In this paper, we model the optimisation of the resource allocation in cloud computing as a constraint satisfaction problem considering three types of resources (CPU, RAM and bandwidth) and design a Choco-Based algorithm (CB) for VM resource allocation in virtualised cloud data centres. We also propose an Improved First-Fit Decreasing Algorithm (IFFD) and an Improved Best-Fit Decreasing Algorithm (IBFD) and conduct performance evaluation experiments using Choco. The experimental results show that CB has better results, whereas its solution time is longer than IFFD and IBFD in resource allocation. Moreover, to reduce the complexity of solving the problem of CSP-based resource allocation, we propose an equivalence optimisation which can greatly reduce the search space for resource allocation by making tree pruning with resource equivalence. Then, a resource allocation algorithm based on Equivalent Optimisation (EO) is designed. Experimental results also show that compared with CB, EO greatly reduces the time of allocating resource of cloud computing.