Evaluating genetic algorithms that optimize welding sequence with respect to geometrical assembly variation

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. In this paper, we evaluate the performance of genetic algorithms, GAs, for welding sequence optimization with respect to dimensional variation. As sequence fitness evaluations constitute the absolute majority of computation running times, they need to be kept to a minimum. Furthermore, 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 solution has reached. Therefore, for two reference assemblies, each involving 7 welds and thus 7!=5040 possible welding sequences, we investigate the number of fitness evaluations, that is required to find an optimal or a near-optimal sequence. This is done by exhaustive assembly variation calculation for all possible sequences of the two reference assemblies, determining the optimal sequence for a fact. Then GAs are succesfully applied on the two reference assemblies. Two alternative evolution approaches are examined. For one of the reference assemblies, the optimal sequence is found in 100 GA trials out of 100, having searched through in average 1.3% of all possible sequences. For the other reference assembly, an average result within 0.1% from optimum is obtained, having searched through in average 2.1% of all possible sequences (the span from best to worst sequence result constitutes 100%). Furthermore, this work indicates that a custom encoding evolution approach is more effective than a custom operator evolution approach.