A binary multi-objective approach for solving the WMNs topology planning problem

This paper addresses the multi-objective topology planning problem in Wireless Mesh Networks (WMNs), traditionally solved using Multi-Objective Particle Swarm Optimization (MOPSO), Multi-Objective Genetic Algorithm (MOGA), and Non-dominated Sorting Genetic Algorithm-II (NSGA-II). While effective, these methods face challenges such as balancing exploration and exploitation, high computational complexity, slow convergence, and limited scalability. To address these challenges, we propose the Multi-Objective Bonobo Optimizer (MOBO), inspired by the NSGA-II framework, which excels in balancing exploitation and exploration, achieving faster convergence, and reducing computational complexity. The primary objective of our planning problem is to select the minimum number of Candidate Sites (CSs) to host Mesh Routers (MRs) while satisfying full coverage and full connectivity requirements in WMNs. To adapt the proposed method to the binary optimization required in WMNs, we employ the V-shaped transfer function V4 for converting the continuous search space into binary solutions effectively, leading to Binary Multi-Objective Bonobo Optimizer (BMOBO). The proposed approach was validated using MATLAB (R2020a) simulations across various scenarios, including different numbers of CSs, Mesh Clients (MCs), and Coverage Radius (CR) values. Performance was evaluated by analyzing the number of installed MRs and uncovered MCs, and compared with Binary MOPSO (BMOPSO). The experimental results demonstrate that BMOBO consistently outperforms BMOPSO in terms of mean performance and standard deviation, although the differences were not statistically significant (\(p-values > 0.05\)). These findings underscore the effectiveness and robustness of BMOBO for large-scale WMN topology planning.