A modified multi-level cross-entropy algorithm for optimization of problems with discrete variables

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.