Our topic is performance differences between using random and chaos for particle swarm optimization (PSO). We take random sequences with different probability distributions and compare them to chaotic sequences with different but also with same density functions. This enables us to differentiate between differences in the origin of the sequences (random number generator or chaotic nonlinear system) and statistical differences expressed by the underlying distributions. Our findings (obtained by evaluating the PSO performance for various benchmark problems using statistical hypothesis testing) cast considerable doubt on previous results which compared random to chaos and suggested that the choice leads to intrinsic differences in performance.

翻译：本文探讨了粒子群优化（PSO）中使用随机序列与混沌序列所产生的性能差异问题。我们选取了具有不同概率分布的随机序列，并将其与具有不同密度函数（包括相同密度函数）的混沌序列进行比较。这使我们能够区分序列来源差异（随机数生成器或混沌非线性系统）与底层分布所体现的统计差异。通过统计假设检验评估多种基准问题的PSO性能，我们的研究结果对以往比较随机与混沌序列并认为该选择会导致内在性能差异的结论提出了重大质疑。