Oriol Lordan

Optimal Allocation of Node Capacity in Cascade-Robustness Networks

The robustness of large scale critical infrastructures, which can be modeled as complex networks, is of great significance. One of the most important means to enhance robustness is to optimize the allocation of resources. Traditional allocation of resources is mainly based on the topology information, which is neither realistic nor systematic. In this paper, we try to build a framework for searching for the most favorable pattern of node capacity allocation to reduce the vulnerability to cascading failures at a low cost. A nonlinear and multi-objective optimization model is proposed and tackled using a particle swarm optimization algorithm (PSO). It is found that the network becomes more robust and economical when less capacity is left on the heavily loaded nodes and the optimized network performs better resisting noise. Our work is helpful in designing a robust economical network.

Study of the robustness of the European air routes network

In this working paper we make analysis on flight flow network structure of Europe. The aim of this study is to analyze the robustness of the European civil European air transportation network from the perspective of the theory of complex networks. This study is based on analyzing the behavior of the network when its nodes (airports) are removed by random attacks and deliberate attacks. The selection of nodes on deliberate attacks is based on four criteria: degree, betweenness, pagerank and eigenvector. This study aims to contribute to the understanding of the logistics network of European commercial flights, analyzing their strengths and weaknesses. The calculation of network statistical indicators as degree and betweenness distribution reveals that the flight flow network has the small-world characteristics and scale-free property.

Cascades Tolerance of Scale-Free Networks with Attack Cost

Network robustness against cascades is a major topic in the fields of complex networks. In this paper, we propose an attack-cost-based cascading failure model, where the attack cost of nodes is positively related to its degree. We compare four attacking strategies: the random removal strategy (RRS), the low-degree removal strategy (LDRS), the high-degree removal strategy (HDRS) and the genetic algorithm removal strategy (GARS). It is shown that the network robustness against cascades is heavily affected by attack costs and the network exhibits the weakest robustness under GARS. We also explore the relationship between the network robustness and tolerance parameter under these attacking strategies. The simulation results indicate that the critical value of tolerance parameter under GARS is greatly larger than that of other attacking strategies. Our work can supply insight into the robustness and vulnerability of complex networks corresponding to cascading failures.

Cascading failures with local load redistribution in interdependent Watts–Strogatz networks

Cascading failures of loads in isolated networks have been studied extensively over the last decade. Since 2010, such research has extended to interdependent networks. In this paper, we study cascading failures with local load redistribution in interdependent Watts–Strogatz (WS) networks. The effects of rewiring probability and coupling strength on the resilience of interdependent WS networks have been extensively investigated. It has been found that, for small values of the tolerance parameter, interdependent networks are more vulnerable as rewiring probability increases. For larger values of the tolerance parameter, the robustness of interdependent networks firstly decreases and then increases as rewiring probability increases. Coupling strength has a different impact on robustness. For low values of coupling strength, the resilience of interdependent networks decreases with the increment of the coupling strength until it reaches a certain threshold value. For values of coupling strength above this threshold, the opposite effect is observed. Our results are helpful to understand and design resilient interdependent networks.

Modeling and Solving Linear Programming with R

Linear programming is one of the most extensively used techniques in the toolbox of quantitative methods of optimization. One of the reasons of the popularity of linear programming is that it allows to model a large variety of situations with a simple framework. Furthermore, a linear program is relatively easy to solve. The simplex method allows to solve most linear programs efficiently, and the Karmarkar interior-point method allows a more efficient solving of some kinds of linear programming. The power of linear programming is greatly enhanced when came the opportunity of solving integer and mixed integer linear programming. In these models all or some of the decision variables are integers, respectively. In this book we provide a brief introduction to linear programming, together with a set of exercises that introduce some applications of linear programming. We will also provide an introduction to solve linear programming in R. For each problem a possible solution through linear programming is introduced, together with the code to solve it in R and its numerical solution.