In the last several decades fluid power has been used extensively in diverse industries such as agriculture, construction, marine, offshore resource extraction, and even entertainment. With a vast and ever-increasing spectrum of potential applications, the design of efficient and leak-free components in fluid power systems has become essential. Previous experiments and studies have shown that the use of microtextured surfaces in hydraulic components achieves performance enhancement by reducing friction and leakage. This article aims to build on this recent work through a systematic optimization-based study of performance improvement through microtexture surface design. These studies evaluate the potential of Newtonian fluid properties, coupled with varying surface features, to achieve design objectives for efficiency. This early-stage design strategy aims to find optimal surface features that minimize apparent fluid viscosity (low friction) and the area of the microtexture. The resulting multi-objective optimization (MOO) problem involves a computationally intensive simulation of the system based on computational fluid dynamics (CFD). As a strategy to reduce overall computational expense, this paper describes the development of a new adaptive surrogate modeling strategy for multi-objective optimization. Two case studies are presented: a simple analytical case study illustrating the details of the method and a more sophisticated case study involving the two-dimensional CFD simulation of Newtonian fluids on symmetric surface textures. This design approach embraces the potential of using rheologically complex fluids in engineering system design and optimization. This study can be further extended to a more generalized problem by coupling both fluid and geometrical design decisions.