Linear equality constraints and homomorphous mappings in PSO

We present a homomorphous mapping that converts problems with linear equality constraints into fully unconstrained and lower-dimensional problems for optimization with PSO. This approach, in contrast with feasibility preservation methods, allows any unconstrained optimization algorithm to be applied to a problem with linear equality constraints, making available tools that are known to be effective and simplifying the process of choosing an optimizer for these kinds of constrained problems. The application of some PSO algorithms to a problem that has undergone the mapping presented here is shown to be more effective and more consistent than other approaches to handling linear equality constraints in PSO