. The use of random mechanisms in school allocation might improve spatial equality, with lotteries applied in some choice-based systems. China uses a proximity-based assignment, yet the optimization of spatial equality of educational opportunity by introducing a lottery has received little consideration. To achieve the maximum spatial equality of educational opportunity, in this study, a random proximity-based model was developed, and the swarm optimization method was used to solve the model. A case study in the Shijingshan district of Beijing was used to illustrate the model outputs. For comparison, a proximity-based model was also developed and solved. After introducing a lottery into a proximity-based enrollment system, the spatial disparity of educational opportunity was reduced by 70 percent. The average travel distance to school increased 3.5-fold but was still much less than the actual average distance of 4.3 km. Relaxing the maximum travel distance constraint could significantly improve spatial inequality. Although total equality was significantly improved, only 51 percent of students benefited from increased opportunities, which implies that the model could be adopted in a centralized institutional context, such as China, but might be ineffective in a democratic system.