Topology and shape optimization methods using evolutionary algorithms: a review

Abstract

Topology optimization has evolved rapidly since the late 1980s. The optimization of the geometry and topology of structures has a great impact on its performance, and the last two decades have seen an exponential increase in publications on structural optimization. This has mainly been due to the success of material distribution methods, originating in 1988, for generating optimal topologies of structural elements. Previous methods suffered from mathematical complexity and a limited scope for applicability, however with the advent of increased computational power and new techniques topology optimization has grown into a design tool used by industry. There are two main fields in structural topology optimization, gradient based, where mathematical models are derived to calculate the sensitivities of the design variables, and non gradient based, where material is removed or included using a sensitivity function. Both fields have been researched in great detail over the last two decades, to the point where structural topology optimization has been applied to real world structures. It is the objective of this review paper to present an overview of the developments in non gradient based structural topology and shape optimization, with a focus on evolutionary algorithms, which began as a non gradient method, but have developed to incorporate gradient based techniques. Starting with the early work and development of the popular algorithms and focusing on the various applications. The sensitivity functions for various optimization tasks are presented and real world applications are analyzed. The article concludes with new applications of topology optimization and applications in various engineering fields.