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As a future trend of healthcare, personalized medicine tailors medical treatments to individual patients. It requires to identify a subset of patients with the best response to treatment. The subset can be defined by a biomarker (e.g. expression of a gene) and its cutoff value. Topics on subset identification have received massive attention. There are over 2 million hits by keyword searches on Google Scholar. However, how to properly incorporate the identified subsets/biomarkers to design clinical trials is not trivial and rarely discussed in the literature, which leads to a gap between research results and real-world drug development. To fill in this gap, we formulate the problem of clinical trial design into an optimization problem involving high-dimensional integration, and propose a novel computational solution based on Monte-Carlo and smoothing methods. Our method utilizes the modern techniques of General-Purpose computing on Graphics Processing Units for large-scale parallel computing. Compared to the standard method in three-dimensional problems, our approach is more accurate and 133 times faster. This advantage increases when dimensionality increases. Our method is scalable to higher-dimensional problems since the precision bound is a finite number not affected by dimensionality. Our software will be available on GitHub and CRAN, which can be applied to guide the design of clinical trials to incorporate the biomarker better. Although our research is motivated by the design of clinical trials, the method can be used widely to solve other optimization problems involving high-dimensional integration.