In the field of VLSI circuit optimization, the scaling of semiconductor devices has led to the miniaturization of the feature sizes resulting in a significant increase in the integration density and size of the circuits. At the nanometer level, due to the effects of manufacturing process variations, the design optimization process has transitioned from the deterministic domain to the stochastic domain, and the inter-relationships among the specification parameters like delay, power, reliability, noise and area have become more intricate. New methods are required to examine these metrics in a unified manner, thus necessitating the need for multi-metric optimization. The optimization algorithms need to be accurate and efficient enough to handle large circuits. As the size of an optimization problem increases significantly, the ability to cluster the design metrics or the parameters of the problem for computational efficiency as well as better analysis of possible trade-offs becomes critical. In this dissertation research, several utilitarian methods are investigated for variation aware multi-metric optimization in VLSI circuit design and spatial pattern clustering. A novel algorithm based on the concepts of utility theory and risk minimization is developed for variation aware multi-metric optimization of delay, power and crosstalk noise, through gate sizing. The algorithm can model device and interconnect variations independent of the underlying distributions and works by identifying a deterministic linear equivalent model from a fundamentally stochastic optimization problem. Furthermore, a multi-metric gate sizing optimization framework is developed that is independent of the optimization methodology, and can be implemented using any mathematical programming approach. It is generalized and reconfigurable such that the metrics can be selected, removed, or prioritized for relative importance depending upon the design requirements. In multi-objective optimization, the existence of multiple conflicting objectives makes the clustering problem challenging. Since game theory provides a natural framework for examining conflicting situations, a game theoretic algorithm for multi-objective clustering is introduced in this dissertation research. The problem of multi-metric clustering is formulated as a normal form multi-step game and solved using Nash equilibrium theory. This algorithm has useful applications in several engineering and multi-disciplinary domains which is illustrated by its mapping to the problem of robot team formation in the field in multi-emergency search and rescue. The various algorithms developed in this dissertation achieve significantly better optimization and run times as compared to other methods, ensure high utility levels, are deterministic in nature and hence can be applied to very large designs. The algorithms have been rigorously tested on the appropriate benchmarks and data sets to establish their efficacy as feasible solution methods. Various quantitative sensitivity analysis have been performed to identify the inter-relationships between the various design parameters.