Table 1: The main symbols.

S T 𝑖 The 𝑖 th subtree of the tree of the H-WSNs
𝑁 S T 𝑜 The number of the sensor nodes in S T 𝑖
𝑃 S T 𝑠 The state information of all the nodes in S T 𝑖
𝑛 𝑠 One of the source nodes in S T 𝑖
𝑛 𝑟 The root node (macronode) in S T 𝑖
𝑃 ( 𝑠 , 𝑟 ) The set of all the possible paths between 𝑛 𝑠 and 𝑛 𝑟 in S T 𝑖
𝑝 𝑖 ( 𝑠 , 𝑟 ) The 𝑖 th path between 𝑛 𝑠 and 𝑛 𝑟 in S T 𝑖
𝑛 f a i l The failed relay node of 𝑝 𝑖 ( 𝑠 , 𝑟 ) in S T 𝑖
𝑛 f a i l 𝑐 The child node of 𝑛 f a i l of 𝑝 𝑖 ( 𝑠 , 𝑟 ) in S T 𝑖
𝑛 f a i l 𝑝 The parent node of 𝑛 f a i l of 𝑝 𝑖 ( 𝑠 , 𝑟 ) in S T 𝑖
𝑛 𝑖 The 𝑖 th sensor node of 𝑝 𝑖 ( 𝑠 , 𝑟 ) in S T 𝑖
𝑝 𝑏 The optimal path of 𝑃 ( 𝑠 , 𝑟 ) with optimal fitness in S T 𝑖
𝑛 𝑝 𝑏 𝑖 The 𝑖 th sensor node of 𝑝 𝑏 in S T 𝑖