A numerical gradient based technique and directed neighborhood structure for Constrained Particle Swarm Optimization

In this paper, a new method to deal with equality or inequality constraints in constrained optimization and a new neighborhood structure for Particle Swarm Optimization (PSO) called Grouped Directed Structure (GDS) are proposed. We use the new method and GDS together with the PSO algorithm to solve the well-known 24 benchmark constrained optimization problems in the literature. The PSO algorithm is well known for its fast convergence to the possible optimal position. However, in constrained optimization, the performance of PSO is not as good as it is in unconstrained optimization, partly because PSO is not good at finding the feasible region. Due to the motivation by this weakness of PSO, we develop a method called Numerical Gradient (NG) to find the feasible region. By means of the information that NG can provide, we utilize the PSO algorithm with GDS to find the optimal position of the problem. We call this new PSO variant Numerical Gradient Particle Swarm Optimization (NGPSO). A detailed description of the mechanism for NGPSO is provided and some numerical results are presented compared with the results from the existing PSO variants dealing with constraint optimization problems.