New Mathematical And Evolutionary Optimization Methods To Achieve Fair Division In Multi-Agent Resource Allocation

The problem of resource allocation among a group of agents naturally arises in a wide range of real-life events. The subject has earned popularity across the disciplines of Economics, Computer Science, Artificial Intelligence Operations Research and Social Welfare. This resource allocation problem can be commonly referred to as Multi-Agent Resource Allocation (MARA). This work considers a MARA problem where a central agent decides to allocate a set of divisible and non-divisible goods. MARA is considered to be part of an interdisciplinary research area in which the literature is vast and rapidly developing. However, most of the available literature mainly focuses on the computational and theoretical aspects of the MARA and the representation of agents\u27 preferences. In order to expand on the existent literature this work introduces two new algorithms and provides a set of numerical examples to show potential engineering and financial applications. The first algorithm provides a new mathematical definition of envy that is employ as an optimization criterion. The second algorithm is a new preference representation system that converts agents\u27 ordinal preferences into a cardinal. In addition, the low computational complexity of the latter algorithm makes of it a very promising tool in multi-criteria optimization