Variable Pipeline Cool Mega Array (VPCMA) is an low power Coarse Grained Reconfigurable Architecture (CGRA) based on the concept of CMA (Cool Mega Array). It implements a pipeline structure that can be configured depending on performance requirements, and the silicon on thin buried oxide (SOTB) technology that allows to control its body bias voltage to balance performance and leakage power. In this paper, we propose a methodology to optimize exactly with an Integer Linear Program the VPCMA body bias while considering simultaneously its variable pipeline structure. For the studied applications, we evaluate that it is possible to achieve an average reduction of energy consumption of 19.3% and 11.8% when compared to respectively the zero bias (without body bias control) and the uniform (control of the whole PE array) cases, while respecting performance constraints. Besides, with appropriate body bias control, it is possible to extend the possible performance, hence enabling broader trade-off analyzes between consumption and performance. These promising results show that applying an adequate optimization technique for the body bias control while simultaneously considering pipeline structures can not only enable further power reduction than previous methods, but also allow more trade-off analysis possibilities.