Truss optimization with discrete design variables: a critical review

Abstract

This review presents developed models, theory, and numerical methods for structural optimization of trusses with discrete design variables in the period 1968 --- 2014. The comprehensive reference list collects, for the first time, the articles in the field presenting deterministic optimization methods and meta heuristics. The field has experienced a shift in focus from deterministic methods to meta heuristics, i.e. stochastic search methods. Based on the reported numerical results it is however not possible to conclude that this shift has improved the competences to solve application relevant problems. This, and other, observations lead to a set of recommended research tasks and objectives to bring the field forward. The development of a publicly available benchmark library is urgently needed to support development and assessment of existing and new heuristics and methods. Combined with this effort, it is recommended that the field begins to use modern methods such as performance profiles for fair and accurate comparison of optimization methods. Finally, theoretical results are rare in this field. This means that most recent methods and heuristics are not supported by mathematical theory. The field should therefore re-focus on theoretical issues such as problem analysis and convergence properties of new methods.