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.

翻译：大量研究致力于开发能够在基于梯度的优化器传统上难以应对的场景中寻找全局最优解的元启发式优化方法。其中，所谓的粒子群优化方法已在多个应用领域展现出高效性。鉴于粒子群优化领域的成熟度，PSO算法的新变体在性能上可能仅能带来边际收益——毕竟没有免费的午餐。本文认为，与其仅追求基准优化函数集上的性能，不如将研究精力投入到同时具备其他有用属性的算法开发中。本研究提出了一种高度通用且可解释的PSO算法变体——粒子吸引子算法。此外，该算法被设计为能够精确计算每一步的闭式转移密度（描述粒子从一代到下一代的运动）。获得闭式转移密度对密切相关的序贯蒙特卡洛领域具有重要意义。为证明这些有用属性不以牺牲性能为代价，本研究将PAO与其他几种最先进的启发式优化算法进行了基准对比研究。