This paper presents the study and implementation of a new efficient yield optimization technique for multi-objective optimization-based automatic analog integrated circuit sizing. The approach uses a commercial electrical simulator and standard process design kit (PDK) models to perform, during the optimization process, the same Monte Carlo (MC) simulations that designers use. The proposed yield estimation technique reduces the number of required MC simulations by using the k-means algorithm, with a variable number of clusters, to select only a handful potential solutions where the MC simulations are performed. Due to the use of a commercial simulator tool and foundry supplied PDK models the developed methodology provides the most accurate and reliable results, and also, the variable k-means algorithm is able to achieve 91% reduction in the total number of the MC simulations required for an optimization, when considering MC simulations for all solutions. Moreover, this new approach presents a 50% increase in speed performance when comparing to a previous yield optimization technique also using k-means and MC simulations.