Searching for Pareto-optimal Randomised Algorithms

Randomised algorithms traditionally make stochastic decisions based on the result of sampling from a uniform probability distribution, such as the toss of a fair coin. In this paper, we relax this constraint, and investigate the potential benefits of allowing randomised algorithms to use non-uniform probability distributions. We show that the choice of probability distribution influences the non-functional properties of such algorithms, providing an avenue of optimisation to satisfy non-functional requirements. We use Multi-Objective Optimisation techniques in conjunction with Genetic Algorithms to investigate the possibility of trading-off non-functional properties, by searching the space of probability distributions. Using a randomised self-stabilising token circulation algorithm as a case study, we show that it is possible to find solutions that result in Pareto-optimal trade-offs between non-functional properties, such as self-stabilisation time, service time, and fairness.