Nowadays, the advancement of technology and the increase in the power of computer processing have enabled using these processors to solve different problems in the shortest possible time. Many scholars throughout the world seek to shorten the time needed to solve various problems. As engineering science has a wide range of problems with different natures, it is impossible to claim whether a particular method can solve all the problems faced. Considering the aim of developing optimization methods, in this study, a new method is used by combining a multi-level cross-entropy optimizer (MCEO) algorithm with sigmoid functions to smooth the space of the problems with discrete variables. It is named modified multi-level cross-entropy optimizer (MMCEO). Four problems including designing vessel, speed reducer, 15-member, and 52-member trusses were considered to examine the effectiveness of the proposed algorithm in dealing with various problems. It is of note that all of these problems have discrete variables and they are defined in very difficult spaces. The results regarding the first two problems (i.e., pressure vessel and speed reducer) indicated the very high accuracy of the proposed method and the improvement of the response (in terms of function calls) and in trusses designing. Moreover, they suggested its higher speed compared to the best algorithms in designing the stated structures.

如今，随着技术的进步和计算机处理能力的增强，使用这些处理器可以在最短的时间内解决各种问题。世界各地的许多学者都在寻求缩短解决各种问题所需的时间。由于工程科学具有各种性质不同的问题，因此无法断言某种特定的方法是否可以解决所有面临的问题。考虑到开发优化方法的目的，本研究中使用了一种新方法，该方法将多级交叉熵优化器（MCEO）算法与S型函数相结合，以平滑离散变量问题的空间。它被称为改进的多级交叉熵优化器（MMCEO）。设计容器，减速器，15构件，并考虑使用52人桁架来检验该算法在处理各种问题上的有效性。值得注意的是，所有这些问题都有离散变量，并且它们定义在非常困难的空间中。有关前两个问题（即压力容器和减速器）的结果表明，所提出方法的准确性非常高，并且响应（在函数调用方面）和桁架设计方面都得到了改善。此外，他们建议与设计所述结构的最佳算法相比，它具有更高的速度。压力容器和减速器）表明了所提出方法的非常高的准确性，并且在桁架设计中（在功能调用方面）响应得到了改善。此外，他们建议与设计所述结构的最佳算法相比，它具有更高的速度。压力容器和减速器）表明了所提出方法的非常高的准确性，并且在桁架设计中（在功能调用方面）响应得到了改善。此外，他们建议与设计所述结构的最佳算法相比，它具有更高的速度。