This paper develops cloud based software computing as a service (SCaaS) in hybrid evolution algorithm with feedback assistance to find the optimal solution of NP-complete problems such as job shop scheduling problems. In this paper, the different steps and types of the evolution algorithm can be established via individual thread procedures and various virtual machines in cloud. During the evolution steps, methods, or procedures of the genetic algorithm, the fitness evaluation result and survival ratio of different crossover methods in the current generation can be used for the feedback assistance method. The proposed feedback assistance method can be added into the evolution procedure and dynamically emphasize the corresponding methods or procedures with better performance in optimal solution searching. All the steps or methods in genetic algorithm are created similar to the MapReduce structure. Furthermore, via using the feedback assistance, the convergence time of the optimal solution can be enhanced.