Towards the Design of Complex Evolving Networks with High Robustness and Resilience

Abstract

Network design and optimization research has traditionally been focused on networks where the designers have direct control over the nodes and their connectivity. However there is increasing importance of social, economic and technical networks whose structures are not under the direct control of the designers, but evolve as a result of decisions and behaviors of individual self- directed entities. These networks are endogenous in nature, where the local characteristics and behaviors of nodes affect the overall structures. The structure of a network affects its properties, and the properties affect the system's performance. Hence, the problem of designing such endogenously evolving networks involves determining the node-level characteristics and behaviors through appropriate incentives to achieve the desired system-level performance. In this paper, our goal is to illustrate the problem of designing endogenously evolving networks, and to present a specific illustrative example. We perform a conceptual exploration of the problem, present the current state of the art and identify research gaps. The illustrative example involves designing an endogenous network with two objectives, robustness to random node failure and resilience to targeted attack, considering specific node-level characteristics, additional attractiveness, as the design variables. The impact of the design variables on the performance of the network, and potential applications are discussed.