Meta-heuristic optimization reloaded

We consider the meta-heuristic approach to optimization as to be performed in four stages (model, optimality, algorithm, verification), and point out the potential of varying the optimality stage, in contrary to the design of new algorithms. Thus, we can also apply the meta-heuristic approach to optimization to the task of fair distribution of indivisible or elastic goods, where the optimality is represented by (set-theoretic) fairness relations. As a demonstration, we fix a meta-heuristic algorithm (here a generalized version of the Strength Pareto Evolutionary Algorithm SPEA2) and provide a set of 15 fairness relations, along with the discussion of general design principles for relations, to handle the Wireless Channel Allocation problem. For validation, comparison with an equal-effort random search is used. The demonstration shows that while all relations represent a similar model (they are all directly or indirectly related to the Bottleneck Flow Control algorithm), the performance varies widely. In particular, representing fairness of distribution by ordered proportional fairness or by exponential Ordered-Ordered Weighted Averaging appears to be in favour of a successfull meta-heuristic search.