An Efficient Method for Solving Router Placement Problem in Wireless Mesh Networks Using Multi-Verse Optimizer Algorithm  
[PERSON]  
1 Faculty of Information Technology, University of Sciences, Hue University, Hue City 49000, Vietnam; 1  
[PERSON]  
coverage metrics, this work has not yet considered connectivity to the gateway of mesh routers. This is a requirement for covered users to access the internet. As a result, the proposed algorithm in [3] is only appropriate for WMN peer-to-peer network models, such as mobile ad hoc network (MANET), which are only concerned with data transmission between users. The authors of [10] used the algorithm accelerated PSO algorithm (APSO) to solve MRP-WMN. The APSO algorithm was chosen for this project because of its fast convergence and low computational complexity. In terms of coverage and connectivity, simulation results using the C and MATLAB programming languages show that the APSO algorithm outperforms the linearly decreasing weight particle swarm optimizer (LDWPSO) algorithm [19]. By optimizing the metrics of the coverage and connectivity, the authors of [11] have proposed an optimal algorithm, namely the Chemical Reaction Optimization algorithm (CRO), to solve the MRP-WMN. The CRO algorithm is inspired by the interactions between molecules in chemical reactions to reach a low, stable energy state. Simulation results show that their proposed algorithm can improve client coverage and network connectivity compared to the GA algorithm. In [20], the authors have proposed a Genetic Algorithm in addition to the approach that was derived from the circle packing problem. Their proposed algorithm has two goals, maximizing network connectivity as well as coverage area. The testing findings demonstrated the effectiveness of their approach in generating high-quality and appropriate mesh router node placement solutions in WMN.  
Another study utilized a genetic algorithm and simulated annealing to find a low-cost WMN configuration while satisfying constraints and figuring out how many gateways were needed [22]. The performance of the genetic algorithm and simulated annealing in decreasing WMN network expenses while maintaining quality of service (QoS) was demonstrated in experiments. The new models are shown to outperform existing solutions significantly. In [23], the QoT was also considered in the MPR-WMN problem. The authors have presented a novel particle swarm optimization approach to maximize both network connectivity and client coverage. The QoS constraints of this work are delay, relay load, and Internet gateway capacity.  
We concluded from our review of the above publications that approximation optimization methods can be employed effectively to solve the MRP-WMN problem. We continue to develop this research topic in this paper. Using the Multi-Verse Optimizer algorithm (MVO), we provide an efficient technique for solving the MRP-WMN problem. The following are the primary contributions of this paper:  
Figure 1: The general architecture of the WMN [21].  
* Proposed an efficient method for solving the RNP-WMN problem using an MVO algorithm to improve the percentage of covered clients under the connection constraint to the gateway.
* Formulate a multi-objective function for the RNP-WMN problem to simultaneously maximize two important performance metrics, namely connected client ratio and connected router ratio.
* Evaluation and comparison of the performance of the MVO algorithm with algorithms PSO, WOA and GA in solving RNP-WMN problem.  
The next sections of this paper are organized as follows. Section 2 describes the formulation of the RNP-WMN problem. Section 3 presents the MVO algorithm and its application to solve the RNP-WMN problem. Section 4 presents the simulation results and discussion. Finally, concluding remarks and promising future study items are given in Section 5.