Meta-heuristic approach to proportional fairness

Proportional fairness is a concept from resource sharing tasks among n users, where each user receives at least 1/n of her or his total value of the infinitely divisible resource. Here we provide an approach to proportional fairness that allows its extension to discrete domains, as well as for the direct application of evolutionary computation to approximate proportional fair states. We employ the concept of relational optimization, where the optimization task becomes the finding of extreme elements of a binary relation, and define a proportional fairness relation correspondingly. By using a rank-ordered version of proportional fairness, the so-called ordered proportional fairness, we can improve the active finding of maximal proportional fair elements by evolutionary meta-heuristic algorithms. This is demonstrated by using modified versions of the Strength Pareto Evolutionary Algorithm (version 2, SPEA2) and Multi-Objective Particle Swarm Optimization (MOPSO). In comparison between proportional and ordered proportional fairness, and by using relational SPEA2, the evolved maximum sets of ordered proportional fairness achieve 10% more dominance cases against a set of random vectors than proportional fairness.