The gap between abstraction levels in analog design is a major obstacle for advancing analog and mixed-signal (AMS) design automation and computer-aided design (CAD). Intelligent models for low-level analog building blocks are needed to bridge the accuracy gap between behavioral and transistor-level simulations. The models should be able to accurately estimate the characteristics of the analog block over a large design space. Machine learning (ML) models based on actual silicon have the capabilities of capturing detailed characteristics of complex designs. In this paper, a ML model called Artificial Neural Network Metamodels (ANNM) have been explored to capture the highly nonlinear nature of analog blocks. The application of these intelligent models to multi-objective AMS block optimization is demonstrated. Parameterized behavioral models in Verilog-AMS based on the ANN metamodels are constructed for efficient AMS design exploration. To the best of the authors' knowledge this is the first paper to integrate ANN models in Verilog-AMS, which is called iVAMS 2.0. To demonstrate the application of iVAMS 2.0, this paper presents two case studies: an operational amplifier (OP-AMP) and a phase-locked loop (PLL). A biologically-inspired "firefly optimization algorithm" is applied to an OP-AMP design in the iVAMS 2.0 framework. The optimization process is sped up by 5580X due to the use of iVAMS with negligible loss in accuracy. Similarly, for a PLL design, the physical design aware ANNs are trained and used as metamodels to predict its frequency, locking time, and power. Thorough experimental results demonstrate that only 100 sample points are sufficient for ANNs to predict the output of circuits with 21 design parameters within 3% accuracy. A proposed artificial bee colony (ABC) based algorithm performs optimization over the ANN metamodels of the PLL.