  A great deal of research has been conducted in the consideration of
meta-heuristic optimisation methods that are able to find global optima in
settings that gradient based optimisers have traditionally struggled. Of these,
so-called particle swarm optimisation (PSO) approaches have proven to be highly
effective in a number of application areas. Given the maturity of the PSO
field, it is likely that novel variants of the PSO algorithm stand to offer
only marginal gains in terms of performance -- there is, after all, no free
lunch. Instead of only chasing performance on suites of benchmark optimisation
functions, it is argued herein that research effort is better placed in the
pursuit of algorithms that also have other useful properties. In this work, a
highly-general, interpretable variant of the PSO algorithm -- particle
attractor algorithm (PAO) -- is proposed. Furthermore, the algorithm is
designed such that the transition densities (describing the motions of the
particles from one generation to the next) can be computed exactly in closed
form for each step. Access to closed-form transition densities has important
ramifications for the closely-related field of Sequential Monte Carlo (SMC). In
order to demonstrate that the useful properties do not come at the cost of
performance, PAO is compared to several other state-of-the art heuristic
optimisation algorithms in a benchmark comparison study.
