## 3 The Proposed Sensor Deployment Algorithms
### The Particle Swarm/Genetic Hybrid Algorithm  
Based on the above analysis, the optimization objectives include four metrics: deployment cost, energy consumption, sensing probability, and connectivity. Essentially, this problem is a multi-objective optimization problem. In the previous analysis, we converted the multi-objective optimization problem into a single-objective optimization problem by assigning weights to each objective. Our aim is to determine a deployment scheme that maximizes overall network performance. Since network performance comprises four metrics, it is highly likely that, during optimization, the magnitude of increases or decreases in metrics \(f_{1}\), \(f_{2}\), \(f_{3}\), and \(f_{4}\) will vary, possibly resulting in multiple peaks in the objective function. Consequently, the objective function \(F\) is likely a multi-peak function and genetic algorithms are well suited for solving such problems with multiple optimal values. This analysis confirms that genetic algorithms are suitable for optimizing network performance in this chapter. Now, consider the first part of the algorithm, which focuses on optimizing the number of sensors. Based on the analysis, we know that the optimal network performance associated with a particular sensor count may only represent a local optimum. The optimal sensor count does not necessarily correspond to the lowest possible sensor count but rather to the overall optimal network performance, which serves as the global optimum. In particle swarm optimization (PSO), particle movement is guided by two pieces of information: a local best and a global best. The local best represents the best position found by the particle in its history, corresponding to the optimal network performance for the current sensor count. The global best represents the best position discovered by the entire swarm, corresponding to the overall optimal network performance for the best sensor count. During particle updates of position and velocity, two factors typically influence the process: an individual cognitive component and a social cognitive component. At the beginning of iterations, we prefer particles to explore a broader search space to avoid local optima. This can be achieved by decreasing the individual cognitive component and increasing the social cognitive component. This approach promotes information exchange and cooperation between particles, encouraging them to explore new regions rather than relying solely on individual experiences. As iterations proceed, we can gradually adjust the weights of these components to strengthen local search and focus particles on the vicinity of the global optimal solution. Based on this analysis, PSO is indeed suitable for optimizing sensor count. Here is a brief overview of the PSGH algorithm steps to solve the problem in this chapter. First, we set the PSO population size \(N\) and the maximum number of iterations \(M\). Sensor counts are initialized randomly within an upper and lower limit, with the lower limit as 0 and the upper limit as the total number of deployment positions. Next, sensor candidate locations and target monitoring locations are generated. Moving to the GA part, the sensor count initialized by PSO determines the GA population size. For each individual, the fitness value (comprehensive network performance) is calculated, and the population's best individual and value are updated, leading to the sensor count that achieves optimal network performance. The GA population is then updated through selection, crossover, and mutation, recalculating each new individual fitness value. This cycle continues until the maximum number of iterations is reached, and the best individual and corresponding fitness values are passed back to PSO. The PSO population is updated, and the new PSO individuals (corresponding to the updated sensor count) are fed into the GA. The GA steps are repeated until the PSO algorithm reaches its maximum iterations, resulting in the optimal sensor count and network performance.