# Optimal Arrangement Strategy of IoT Sensors in Urban Drainage Networks: A Review
## 3 Arrangement of IoT Sensors in the Drainage Network
### Optimization of Monitoring Point Locations
#### 3.3.2 Design Evaluation Methods Based on Information Theory  
Information theory can also be used for the design evaluation of optimized sensor layouts. Entropy is defined as a reduction in the uncertainty of a random variable X [68] in information theory. When a signal is observed, the amount of information obtained indirectly measures the reduction in uncertainty. To some extent, the concepts of information and uncertainty can be equated [69]. Information entropy and some of its related concepts, as shown in Table 3, have been applied to the design and evaluation of a variety of hydrological measurement networks, including precipitation [70; 71], runoff [72; 73; 74], water quality [69], groundwater [21; 75], colder [26], and water supply networks [6].  
[PERSON] et al. [76] proposed a generalized maximum information minimum redundancy (MIMR) criterion for the design and evaluation of hydrological networks, which satisfies the three objectives of maximum overall information (joint entropy), maximum information transformation capability (ubiquitous information), and minimum redundancy information (total correlation). The design and evaluation of monitoring schemes based on the MIMR  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Entropy-Based** & **Calculation Formula** & **Meaning** \\ \hline Entropy (high uncertainty entropy, information entropy or marginal entropy) & \(H(X)=-\sum\limits_{k=1}^{K}p(x_{k})\log[p(x_{k})]\) & Amount of information provided by each monitoring point \\ Joint entropy (joint information entropy, total entropy, multivariate joint entropy) & \(H(X_{1},X_{2},\ldots,X_{N})=\) & Total amount of information provided by multiple monitoring points together \\ Total correlation & \(C(X_{1},X_{2},\ldots,X_{N})=\sum\limits_{i=1}^{N}H(X_{i})-H(X_{1},X_{2},\ldots,X_{N})\) & Redundancy of information between variables \\ Transinformation (mutual information) The special cases of total correlation, where \(n=2\)[26] & \(I(X_{1},X_{2})=H(X_{1})+H(X_{2})-H(X_{1},X_{2})\) & Components of redundant information in the monitoring network \\ Conditional entropy & \(H(X_{1}|X_{2})=H(X_{1},X_{2})-H(X_{2})\) & during the trans-information process between random variates \(X_{1}\) and \(X_{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Formulas and meanings of entropy and its related concepts [76].  
criterion can accurately and efficiently represent information. This criterion has been further supplemented and improved by researchers in the field. Combining heuristics, such as greedy algorithms, genetic algorithms, and evolutionary algorithms, it has also been widely applied to the optimized layout of IoT sensors in UDNs and hydrological network monitoring [1,27].  
Based on the principle of information theory, high entropy corresponds to high uncertainty (and high information content) in measurements owing to a large number of possible events [1]. Therefore, locations with high entropy values [37,77] are usually selected as monitoring points. However, points with high information content may not necessarily have high monitoring value. [PERSON] and [PERSON] [28] introduced the concept of information value when designing hydrological monitoring networks. Different decisions were made based on the information acquired from monitoring points. The resulting consequences corresponded to different information values, and locations with high information values [6,78] served as monitoring points. This method can guide the decision-making process regarding the operational status of water conservancy facilities. A major drawback of entropy-based criteria is that nodes with low redundant information are usually located as far away from each other as possible [77]. As a result, these schemes tend to place sensors on the boundaries of the study area, thus ignoring practical engineering needs. Moreover, population density and socio-geographical issues are not considered [79].