In this article, we propose novel strategies for the efficient determination of multiple solutions for a single objective, as well as globally optimal pareto fronts for multiobjective, optimization problems using Constraint Programming (CP). In particular, we propose strategies to determine, (i) all the multiple (globally) optimal solutions of a single objective optimization problem, (ii) K-best feasible solutions of a single objective optimization problem, and (iii) globally optimal pareto fronts (including non-convex pareto fronts) along with their multiple realizations for multiobjective optimization problems. It is shown here that the proposed strategy for determining K-best feasible solutions can be tuned as per the requirement of the user to determine either K-best distinct or nondistinct solutions. Similarly, the strategy for determining globally optimal pareto fronts can also be modified as per the requirement of the user to determine either only the distinct set of pareto points or determine the pareto points along with all their multiple realizations. All the proposed techniques involve appropriately modifying the search techniques and are shown to be computationally efficient in terms of not requiring successive re-solving of the problem to obtain the required solutions. This work therefore convincingly addresses the issue of efficiently determining globally optimal pareto fronts; in addition, it also guarantees the determination of all the possible realizations associated with each pareto point. The uncovering of such solutions can greatly aid the designer in making informed decisions. The proposed approaches are demonstrated via two case studies, which are nonlinear, combinatorial optimization problems, taken from the area of sensor network design. (C) 2009 American Institute of Chemical Engineers AIChE J, 56: 387-404, 2010