Social Optimization: Framework,Algorithms and Applications

摘要

The efficient design, management and control of today's technological systems and solutions is to an increasing degree characterized by societal aspects. This also applies to the classical task of optimization as it appears now in new domains like group decision making, fair distribution, equity of resource sharing and we can find among the application domains communication networks, cloud computing, risk assessment, pattern recognition, computational security, collaborative and recommendation systems. These tasks can often not be expressed by simple function evaluations anymore. Relational mathematics, which is studied in mathematical economics and social choice theory, provides a rich and general framework and appears to be a natural and direct way to express corresponding optimization goals, to represent user preferences, to justify fairness criterions, or to valuate utility. The talk will have two main parts. In the first part, basic approaches from mathematical economics to the problemacy of fairness (in distribution and allocation) are recalled. It is followed by the presentation of a set of relations that are able to represent various aspects of fairness along with their motivation. Starting with the "classical" fairness relations maxmin fairness, proportional fairness and lexicographic maxmin, we can recover their mutual relationships and their design flexibility in order to define further relations, with regard to e.g. multi-resource problems, ordered fairness, self-weighted fairness, collaborative fairness, and fuzzy fairness. In the second part, we want to illustrate and demonstrate the application of these concepts to basic data processing and optimization tasks, especially in data mining, multi-agent systems, pattern recognition and performance comparison of metaheuristic algorithms. In this part we will also mention the tractability of larger-scaled problems by presenting algorithmic approaches by meta-heuristic algorithms derived from well-known evolutionary multi-objective optimization algorithms, as a side note also show that the No-Free-Lunch theorems do not apply to the proposed relational optimization.