A heuristic metric is presented to achieve the optimal connected set covering problem （SCP） in sensor networks. The coverage solution with the energy efficiency can guarantee that all targets are fully covered. Among targets, the crucial ones are redundantly covered to ensure more reliable monitors. And the information collected by the above coverage solution can be transmitted to Sink by the connected data-gathering structure. A novel ant colony optimization （ACO） algorithm--improved-MMAS-ACS-hybrid algorithm （IMAH） is adopted to achieve the above metric. Based on the design of the heuristic factor, artificial ants can adaptively detect the coverage and energy status of sensor networks and find the low-energy-cost paths to keep the communication connectivity to Sink. By introducing the pheromone-judgment-factor and the evaluation function to the pheromone updating rule, the pheromone trail on the global-best solution is enhanced, while avoiding the premature stagnation. Finally, the energy efficiency set can be obtained with high coverage-efficiency to all targets and reliable connectivity to Sink and the lifetime of the connected coverage set is prolonged.
