Gradient-based Mechanism For PSO Algorithm: A Comparative Study On Numerical Benchmarks

Due to the growing need for metaheuristics with features that allow their implementation for highly complex and real-time problems, this paper describes a gradient-based mechanism to handle with the constraints and dimensional limits of the search space in an optimization problem. The proposed mechanism aims to control the flight of the particles in the Particle Swarm Optimization (PSO) algorithm, improving its application in complex domains. As a result, the gradient-based PSO presents efficient convergence when compared to other variations of this algorithm. The proposed algorithm is also suitable for real-time problems when the actual optimum is difficult to be reached since a feasible and optimized solution is found in comparison to an initial solution. In this sense, the gradient-based PSO is tested using eight benchmark functions in the continuous domain, namely: Sphere, Rosenbrock, Rastrigin, Griewank, Alpine, Schaffer, Schwefel, and Ackley. The proposed PSO was compared to other three algorithms (with adaptive individual inertia, with constant inertia weight and with linearly decreasing inertia weight). This way, the proposed PSO algorithm was able to reach better-optimized results in seven out of the eight tested benchmark functions at the end of 2000 iterations. By means of the obtained results, it is noteworthy to mention that the proposed constraint-handling mechanism features extremely efficient convergence for the PSO algorithm.