Chaotically Enhanced Meta-Heuristic Algorithms for Optimal Design of Truss Structures with Frequency Constraints

Abstract

The natural frequencies of any structure contain useful information about the dynamic behavior of that structure, and by controlling these frequencies, the destructive effects of dynamic loads, including the resonance phenomenon, can be minimized. Truss optimization by applying dynamic constraints has been widely welcomed by researchers in recent decades and has been presented as a challenging topic. The main reason for this choice is quick access to dynamic information by examining natural frequencies. Also, frequency constraint relations are highly nonlinear and non-convex and have implicit variables, so using mathematical and derivative methods will be very difficult and time consuming. In this regard, the use of meta-heuristic algorithms in truss weight optimization with frequency constraints has good results, but with the introduction of form variables, these algorithms trap at local optima. In this research, by applying chaos map in meta-heuristic algorithms, suitable conditions have been provided to escape from local optima and access to global optimums. These algorithms include Chaotic Cyclical Parthenogenesis Algorithms (CCPA), Chaotic Biogeography-Based Optimization (CBBO), Chaotic Teaching-Learning-Based Optimization (CTLBO) and Chaotic Particle Swarm Optimization (CPSO), respectively. Also, by using different scenarios, a good balance has been achieved between the exploration and exploitation of the algorithms.