The Particle Swarm Optimisation (PSO) algorithm consists of a population (or swarm) of particles that are
“flown” through an n-dimensional space in search of a global best solution to an optimisation problem.
PSO operates in Cartesian space, producing Cartesian solution vectors. By making use of an appropriate
mapping function the algorithm can be modified to search in polar space. This mapping function is used
to convert the position vectors (now defined in polar space) to Cartesian space such that the fitness value
of each particle can be calculated accordingly. This paper introduces the polar PSO algorithm that is able
to search in polar space. This new algorithm is compared to its Cartesian counterpart on a number of
benchmark functions. Experimental results show that the polar PSO outperforms the Cartesian PSO in
low dimensions when both algorithms are applied to the search for eigenvectors of different n × n square
matrices. Performance of the polar PSO on general unconstrained functions is not as good as the Cartesian
PSO, which emphasizes the main conclusion of this paper, namely that the PSO is not an efficient search algorithm for general unconstrained optimisation problems defined in polar space.