# An Accuracy-Aware Energy-Efficient Multipath Routing Algorithm for WSNs
## 1 Introduction
However, there is a trade-off between data accuracy and data transmission reliability [11]--more coding packets can enhance the reliability of data transmission, whereas multiple aggregations of copies during routing can reduce data accuracy at the destination. As aggregation instances increase, the loss of data accuracy becomes more pronounced, which makes the accuracy-aware data collection algorithms less effective. To tackle the aforementioned challenge, a multipath routing algorithm EMRAR (Energy-efficient Multipath Routing algorithm balancing data Accuracy and transmission Reliability) is proposed in this paper. The core concept behind EMRAR is to jointly optimize transmission reliability and data accuracy while considering energy consumption. Recognizing that data accuracy is influenced by the number of intermediate aggregation nodes, our approach aims to minimize this count. To achieve this goal, the measurement methods for transmission reliability and data accuracy are defined first. Taking transmission reliability and path energy consumption as the optimization objectives, an accuracy constraint-based optimization model is formulated to transform the routing problem into a multi-objective optimization problem with the help of a fitness function to assess the solutions and identify the optimal Pareto solution set for the algorithm. To enhance optimization performance, the Improved Adaptive Artificial Immune Algorithm (IAAIA) [16] is employed. To adapt IAAIA to multipath routing, multiple adaptive immune operators are introduced, which not only retain the search capabilities of the artificial immune algorithm but also harness the adaptive nature of immune operators to avoid \"premature\" convergence. Experimental results show that the proposed routing algorithm can efficiently find a solution to multipath within a reasonable convergence time, meeting the criteria for transmission reliability and data accuracy. The main contributions of this work include:  
1. A multipath routing algorithm EMRAR is proposed. Unlike existing schemes that either construct a congestion-free transmission route to guarantee data accuracy at the expense of reliability or solely ensure data accuracy at the source node, EMRARcan concurrently guarantee transmission reliability and data accuracy at the destination node. It accomplishes this by efficiently controlling the number of paths and aggregation nodes to minimize accuracy loss. 2. A constraint-based multi-objective optimization formula is constructed. This formula considers both transmission reliability and path energy consumption as optimization objectives under the constraints of accuracy loss and node residual energy. This approach ensures a balanced trade-off between these critical factors. 3. The IAAIA algorithm is adopted and customized. To address the multi-objective optimization problem and apply it to the multipath routing scheme, the adaptation includes the design of an antibody initialization method and enhancements to the antibody incentive calculation method and immune operation. These modifications optimize the algorithm's effectiveness in the context of multipath routing. The organization of the rest of this paper is arranged as follows. In Section 2, the existing research on multipath routing is discussed, with a particular focus on examining various multipath construction methods. In Section 3, the system model is established to obtain the reliability and energy optimization objectives while adhering to the accuracy loss constraint. In Section 4, the solution for the multi-objective optimization is proposed. The antibody population update strategy is designed, and the fitness function is constructed to evaluate the antibody individuals. In Section 5, the time complexity and message complexity of the algorithm are analyzed. In Section 6, the simulations are carried out to compare EMRAR with existing algorithms. Finally, the conclusions and future work are given in Section 7.