MEGA: Maximum-Entropy Genetic Algorithm for Router Nodes Placement in Wireless Mesh Networks

TL;DR

The paper addresses the NP-hard problem of mesh router placement in Wireless Mesh Networks by introducing MEGA, a maximum-entropy genetic algorithm. MEGA integrates a genetic algorithm with entropy-based fitness, using Shannon entropy to balance coverage dispersion and connectivity across the network, with the final objective $F = H_{cov} - H_{con}$ normalized to 1 in optimal cases. Empirical results show MEGA consistently outperforms COA, FA, GA, and PSO in both user coverage and network connectivity across varying numbers of clients, routers, and coverage radii. This demonstrates the practical viability of entropy-guided evolutionary search for efficient WMN deployment and opens avenues for applying MEGA to gateway placement, antenna positioning, routing, and channel allocation.

Abstract

Over the past decade, Wireless Mesh Networks (WMNs) have seen significant advancements due to their simple deployment, cost-effectiveness, ease of implementation and reliable service coverage. However, despite these advantages, the placement of nodes in WMNs presents a critical challenge that significantly impacts their performance. This issue is recognized as an NP-hard problem, underscoring the necessity of development optimization algorithms, such as heuristic and metaheuristic approaches. This motivates us to develop the Maximum Entropy Genetic Algorithm (MEGA) to address the issue of mesh router node placement in WMNs. To assess the proposed method, we conducted experiments across various scenarios with different settings, focusing on key metrics such as network connectivity and user coverage. The simulation results show a comparison of MEGA with other prominent algorithms, such as the Coyote Optimization Algorithm (COA), Firefly Algorithm (FA), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO), revealing MEGA's effectiveness and usability in determining optimal locations for mesh routers.

Figures (8)

• Figure 1: Wireless Mesh Network architecture.
• Figure 2: Flowchart of the MEGA.
• Figure 3: The scenario illustrates an equal coverage probability distribution, where blue nodes represent mesh routers (3 units) and purple nodes represent mesh clients (9 units). Each $P_i$ is equal to $\frac{1}{3}$, resulting $H_{\text{cov}}$ = 1.
• Figure 4: The scenario illustrates case when $H_{\text{con}}$ = 0, resulting in best connectivity among nodes. Here, blue nodes represent mesh routers, purple nodes represent mesh clients, and blue lines represent the connectivity between mesh routers.
• Figure 5: The optimal placement of mesh routers obtained using MEGA. Green nodes denote mesh routers, red nodes indicate mesh clients, and lines between routers show connectivity.