Cross-Sestion Optimisation for Cold-Rolled Steel Beams Using a Genetic Algorithm

Since the use of cold-rolled steel sections is a standard method in mechanical engineering and steelwork and cost efficiency is always a big issue, it is of great interest to address the highly non convex problem of cross-section optimisation. At a first glance classic genetic algorithms already seem to be suitable for this problem, because they are powerful search heuristics for solutions in non convex problems. But in addition to the great number of local optima, which can occur in the optimisation process, the problem is also constrained due to constructive needs and limitations in manufacturing. Constraints highly affect the ability of genetic algorithms to overcome local optima, especially under high selection pressure. This high selection pressure comes from the need to suit the given use case in terms of physical stability. Therefore we had to handle the restrictions more flexible, so that the algorithm can temporarily violate our stability criteria to overcome a local optimum, but will end up with a solution within our given boundaries. To achieve this we negatively coupled the penalty factor for stability criteria violations to the mutation strength, thus allowing adaptive radiation with rather freewheeling restriction handling, followed by a rigid selection process approaching the optimal solution. Additionally we introduced an inbreed avoiding recombination system to speed-up the exploration of the fitness landscape. This yielded material savings of about 20 %. To speed up the method, parallelisation was applied and the algorithm could be implemented on a 60-core Linux cluster.