Maximizing algebraic connectivity in air transportation networks
Abstract
In air transportation networks the robustness of a network regarding node and link failures is a key factor for its design. An experiment based on the real air transportation network is performed to show that the algebraic connectivity is a good measure for network robustness. Three optimization problems of algebraic connectivity maximization are then formulated in order to find the most robust network design under different constraints. The algebraic connectivity maximization problem with flight routes addition or deletion is first formulated. Three methods to optimize and analyze the network algebraic connectivity are proposed. The Modified Greedy Perturbation Algorithm (MGP) provides a sub-optimal solution in a fast iterative manner. The Weighted Tabu Search (WTS) is designed to offer a near optimal solution with longer running time. The relaxed semi-definite programming (SDP) is used to set a performance upper bound and three rounding techniques are discussed to find the feasible solution. The simulation results present the trade-off among the three methods. The case study on two air transportation networks of Virgin America and Southwest Airlines show that the developed methods can be applied in real world large scale networks. The algebraic connectivity maximization problem is extended by adding the leg number constraint, which considers the traveler's tolerance for the total connecting stops. The Binary Semi-Definite Programming (BSDP) with cutting plane method provides the optimal solution. The tabu search and 2-opt search heuristics can find the optimal solution in small scale networks and the near optimal solution in large scale networks. The third algebraic connectivity maximization problem with operating cost constraint is formulated. When the total operating cost budget is given, the number of the edges to be added is not fixed. Each edge weight needs to be calculated instead of being pre-determined. It is illustrated that the edge addition and the weight assignment can not be studied separately for the problem with operating cost constraint. Therefore a relaxed SDP method with golden section search is developed to solve both at the same time. The cluster decomposition is utilized to solve large scale networks.
Degree
Ph.D.
Advisors
Sun, Purdue University.
Subject Area
Aerospace engineering|Operations research
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