Towards a Learning Automata Solution to the Multi-Constraint Partitioning Problem

We consider the problem of partitioning a set of elements (or objects) into mutually exclusive classes (or groups), where elements which are "similar" to each other are, hopefully, located in the same class. This problem has been shown to be NP-hard, and the literature reports solutions in which the similarity constraint consists of a single index. For example, typical "similarity" conditions that have been used in the literature include those in which "similar" objects are accessed together, or when they communicate (as processes do) with each other. In this paper, we present the first reported solution to the case when the objects could be linked together in a multi-constraint manner, and indeed, visit the scenario when the constraints could, themselves, be contradictory. The solution we propose is based on the theory of estimator-based learning automata (LA), operating in non-stationary environments. Rather than use traditional estimates, we advocate the use of stochastic weak-estimates (B. J. Oommen and L. Rueda, 2006) and the specific digraph properties of the relations between the elements. Although the solutions proposed perform admirably when the number of elements is small, the simulated results demonstrate that the quality of the final solution decreases with the number of elements. Thus, although this is the first reported solution to the problem which incorporates specific digraph properties of the objects, the scalability of the solution remains open