Evolutionary population-based methods have found their applications in dealing with many real-world simulation experiments and mathematical modelling problems. The Moth-flame optimization (MFO) algorithm is one of the swarm intelligence algorithms and it can be used with constrained and unknown search spaces. However, there are still some defects in its performance, such as low solution accuracy, slow convergence, and insufficient exploration capability. This study improves the basic MFO algorithm from the perspective of improving exploration capability and proposes a hybrid swarm-based algorithm called SMFO. The essential notion is to further explore and scan the feature space with taking advantages of the sine cosine strategy. We methodically investigated the efficacy, solutions, and optimization compensations of the developed SMFO using more than a few demonstrative benchmark tests, together with unimodal, multimodal, hybrid and composition tasks, and two widely applied engineering test problems. The simulations point towards this fact that the diversification and intensification inclinations of the original MFO and its convergence traits are fortunately upgraded. The findings and remarks show that the suggested SMFO is a favourable algorithm and it can show superior efficacy compared to other techniques.

基于进化种群的方法已发现其在处理许多现实世界中的模拟实验和数学建模问题中的应用。蛾-火焰优化（MFO）算法是群体智能算法之一，可与受约束和未知的搜索空间一起使用。但是，其性能仍然存在一些缺陷，例如，解决方案精度低，收敛速度慢以及勘探能力不足。本研究从提高勘探能力的角度出发，对基本的MFO算法进行了改进，并提出了一种基于混合群的算法，称为SMFO。基本概念是利用正弦余弦策略进一步探索和扫描特征空间。我们有条不紊地研究了功效，解决方案，使用多个示范性基准测试以及单峰，多峰，混合和合成任务以及两个广泛应用的工程测试问题对已开发的SMFO进行优化和优化补偿。模拟指出了这一事实，幸运的是，原始MFO的多元化和集约化倾向及其趋同性得到了提升。结果和评论表明，所提出的SMFO是一种有利的算法，并且与其他技术相比，它可以显示出更高的功效。模拟指出了这一事实，幸运的是，原始MFO的多元化和集约化倾向及其趋同性得到了提升。结果和评论表明，所提出的SMFO是一种有利的算法，并且与其他技术相比，它可以显示出更高的功效。模拟指出了这一事实，幸运的是，原始MFO的多元化和集约化倾向及其趋同性得到了提升。结果和评论表明，所提出的SMFO是一种有利的算法，并且与其他技术相比，它可以显示出更高的功效。