An Application of Membrane Computing to Humanitarian Relief via Generalized Nash Equilibrium
Alejandro Luque-Cerpa, David Orellana-Martín, Miguel A. Gutiérrez-Naranjo
TL;DR
This paper demonstrates that Membrane Computing, via transition P systems with membrane polarization, can model and compute Generalized Nash Equilibria for post-disaster humanitarian relief. By formulating the relief distribution problem with $m$ NGOs and $n$ demand locations as a GNE and solving it through an Euler-method-based iterative scheme, the authors design a P-system architecture with three stages (Initialization, Update, Comparison) and analyze its time complexity, showing practical efficiency ($\mathcal{O}(t)$ in experiments) and modularity. Experiments on NagurneyMain toy cases and Hurricane Katrina data validate the approach, with small average errors (≈$2\%$ for Katrina) and exact matches on toy examples, supporting the viability of Membrane Computing as a tool for humanitarian logistics. The work provides a novel bridge between membrane computing and real-world relief optimization, offering a scalable, parallel framework that can incorporate additional agents and constraints in future deployments.
Abstract
Natural and political disasters, including earthquakes, hurricanes, and tsunamis, but also migration and refugees crisis, need quick and coordinated responses in order to support vulnerable populations. In such disasters, nongovernmental organizations compete with each other for financial donations, while people who need assistance suffer a lack of coordination, congestion in terms of logistics, and duplication of services. From a theoretical point of view, this problem can be formalized as a Generalized Nash Equilibrium (GNE) problem. This is a generalization of the Nash equilibrium problem, where the agents' strategies are not fixed but depend on the other agents' strategies. In this paper, we show that Membrane Computing can model humanitarian relief as a GNE problem. We propose a family of P systems that compute GNE in this context, and we illustrate their capabilities with Hurricane Katrina in 2005 as a case study.