Optimization of nonlinear constrained particle swarm

Abstract

We propose an algorithm based on the particle swarm paradigm (PSP) to address nonlinear constrained optimization problems. While some algorithms based on PSP have already been proposed in this context, the equality constraints have been posing some difficulties. The proposed algorithm is based on the relaxation of the dominance concept introduced in the multiobjective optimization. This concept is used to select the best particle position and the best ever particle swarm position. We propose also a stopping criterion for the algorithm and present numerical results with some problems collected from the literature. The new algorithm is implemented in a solver connected with AMPL, allowing easy coding and solving of problems.