Resource allocation strategy has been a hot and difficult research topic in cloud computing field. In view of the fair distribution of multi-dimensional resources in heterogeneous cloud computing environment, two resource allocation strategies were proposed by combining Genetic Algorithm (GA) and Different Evolution (DE) algorithm and taking into account both fairness and efficiency in heterogeneous cloud environment. The solution matrix was improved to convert the Dominant Resource Fairness allocation in Heterogeneous systems (DRFH) model into Integer Linear Programming (ILP) model, a Max Task Match (MTM) based algorithm was used to generate initial solutions, and a revising operation was brought to change infeasible solutions into feasible solutions, which can accelerate the convergence to acquire the optimal solution quickly and effectively. Experimental results demonstrate that the multi-dimensional resources fair allocation strategies based on GA and DE algorithm can obtain near-optimal solutions; and in aspects of maximizing the value of minimum global dominant share and resource utilization, it is superior to Best-Fit DRFH and Distributed-DRFH, and has higher environmental adaptability to the resource requirement of different task types.