The service (task) allocation problem in the distributed computing is one form of multidimensional knapsack problem which is one of the best examples of the combinatorial optimization problem. Nature-inspired techniques represent powerful mechanisms for addressing a large number of combinatorial optimization problems. Computation of getting an optimal solution for various industrial and scientific problems is usually intractable. The service request allocation problem in distributed computing belongs to a particular group of problems, i.e., NP-hard problem. The major portion of this chapter constitutes a survey of various mechanisms for service allocation problem with the availability of different cloud computing architecture. Here, there is a brief discussion towards the implementation issues of various metaheuristic techniques like Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Ant Colony Optimization (ACO), BAT algorithm, etc. with various environments for the service allocation problem in the cloud.