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Cloud computing is emerging as a prominent computing model. It provides a low-cost, highly accessible alternative to other traditional high-performance computing platforms. It also has many other benefits such as high availability, scalability, elasticity, and free of maintenance. Given these attractive features, it is very desirable if automated planning can exploit the large, affordable computational power of cloud computing. However, the latency in inter-process communication in cloud computing makes most existing parallel planning algorithms unsuitable for cloud computing. In this paper, we propose a portfolio stochastic search framework that takes advantage of and is suitable for cloud computing. We first study the running time distribution of Monte-Carlo Random Walk (MRW) search, a stochastic planning algorithm, and show that the running time distribution usually has remarkable variability. Then, we propose a portfolio search algorithm that is suitable for cloud computing, which typically has abundant computing cores but high communication latency between cores. Further, we introduce an enhanced portfolio with multiple parameter settings to improve the efficiency of the algorithm. We implement the portfolio search algorithm in both a local cloud and the Windows Azure cloud. Experimental results show that our algorithm achieves good, in many cases super linear, speedup in the cloud platforms. Moreover, our algorithm greatly reduces the running time variance of the stochastic search and improves the solution quality. We also show that our scheme is economically sensible and robust under processor failures.