Determining the optimal cross-section of beams

Abstract

Constrained shape discovery and optimisation are difficult engineering problems. Shape discovery deals with evolving randomly generated solutions into useful intermediate solutions. These intermediate solutions are then optimised to suite their environment. In this paper a Genetic Algorithm (GA) is applied to the problem of finding the optimum cross-section of a beam, subject to various loading conditions. Previous work using GAs for this problem has relied heavily on heuristics and domain knowledge that operates directly on the genotype to guide the search. It is sound engineering practice to utilise all available information to reduce design and evaluation times, and encourage the formulation of useful solutions. However, domain design knowledge is not always available. This research attempts to explore the efficiency and effectiveness of a GA, when applied to a difficult design task, without being unnecessarily constrained by preconceptions of how to solve the task. Heavy guidance of a GA potentially stifles innovation, can only be applied to situations where the correct answer is known and limits the generic abilities of the search system. This research demonstrates the ability of the GA to evolve good, near optimal solutions without direct guidance. Performing an unbiased search, using only the evolutionary process to search for good solutions, allows a GA to be applied with a high degree of confidence to situations where a priori knowledge of the optimum solution is unavailable. Advanced two-dimensional genetic operators, in conjunction with a suitably designed fitness function, allow a productive evolutionary search. The initial test case is the evolution of an optimal I-beam cross-section, subject to several load cases, starting with an initial random population. It is shown that the methods developed lead to consistently good solutions, despite the complexity of the process.