By: Chao Wang ,Ziqiong Wang, Ye Tian, Xingyi Zhang，Senior Member, lEEE, and Jianhua Xiao

Abstract- Due to natural disasters or system failures, the facility has the risk of disruption, and thus improving the location reliability under uneertainty of facilities becomes an important issue. In this paper, we propose a multi-objective facility location problem under uncertainty of facilities, where two objectives on reliability are constructed and multiple coverage with variable radius is imposed to reduce the infuence caused by the facility disruption. A dual-population based evolutionary algorithm is also suggested to address this problem, where one population is for the location optimization and the other population is for the radius optimization. These two populations iteratively exchange the information obtained from elite solutions during the evolution to collaboratively search for the optimal solutions of the problem. The location population provides the high-quality location schemes for radius population in evaluating the quality of radii of each location, whereas the radius population equips the proper radii for location population in determining the good location schemes. Experimental results indicate that the proposed model can effectively improve the location reliability and the proposed method can obtain higher quality optimal solutions in comparison with four state-of-the-art algorithms. Moreover, the proposed method is applied to a real-world facility location with uncertainty of express cabinets in Tianjin, China, and it produces satisfactory location schemes.