Final solutions to benchmark engineering optimization problems by cylindrical algebraic decomposition

Abstract

This study presents a method for determining globally optimal solutions to optimization problems in analytical form. The method is based on the Cylindrical Algebraic Decomposition (CAD) algorithm, in tandem with powerful symbolic computations. Exact solutions are derived for several widely used benchmark engineering optimization problems. These analytical solutions are final in the sense that they are feasible and cannot be improved. Building upon earlier work by Charalampakis and Chatzigiannelis on truss sizing optimization using CAD, the present study extends the methodology to a broader class of benchmark problems. To the best of our knowledge, no previous work has attempted such a general application of CAD-based symbolic optimization. Future advancements in CAD algorithm implementation and computing power may lead to the solution of even more complex problems.