In many real optimisation scenarios, instances arrive in a stream and an algorithm selector is used to select the  most appropriate solver for a given instance. However, if the data distribution of instances in the stream changes over time, new solvers may be required at some point downstream to continue to provide the best solutions to new instances. This requires  a selector to be periodically updated to incorporate new class labels while at the same time, continuing to perform well on previously seen data (i.e. avoid ‘catastrophic forgetting’). Class Incremental Learning (CIL) techniques are designed to deal with this situation, but although commonly used in machine-learning, have rarely been studied in the context of algorithm selection in an optimisation setting. To address this gap, we benchmark 8 CIL methods with respect to their ability to withstand catastrophic forgetting using instances from a commonly used benchmark in continuous optimisation. We find that rehearsal-based  CIL methods that save exemplars of previous data and use them when retraining significantly outperform other methods. While there is some evidence of forgetting, the loss is small at around \(7\%\) . Overall accuracy of the final model at the end of the stream is \({\ge } 91\%\) . Hence, these methods appear to be a viable approach to continual learning in streaming optimisation scenarios on continuous optimisation benchmarks.