Constrained Optimization Problems (COP’s) are encountered in many scientific fields concerned with industrial applications such as kinematics, chemical process optimization, molecular design, etc. When non-linear relationships among variables are defined by problem constraints resulting in non-convex feasible sets, the problem of identifying feasible solutions may become very hard. Consequently, finding the location of the global optimum in the COP is more difficult as compared to bound-constrained global optimization problems. This chapter proposes a new interval partitioning method for solving the COP. The proposed approach involves a new subdivision direction selection method as well as an adaptive search tree framework where nodes (boxes defining different variable domains) are explored using a restricted hybrid depth-first and best-first branching strategy. This hybrid approach is also used for activating local search in boxes with the aim of identifying different feasible stationary points. The proposed search tree management approach improves the convergence speed of the interval partitioning method that is also supported by the new parallel subdivision direction selection rule