An efficient imperialist competitive algorithm with likelihood assimilation for topology, shape and sizing optimization of truss structures

•A new enhanced discrete optimization method (CA-ICEA) is developed for topology and size optimization of truss structures.•A new CA-based approach is employed to introduce CA-ICEA.•The introduced CA-based approach can be used to improve other stochastic optimization algorithms.•The proposed approach was successfully tested in topology and sizing optimization problems of some benchmark structures.•The CA-ICEA was very competitive and could always find the best design overall requiring less computational effort. This article presents an efficient hybrid meta-heuristic algorithm for topology, layout and sizing optimization of truss structures. A new assimilation scheme is implemented in the imperialist competitive algorithm (ICA) in order to improve computational efficiency, the likelihood of occurrence and the neighborhood patterns are used, and the assimilation step of the ICA is enhanced. In this method, the probabilities are assigned to each alternative by the imperialist and its neighbors in the search space; then, the colonies construct new solutions (moving to the relevant imperialist) based on the likelihood of occurrence. Neighborhood patterns are proposed to gather information from the neighboring countries in order to extract features based on the local power variation. In this study, the extended abilities of the proposed algorithm are inspired from the dolphin echolocation (DE) algorithm and the cellular automata (CA) method, which the new algorithm is denoted as CA-ICEA. The optimization results obtained by ICA, DE and CA-ICEA methods are compared. Remarkably, the proposed algorithm outperforms its competitors in terms of optimum weights, their mean and standard deviation.