PUBB: A parallel universes-inspired improvement of the BB-BC algorithm for multi-scale truss optimization

This paper introduces an enhanced version of the Big Bang-Big Crunch (BB-BC) optimization algorithm, based on the theory of parallel universes, to improve its performance in the optimal design of truss structures. The governing equations of the BB-BC optimization algorithm are defined based on the Big Bang phenomenon in our universe. According to the parallel universes theory, it is possible to hypothesize the existence of parallel universes with physical laws that either oppose or differ from those of our universe. These hypothetical physical laws are implemented as transfer functions in the search space of the BB-BC optimization algorithm to enhance its exploration and exploitation phases. This modified approach is termed the Parallel Universes Big Bang-Big Crunch (PUBB) algorithm. In truss size optimization, the cross-sectional areas of the members are used as design variables to reduce the truss's weight, while keeping member stresses and nodal displacements within acceptable limits. The proposed PUBB algorithm is implemented using MATLAB software. To quantitatively evaluate its performance, three groups of truss structures—small-scale (10-, 18-, and 25-member), medium-scale (72-member), and large-scale (200- and 942-member)—are analyzed under diverse loading conditions and multiple design constraints. The results demonstrate that the proposed PUBB algorithm is highly effective and efficient in optimizing truss structures across various scales. Compared to the standard BB-BC algorithm and most population-based algorithms, PUBB exhibits a superior capability to escape local optima, thereby achieving improved convergence and solution quality.