A new particle swarm optimiser for linearly constrained optimisation

A new PSO algorithm, the linear PSO (LPSO), is developed to optimise functions constrained by linear constraints of the form Ax = b. A crucial property of the LPSO is that the possible movement of particles through vector spaces is guaranteed by the velocity and position update equations. This property makes the LPSO ideal in optimising linearly constrained problems. The LPSO is extended to the converging linear PSO, which is guaranteed to always find at least a local minimum.