The task of deploying an energy-conscious wireless sensor networks (WSNs) is challenging. One of the most effective methods for conserving WSNs energy is clustering. The deployed sensors are divided into groups by the clustering algorithm, and each group's cluster head (CH) is chosen to gather and combine data from other sensors in the group. Mobile Wireless Sensor Networks, which enable moving the sink node, aid in reducing energy consumption. Thus, this paper introduces an energy efficient clustering algorithm and optimized path for a mobile sink using a swarm intelligence algorithms. The Chaotic Grey Wolf Optimization (CGWO) approach is used to form clusters and identify CHs. While utilizing the Slime Mould Algorithm (SMA) for determining the shortest path between a mobile sink and CHs. The effectiveness of the suggested routing strategy is evaluated against that of other current, cutting-edge protocols. The findings demonstrate that in terms of overall energy consumption and network lifetime, the suggested algorithm performs better than others. While for stability period the proposed algorithm outperforms three of compared algorithms and was close to the fourth.