## 1 Introduction
[PERSON] and [PERSON] [14] employed a liner programming formulation for the TT-WSN deployment problem and then presented a genetic algorithm based meta-heuristic algorithm to minimize the number of RNs and maximize the connectivity of the network. [PERSON] et al. [15] transformed the RN deployment problem into a minimum geometric disk coverage problem and determined that the problem is NP-complete. Then, they proposed a linear time approximation algorithm to solve it, in which the covering disks used the regular hexagon tessellation of the plane with bounded area. [PERSON] et al. [16] proposed an Artificial Bee Colony algorithm-based deployment method to extend the lifetime of a network by optimizing the parameters of the network and limiting the total number of RNs. Unlike their approach, the RNs in the present work are closer to SNs with limited energy. [PERSON] et al. [17] used a heuristic algorithm to deploy the minimum number of RNs in a TT-WSN under the requirements of connectivity and lifetime satisfaction. To meet the survivability requirement, they studied the 2-connected double-cover problem where each sensor node was covered by two base stations or relay nodes, and the relay nodes formed a 2-connected network with the base stations. [PERSON] et al. [18] used a tree-based connecting algorithm heuristic to optimize the network delay of TT-WSNs. They deployed RNs at a subset of predetermined deployment locations such that each sensor was covered by at least one RN, while ensuring the obedience of delay constraints. From the above studies, RNs are often deployed at certain discrete candidate locations; the energy of RN is limited, and there is a direct communication between each SN and RN. However, in practical applications the deployment space of RNs is often continuous, and RNs can be kept infinitely energetic by means such as solar or geothermal energy supply. To further reduce the number of nodes, not all SNs can communicate with RNs directly. To overcome the above challenges, this study focuses on the problem of RN deployment with infinite energy for multiple hops between SNs under continuous space. It can be seen that Swarm Intelligence algorithms (SI) have been widely used for these types of problems and indeed provide a better approximate solution to this type of problem. Among them, in recent years, the Artificial Bee Colony algorithm (ABC) [19] with strong global optimization ability and simple structure has received much attention. It has been widely used in the combinatorial optimization problem [20], complex weight matrix derivative problem [21], and other problems. In the literature, [PERSON] et al. [16] used this algorithm for the optimization of WSNs. However, in previous studies the characteristics of the problem have not been deeply integrated with the algorithm, and the algorithm needs a lot of adjustment parameters to adapt to the characteristics of the problem; additionally, the parameters of the SI algorithm are often relatively large, and it is difficult to obtain a balance between the global and local search ability of the algorithm. This paper proposes an improved Artificial Bee Colony algorithm based on problem characteristics and dynamic search balance, then uses this algorithm to solve deployment problems and compares it with other algorithms. Simulation experiment results verify that the proposed algorithm improves the global search capability, result stability, and local convergence speed for different problems. This study mainly contributes to optimizing lifetime by RN deployment in TT-WSN, in particular as follows:  
* The dimensional characteristics of the problem are incorporated into the search formula of the ABC. This enables the algorithm to adjust the search step according to the dimensionality of the problem, improving the global search capability of the algorithm in a targeted manner. * The adaptation degree of each individual in the operation of the population intelligence algorithm is integrated into the search process of the algorithm.