A Novel Heuristic to Solve IA Network by Convex Approximation and Weights

Abstract

In this paper we propose a new heuristic to determine a solution of a general interval algebra(IA) network. We make use of a tractable upper approximation by replacing each disjunction of the IA network by its interval closure. The resulting network becomes a convex network and it is well known that the consistency of the convex network can be decided in polynomial time. We start with a singleton labeling of the approximation and gradually work towards a consistent singleton labeling of the original network. We propose a scheme of ranking the basic relations in a disjunction and our search process moves in the decreasing order of this rank to find a solution. We exploit the properties of convex relations and weighted relations to design our heuristic for the general class of problems. The experiment reveals that the convex approximation finds consistency for more number of problems than the algorithm without approximation.