Pareto optimality in multilayer network growth

TL;DR

This paper models multilayer transportation networks as multi-objective optimization problems, demonstrating that real-world systems like airlines tend to operate near Pareto optimality, balancing efficiency and competition.

Contribution

It introduces a multi-objective optimization model for multilayer network growth that explains the structure of real transportation systems and their proximity to Pareto fronts.

Findings

Real-world transportation networks align closely with Pareto optimal solutions.

Airline route networks of major carriers are near the theoretical Pareto front.

The model reproduces diverse systems like air, train, and bus networks.

Abstract

We model the formation of multi-layer transportation networks as a multi-objective optimization process, where service providers compete for passengers, and the creation of routes is determined by a multi-objective cost function encoding a trade-off between efficiency and competition. The resulting model reproduces well real-world systems as diverse as airplane, train and bus networks, thus suggesting that such systems are indeed compatible with the proposed local optimization mechanisms. In the specific case of airline transportation systems, we show that the networks of routes operated by each company are placed very close to the theoretical Pareto front in the efficiency-competition plane, and that most of the largest carriers of a continent belong to the corresponding Pareto front. Our results shed light on the fundamental role played by multi-objective optimization principles in shaping the structure of large-scale multilayer transportation systems, and provide novel insights to service providers on the strategies for the smart selection of novel routes.