Collaboration among logistics facilities in a multicenter logistics delivery network can significantly improve the utilization of logistics resources through resource sharing including logistics facilities, vehicles, and customer services. This study proposes and tests different resource sharing schemes to solve the optimization problem of a collaborative multicenter logistics delivery network based on resource sharing (CMCLDN-RS). The CMCLDN-RS problem aims to establish a collaborative mechanism of allocating logistics resources in a manner that improves the operational efficiency of a logistics network. A bi-objective optimization model is proposed with consideration of various resource sharing schemes in multiple service periods to minimize the total cost and number of vehicles. An adaptive grid particle swarm optimization (AGPSO) algorithm based on customer clustering is devised to solve the CMCLDN-RS problem and find Pareto optimal solutions. An effective elite iteration and selective endowment mechanism is designed for the algorithm to combine global and local search to improve search capabilities. The solution of CMCLDN-RS guarantees that cost savings are fairly allocated to the collaborative participants through a suitable profit allocation model. Compared with the computation performance of the existing nondominated sorting genetic algorithm-II and multi-objective evolutionary algorithm, AGPSO is more computationally efficient. An empirical case study in Chengdu, China suggests that the proposed collaborative mechanism with resource sharing can effectively reduce total operational costs and number of vehicles, thereby enhancing the operational efficiency of the logistics network.