The network reconfiguration technique has been used to reduce network losses, balance transformer loading, and restore the power supply of the outage area in distribution networks. With a large number of uncontrollable distributed generators (DGs) added to distribution networks, the reconfiguration technique can be applied to enhance the available delivery capability (ADC) of distribution networks. This paper presents a two-stage methodology for determining optimal network topologies for improving the ADC of distribution networks for supporting more renewable energies. The first stage is a group-based binary particles swarm optimization (BPSO), which takes advantage of the BPSO's global capability while improving its slowness in finding optimal solutions. The second stage is a hybrid of greedy-based and domain-knowledge-based methods. When applied to multiple scenarios of DGs, the proposed methodology can effectively deal with the uncertainty of the DGs' outputs and time-varying loading conditions. As a byproduct, the optimal network topology found by the proposed methodology also decreases the network power losses due to the increase of the ADC of the distribution networks. The IEEE 123-bus test network and a practical 1001-node distribution network are used to verify the proposed methodology, and the numerical studies demonstrate the effectiveness of the proposed methodology in greatly increasing the ADC via optimal network reconfigurations.