When contagious diseases hit a city, such as MERS, SARS, and COVID-19, the problem arises as how to assign the limited supermarket resources to urban residential communities for government measures. In this study, in order to solve the assignment problem from supermarket resources to urban residential communities under the situation of the epidemic control, the discrete multi-objective particle swarm algorithm can be improved by introducing some new strategies, and the probability matrix can be used to simulate the many-to-many assignment relationship between residential communities and supermarkets. The ultimate purpose of this research is to achieve an optimal way to balance the two conflicting objectives, i.e. minimization of the cross-infection risk and maximization of the service coverage rate. Also, the optimization considers the accessible distance limit and the service capacity constraints of supermarkets for the feasible scheme. For this aim, we redefine the subtraction operator, add operator and multiply operator to generate the Pareto optimal solutions, and introduce a new study strategy based on the idea of differential evolution in the particle swarm algorithm (PSO-DE). In this work, we take the COVID-19 epidemic outbreak in Wuhan city of China as an example in the experiment. The simulation results are compared with the Genetic Algorithm (GA), Simulated Annealing (SA), Ant Colony Algorithm (ACO) and the Particle Swarm Optimization with Roulette Wheel Selection (PSO-R), and these results have been shown that the algorithm PSO-DE proposed in this work has a better optimization performance in both objectives.