Relaxed fuzzy randomization

Abstract

This paper addresses the role of randomization in the solution of a constraint-satisfaction problem (CSP). It is argued that just as the use of heuristics permit the solution of more complex problems than would otherwise be possible, the relaxation of the optimality constraint carries two attendant benefits. First, among the class of NP-hard problems, relaxation permits the solution of otherwise intractable problems (e.g., the TSP). Second, relaxation permits the use of new types of parallel hardware (e.g., SLMs), which offer at least two orders of magnitude speedup. Combining these two improvements defines a new paradigm for soft computing, which we term, relaxed fuzzy randomization (RFR). The definition of RFR necessarily includes an overview of randomness and symmetry and their mutually inclusive roles in defining a different genre of fuzzy computation. This computational class can defy formal analysis in keeping with the dictates of Godel's incompleteness theorem. That is, it is argued that chance plays a greater role in the twin processes of search and knowledge acquisition than has been heretofore acclaimed. This paper represents an attempt to advance that cause.