Randomness as a constraint

Abstract

Some optimisation problems require a random-looking solution with no apparent patterns, for reasons of fairness, anonymity, undetectability or unpredictability. Randomised search is not a good general approach because problem constraints and objective functions may lead to solutions that are far from random. We propose a constraint-based approach to finding pseudo-random solutions, inspired by the Kolmogorov complexity definition of randomness and by data compression methods. Our "entropy constraints" can be implemented in constraint programming systems using well-known global constraints. We apply them to a problem from experimental psychology and to a factory inspection problem.