Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization

The particle swarm optimization (PSO) is a relatively new generation of combinatorial metaheuristic algorithms which is based on a metaphor of social interaction, namely bird flocking or fish schooling. Although the algorithm has shown some important advances by providing high speed of convergence in specific problems it has also been reported that the algorithm has a tendency to get stuck in a near optimal solution and may find it difficult to improve solution accuracy by fine tuning. The present paper proposes a new variation of PSO model where we propose a new method of introducing nonlinear variation of inertia weight along with a particle's old velocity to improve the speed of convergence as well as fine tune the search in the multidimensional space. The paper also presents a new method of determining and setting a complete set of free parameters for any given problem, saving the user from a tedious trial and error based approach to determine them for each specific problem. The performance of the proposed PSO model, along with the fixed set of free parameters, is amply demonstrated by applying it for several benchmark problems and comparing it with several competing popular PSO and non-PSO combinatorial metaheuristic algorithms.