Energy conservation is becoming the main critical issue in wireless sensor network and also the main research area for most of the researchers. For improving the energy efficiency, sink mobility is used with constrain path in wireless sensor network. In order to solve these optimization problems, inter cluster Ant Colony Optimization Algorithm (ACO) is used with mobile sink (MS) and rendezvous nodes (RN). The proposed algorithm will improve 30% more network lifetime than the existing algorithm and prompts high accurate delivery of packets in highly dense network.