Epiphytic Trees: Relational Consistency Applied to Global Optimization Problems

Much effort has been spent to identify classes of CSPs in terms of the relationship between network structure and the amount of consistency that guarantees a backtrack-free solution. In this paper, we address Numerical Constrained global Optimization Problems (NCOPs) encoded as ternary networks, characterizing a class of such problems for which a combination of Generalized Arc-Consistency (GAC) and Relational Arc-Consistency (RAC) is sufficient to ensure a backtrack-free solution, called Epiphytic Trees. While GAC is a domain filtering technique, enforcing RAC creates new constraints in the network. Alternatively, we propose a branch and bound method to achieve a relaxed form of RAC, thus finding an approximation of the solution of NCOPs. We empirically show that Epiphytic Trees are relevant in practice. In addition, we extend this class to cover all ternary NCOPs, for which Strong Directional Relational k-Consistency ensures a backtrack-free solution.

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