For economical benefits, optimisation of mass-produced structural steel products has been widely researched. The objective is to minimise the quantity of material used without sacrificing the strength and practicality of the structural members. Current research focuses on optimising the main dimensions of conventional cross-sectional shapes but rarely considers discovering new optimum shapes. This paper introduces the concepts of a new optimisation method that enables the cross-section to self-shape to an optimum by using the evolution and adaptation benefits of Genetic Algorithm (GA). The feasibility and the accuracy of the method are verified by implementing it to optimise the section capacity of thin-walled profiles. Specifically, the profiles are optimised against simple parameters, for which analytical solutions are known, namely the optimisation of doubly-symmetric closed profiles. Results show that the cross-section accurately self-shapes to its optimum in a low number of generations. Factors influencing the convergence are presented in this paper. The method is extended to optimisation of cold-formed steel open section columns in the companion paper.