Particle Swarm Optimization in Nonlinear Systems

Boundary value problems of fourth order appear in beam equilibrium analysis. Most research focus on the existence of positive solutions with the help of nonlinear analysis tools such as topological indices, critical point theory, etc. The PSO is a stochastic optimization technique inspired by the behavior of a flock of birds, and has found successful applications in searching and optimization. Inspired by the randomized searching nature of PSO, and the widely used dynamic niche technology, this paper presents a new technique of finding positive solutions to fourth order boundary value problems. We propose algorithms to get multiple solutions to the problem.