With the development of big data and artificial intelligence, cloud resource requests present more complex features, such as being sudden, arriving in batches and being diverse, which cause the resource allocation to lag far behind the resource requests and an unbalanced resource utilization that wastes resources. To solve this issue, this paper proposes a proactive resource allocation method based on the adaptive prediction of the resource requests in cloud computing. Specifically, this method first proposes an adaptive prediction method based on the runs test that improves the prediction accuracy of resource requests, and then, it builds a multiobjective resource allocation optimization model, which alleviates the latency of the resource allocation and balances the utilizations of the different types of resources of a physical machine. Furthermore, a multiobjective evolutionary algorithm, the Nondominated Sorting Genetic Algorithm with the Elite Strategy (NSGA-II), is improved to further reduce the resource allocation time by accelerating the solution speed of the multiobjective optimization model. The experimental results show that this method realizes the balanced utilization between the CPU and memory resources and reduces the resource allocation time by at least 43% (10 threads) compared with the Improved Strength Pareto Evolutionary algorithm (SPEA2) and NSGA-II methods.