# Multiparameter Fusion Decision Routing Algorithm for Energy-Constrained Wireless Sensor Networks
## 3 Proposed Routing Optimization Algorithm
### Routing Selection Strategy  
Regarding total forward neighbor nodes of the current node \(i\), the higher the numerical difference in the routing evaluation parameter \(k(1\leq k\leq K)\), the higher its importance on the next-hop selection and the higher the reliability. In contrast, it indicates that it plays a limited role in the decision-making of the next hop, that is, the reliability is low. Therefore, in order to represent this characteristic of routing parameters, the reliability coefficient \(\wp^{k}\) is introduced here, and its specific calculation method is as follows:  
First, the \(k^{th}\) evaluation parameter of the candidate next hop \(j\) is \(v_{jk}\), and the initial matrix \(D=\left\{v_{jk}\right\}\) is established accordingly. Thus, the standard deviation \(\sigma_{k}\) of each parameter can be calculated as follows:  
\[\sigma_{k}=\sqrt{\frac{\sum_{j\in FN(i)}\left(v_{jk}-\overline{v}_{k}\right)^{2 }}{\left|FN(i)\right|-1}} \tag{21}\]  
where \(\overline{v}_{k}\) represents the mean of the \(k^{th}\) parameter value of all forward neighbors and \(\left|FN(i)\right|\) is the modulus of the forward neighbor set, that is, the number of candidate next hops. Then, the reliability coefficient \(\wp_{k}\) of the parameter \(k\) is as follows:  
\[\wp_{k}=\frac{\overline{v}_{k}\cdot\sigma_{k}}{\sum_{k=1}^{K}(\overline{v}_{k }\cdot\sigma_{k})} \tag{22}\]  
where \(K\) is the number of routing evaluation parameters. Here, considering that \(\sigma_{k}\) maybe close to or even equal to each other, to distinguish different optimization parameters, \(\overline{v}_{k}\) is added to the calculation of the reliability coefficient. Furthermore, for the forward neighbor \(j\), its value reflected in each parameter \(k\) contributes to its selection as the next hop. Therefore, the parameter contribution degree \(m_{j}(k)\), as shown in the following equation, is defined in this paper, namely,  
\[m_{j}(k)=\frac{v_{jk}}{\left[\sum_{j=1}^{|FN(j)|}v_{jk}+K(1-\wp_{k})\right]} \tag{23}\]Here, different from the general way of assigning the contribution degree only according to the proportion of the parameter value, this paper introduces a modified value \(K(1-\wp_{k})\) into the denominator of \(m_{j}(k)\), so that the greater the reliability coefficient of parameter \(k\) is, the greater the parameter contribution degree of forward neighbor \(j\), which is selected as the next hop, and vice versa. Therefore, the reliability degree of routing parameters is well integrated into the calculation of the contribution degree, so that the parameter value not only reflects the node state but can also feedback the network state fluctuation of the forward neighbor area on the routing optimization parameters. Generally, when the parameter contribution degree of all routing evaluation parameters of the forward neighbor node \(j\) is obtained, there are two methods for selecting the next hop. One is to choose the node with the maximum contribution degree as the next hop. The other needs to compute a weighted sum of evaluation parameters for each node, then select the maximum sum node as the next hop. However, the former method makes a decision only based on the contribution degree, ignores the other necessary settings, which can also reflect fluctuations in the network status. Meanwhile, the second method may have a more significant deviation due to manually determining the routing parameter weights. Therefore, to avoid a too one-sided selection of the next hop and eliminate subjective factors as much as possible, this paper proposes a multiparameter fusion strategy. In the process of routing, for the sake of setting an appropriate selection of the next hop from \(FN(i)\), this strategy integrates the parameter contribution degree \(m_{j}(k)\) of forward neighbor \(j\) and the fuzzy contribution degree \(m_{\Omega}(k)\) and calculates the fusion contribution degree as the final standard of routing decisions.