Dynamic constrained optimisation problems (DCOPs) widely exist in the real world due to frequently changing factors influencing the environment. Many dynamic optimisation methods such as diversity-driven methods, memory and prediction methods offer different strategies to deal with environmental changes. However, when DCOPs change very fast or have very limited time for the algorithm to react, the potential of these methods is limited due to time shortage for re-optimisation and adaptation. This is especially true for population-based dynamic optimisation methods, which normally need quite a few fitness evaluations to find a near-optimum solution. To address this issue, this paper proposes to tackle fast-changing DCOPs through a smart combination of offline and online optimisation. The offline optimisation aims to prepare a set of good solutions for all possible environmental changes beforehand. With this solution set, the online optimisation aims to react quickly to each truly happening environmental change by doing optimisation on the set. To find this solution set, this paper further proposes to use competitive co-evolution for offline optimisation by co-evolving candidate solutions and environmental parameters. The experimental studies on a well-known benchmark test set of DCOPs show that the proposed method outperforms existing methods significantly especially when the environment changes very fast