Multiobjective Optimal Control Methodology for the Analysis of Certain Sociodynamic Problems

Abstract

Social networks involve studying how relations form between individuals in a group based on their shared preferences and attributes. This research addresses a very difficult question involving how social networks arise and evolve over time. Historically, some researchers have addressed this issue using loglinear modeling, continuous time Markov theory or rational choice theory. In this work, social force theory is used to model social interaction and long-term network dynamics while multiobjective control theory provides a basis for predicting network structural formation. Using computer simulations, we numerically analyze the evolution and long-term behavior of optimal network structures based on the demographics of a small data set. We pay special attention to the effect that memory has on relationship choices, especially clique formation.

After obtaining a snapshop of the network structure, we turn our attention to a very common task involving social networks: missing link prediction. The link prediction problem can be described as uncovering hidden or missing connections between nodes in an observed network. There are several link prediction methods in the literature that rely heavily on network topology to predict links and are primarily used on collaboration networks like email or coauthorship networks. The problem with these networks is that they offer no qualitative information on nodal attributes. In this work, we present a new model for link prediction that is centered on nodal attributes and uses social force theory to provide behavioral rules for nodal interaction.