Searching Nonlinear Systems by Multi-population Differential Evolution

Nonlinear problems are arising more and more often in searching for an approximate solution. One of these nonlinear problems is the boundary value problem. Most researches focus on the existence of positive solutions with the help of nonlinear analysis tools such as topological indices, critical point theory, etc, and the effective searching of an approximate solution is indeed an interesting problem. While many searching methods focus themselves on particle swarm optimization and genetic algorithms, we propose a new searching algorithm based differential evolution (DE). It proves that DE is a simple optimization algorithm effective for real-valued problems. We present new techniques of finding positive solutions to fourth order boundary value problems. We propose algorithms to get solutions together with a simple convergence analysis.