3PGCIC 2011 Keynote

Summary form only given. Relational mathematics, as it is studied in mathematical economics and social choice theory, provides a rich and general framework and appears to to be a natural and direct way to paraphrase optimization goals, to represent user preferences, to justify fairness criterions, or to valuate utility. In this talk, we will focus on the specific application aspects of formal relations in network design and control problems. The talk will have three main parts. In the first part, we want to present a suite of new relations that are able to represent fairness as mediator between user preference and network infrastructure dominance. Starting with the "classical" fairness relations maxmin fairness, proportional fairness and lexmin, we can recover their mutual relationships and their design flexibility in order to define further relations, with regard to e.g. multi-fairness, ordered fairness, self-weighted fairness, grouped fairness, and fuzzy fairness. In the second part, we want to illustrate and demonstrate the application of these relations for basic network design and control problems, esp. routing path selection, congestion control, wireless channel allocation, and relaying. The third part is concerned with the tractability of related problems, and we will present generic approaches by meta-heuristic algorithms, esp. algorithms obtained from suitable modifications of evolutionary multi-objective optimization algorithms that can cope with a broad spectrum of occurring search and approximation problems. We will conclude with the outlook on a concept of generalized optimization.