Gravitational Search Algorithm (GSA) and Particle Swarm Optimization (PSO) are nature-inspired, swarm-based optimization algorithms respectively. Though they have been widely used for single-objective optimization since their inception, they suffer from premature convergence. Even though the hybrids of GSA and PSO perform much better, the problem remains. Hence, to solve this issue, we have proposed a fuzzy mutation model for two hybrid versions of PSO and GSA — Gravitational Particle Swarm (GPS) and PSOGSA. The developed algorithms are called Mutation based GPS (MGPS) and Mutation based PSOGSA (MPSOGSA). The mutation operator is based on a fuzzy model where the probability of mutation has been calculated based on the closeness of particle to population centroid and improvement in the particle value. We have evaluated these two new algorithms on 23 benchmark functions of three categories (unimodal, multimodal and multimodal with fixed dimension). The experimental outcome shows that our proposed model outperforms their corresponding ancestors, MGPS outperforms GPS 13 out of 23 times (56.52%) and MPSOGSA outperforms PSOGSA 17 times out of 23 (73.91%). We have also compared our results against those of some recently proposed optimization algorithms such as Sine Cosine Algorithm (SCA), Opposition-Based SCA, and Volleyball Premier League Algorithm (VPL). In addition, we have applied our proposed algorithms on some classic engineering design problems and the outcomes are satisfactory. The related codes of the proposed algorithms can be found in this link: Fuzzy-Mutation-Embedded-Hybrids-of-GSA-and-PSO.

引力搜索算法（GSA）和粒子群优化（PSO）分别是自然启发式，基于群的优化算法。尽管它们自诞生以来就已被广泛用于单目标优化，但它们会过早收敛。即使GSA和PSO的混合性能更好，问题仍然存在。因此，为解决此问题，我们为PSO和GSA的两个混合版本-引力粒子群（GPS）和PSOGSA提出了一种模糊突变模型。所开发的算法称为基于变异的GPS（MGPS）和基于变异的PSOGSA（MPSOGSA）。变异算子基于模糊模型，其中基于粒子与种群质心的接近程度和粒子值的提高来计算变异的概率。我们已经对三个类别（单峰，多峰和具有固定维数的多峰）的23个基准函数评估了这两种新算法。实验结果表明，我们提出的模型胜过其相应的祖先，MGPS胜过GPS的23倍（56.52％），MPSOGSA胜过PSOGSA的23倍（73.91％）。我们还将我们的结果与最近提出的一些优化算法（例如正弦余弦算法（SCA），基于对立的SCA和排球超级联赛算法（VPL））的结果进行了比较。另外，我们将提出的算法应用于一些经典的工程设计问题，并且结果令人满意。可以在以下链接中找到所提出算法的相关代码：GSA和PSO的模糊突变，嵌入式，混合。