Vol.:(0123456789) 1 3 Asian Journal of Civil Engineering https://doi.org/10.1007/s42107-020-00271-x ORIGINAL PAPER Improved metaheuristics through migration‑based search and an acceptance probability for truss optimization Sumit Kumar 1  · Ghanshyam G. Tejani 2  · Nantiwat Pholdee 3  · Sujin Bureerat 3 Received: 26 May 2020 / Accepted: 8 June 2020 © Springer Nature Switzerland AG 2020 Abstract The proposed study investigated the simultaneous size and topology optimization of planar and spatial truss design subject to static and dynamic constraints. Considering practical construction, discrete cross-sectional areas of the standard design problems are taken. Also, the truss design problems are deemed to have several loading conditions under bounds such as component stresses, natural frequencies, nodal displacements, Euler buckling parameters, and kinematic stability require- ments. Topology optimization of trusses leads to the elimination of superfluous components and nodes from the ground structure (known as highly hyperstatic truss), which in turn reduces the overall weight of the truss. Owing to the superflu- ous number of analyses and singular resolution, the complexities emerge in this technique; thus, the Grubler’s criterion for mobility check and positive definiteness for stability check is applied. Five improved metaheuristics (viz. the improved dragonfly algorithm, improved whale optimization algorithm, improved ant lion optimizer, improved heat transfer search, and improved teaching–learning-based optimization) which are based on a random-migration search and simulated annealing (SA)-based selection have been implemented for solving such challenging issues. The proposed algorithms are applied to three benchmark problems (i.e. 20-bar, 24-bar, and 72-bar (3D) truss problems), and the obtained results are compared with basic optimizers which manifest the superiority in the performance of the proposed techniques. The statistical analysis of the experimental work has been carried out by conducting Friedman’s rank test. Eventually, the results justify the harmony between the local intensification and global diversification of the modified optimizers. Keywords Performance enhancement · Metaheuristic · Migration · Structural optimization · Discrete section · Static and dynamic constraints · Simulated annealing Introduction In the modern era, the truss optimization is a vital field of research by its wide-ranging applications. An optimal con- figuration not only helps to reduce the manufacturing costs but also significantly improves the structural efficiency. Essentially, the problem of truss optimization is categorized into three sub-domains, namely sizing optimization, shape optimization, and topology optimization (Kaveh and Zakian 2014). Optimization of topology is a fast-growing domain of structural engineering that can lead to better safety and greater saving. Topology optimization of truss is a rationally challenging area, because of its sophistication as it involves the consideration of all the distinct topologies produced rather than a specific topology to search for the finest topol- ogy (Deb and Gulati 2001). The effect of sizing and topol- ogy variables on both the objective function and constraints is fairly unlike. Therefore, simultaneous size and topology * Ghanshyam G. Tejani p.shyam23@gmail.com Sumit Kumar sumit21sep1990@gmail.com Nantiwat Pholdee nantiwat@kku.ac.th Sujin Bureerat sujbur@kku.ac.th 1 Department of Mechanical Engineering, GPERI, Gujarat Technological University, Mehsana, Gujarat, India 2 Department of Mechanical Engineering, School of Technology, GSFC University, Vadodara, Gujarat, India 3 Sustainable and Infrastructure Research and Development Center, Department of Mechanical Engineering, Faculty of Engineering, Khon Kaen University, Khon Kaen 40002, Thailand