## 1 Introduction
### The Lifetime Problem  
In the case of WSN-equipped communicating materials, to keep these functionalities as long as possible, one must pay attention to the inner network lifetime. This problem is a well-known issue in the network domain, and many authors tried to address it via different strategies, all leading to an energy-efficient WSN, as listed in Figure 2.  
Figure 1: Example of communicating material. Since lifetime is inversely proportional to energy consumption, a classic strategy is to reduce energy consumption while guaranteeing the network quality of service. For example, sustainability is discussed and frameworks are exposed for the following specific applications: in environmental monitoring [4], in smart city control [5], or in civil infrastructure construction and maintenance [6]. As depicted in Figure 2, some mechanisms are directly linked to the node hardware optimization like directional antennas or energy harvesting implementation (radio optimization or battery repletion) [7]. Others are linked to the communication protocols used in the network (sleep/wake-up schemes [8], energy-efficient routing [9; 10]) or to the data reduction techniques (aggregation, compression, etc.) used to gather information. Protocol techniques could be grouped into the \"software\" solutions, as opposed to the first one, which is more related to the \"hardware\" on the wireless nodes. Since software techniques are designed to optimize communications between nodes in the wireless network, and since the communicating material's lifetime is directly linked to the lifetime of each of them, the rest of this article is focused on this type of technique. Dynamically, through time, it may be necessary to reconfigure the wireless sensor network, in terms of routing, in various cases of disturbances from the network control system (e.g., changes in data collection requirements, network congestion, low node energy levels, or node failure) [9]. Our illustrative example is the following: suppose a communicating concrete be composed of four CNs, each linked to two SNs, its initial routing structure corresponding to the \"initialization\" phase in Figure 3, where data, represented by orange squares, are transmitted, and collected from left to right. The last CN (called a sink) then transmits all these data to the cloud. During this phase, each node's energy consumption is directly related to the amount of data it receives or sends. The closer the node is to the sink, the more data it handles and so the more energy it consumes, resulting in uneven energy levels. When this energy level reaches a certain threshold, a problem is then detected (\"problem detection\" phase in Figure 3) and a reconfiguration must be applied, modifying the initial routing of the embedded WSN (\"reconfiguration\" phase in Figure 3). A change in the operation (or a reconfiguration) of the network can be decided if a long-term energy imbalance is observed or if heterogeneous consumption among the wireless sensor nodes reveals a particular weakness, potentially leading to network failures. To decide whether a reconfiguration is needed, two good criteria can be considered, as follows: the first one is \(\sum_{E}\), the mean of all energy consumptions of each node \(N_{i}\), with \(i\) evolving from 1 to \(N\) being the total number of nodes in the network. This criterion gives an insight into the average node consumption. A second criterion is \(\sigma_{E}\), the standard deviation of the energy consumption of each node \(N_{i}\), which gives information about the repartition of energy consumption in the network. Indeed, some nodes could consume a lot more  
Figure 2: Classification of WSN energy efficient mechanisms [3]. energy than others. Multiplying these two terms ensures that both are optimized together.