Designing Networks: A Mixed-Integer Linear Optimization Approach

TL;DR

This paper introduces a systematic approach using mixed-integer linear optimization to generate networks with specific properties, aiding in network analysis, design, and evolution studies.

Contribution

It develops a novel optimization-based framework for generating networks with guaranteed properties, filling a gap in systematic network design methods.

Findings

Successfully models and generates networks with specified properties

Demonstrates the approach through computational case studies

Provides a flexible framework for network property constraints

Abstract

Designing networks with specified collective properties is useful in a variety of application areas, enabling the study of how given properties affect the behavior of network models, the downscaling of empirical networks to workable sizes, and the analysis of network evolution. Despite the importance of the task, there currently exists a gap in our ability to systematically generate networks that adhere to theoretical guarantees for the given property specifications. In this paper, we propose the use of Mixed-Integer Linear Optimization modeling and solution methodologies to address this Network Generation Problem. We present a number of useful modeling techniques and apply them to mathematically express and constrain network properties in the context of an optimization formulation. We then develop complete formulations for the generation of networks that attain specified levels of connectivity, spread, assortativity and robustness, and we illustrate these via a number of computational case studies.