*Result*: A comparison study of unimodal normal distribution crossover and simplex crossover methods combined with diverse router replacement methods for two islands wireless mesh networks.

*Wireless mesh networks (WMNs) provide reliable and scalable wireless connectivity. They are also capable of dynamic data routing. However, mesh router placement in WMNs is a complex process and is classified as NP-hard problem. In this study, we present a WMN-PSOHCDGA hybrid system, which integrates particle swarm optimization (PSO), hill climbing (HC) and distributed genetic algorithm (DGA) to optimize mesh router placement. We compare two crossover methods: unimodal normal distribution crossover (UNDX) and simplex crossover (SPX) combined with six router replacement methods: constriction method (CM), random inertia weight method (RIWM), linearly decreasing inertia weight method (LDIWM), linearly decreasing V max method (LDVM), rational decreasing V max method (RDVM) and fast convergence rational decreasing V max method (FC-RDVM) for two island and stadium mesh client distributions. Simulation results for small-scale two-island distribution show that in all scenarios all mesh routers were connected and all clients were covered. While UNDX-LDIWM demonstrated better load balancing. For middle-scale two-island distribution, UNDX-LDIWM also achieved good load balancing although not all clients were covered, while both UNDX and SPX maintained full router connectivity. For stadium distribution, all mesh routers remained connected and CM, LDVM, and FC-RDVM achieved full client coverage, while CM and FC-RDVM demonstrated better load balancing. [ABSTRACT FROM AUTHOR]*