Evaluating Genetic Algorithms on Welding Sequence Optimization With Respect to Dimensional Variation and Cycle Time

Abstract

Spot welding is the predominant joining method in car body assembly. Spot welding sequences have a significant influence on the dimensional variation of resulting assemblies and ultimately on overall product quality. It also has a significant influence on welding robot cycle time and thus ultimately on manufacturing cost. In this work we evaluate the performance of Genetic Algorithms, GAs, on multi-criteria optimization of welding sequence with respect to dimensional assembly variation and welding robot cycle time. Reference assemblies are fully modelled in 3D including detailed fixtures, welding robots and weld guns. Dimensional variation is obtained using variation simulation and part measurement data. Cycle time is obtained using automatic robot path planning. GAs are not guaranteed to find the global optimum. Besides exhaustive calculations, there is no way to determine how close to the actual optimum a GA trial has reached. Furthermore, sequence fitness evaluations constitute the absolute majority of optimization computation running time and do thus need to be kept to a minimum. Therefore, for two industrial reference assemblies we investigate the number of fitness evaluations that is required to find a sequence that is optimal or a near-optimal with respect to the fitness function. The fitness function in this work is a single criterion based on a weighted and normalized combination of dimensional variation and cycle time. Both reference assemblies involves 7 spot welds which entails 7!=5040 possible welding sequences. For both reference assemblies, dimensional variation and cycle time is exhaustively calculated for all 5040 possible sequences, determining the optimal sequence, with respect to the fitness function, for a fact. Then a GA that utilizes Random Key Encoding is applied on both cases and the performance is recorded. It is found that in searching through about 1% of the possible sequences, optimum is reached in about half of the trials and 80–90% of the trials reach the ten best sequences. Furthermore the optimum of the single criterion fitness function entails dimensional variation and cycle time fairly close to their respective optimum. In conclusion, this work indicates that genetic algorithms are highly effective in optimizing welding sequence with respect to dimensional variation and cycle time.