Weighted Algebraic Connectivity: An Application to Airport Transportation Network

The airport transportation network structure and its performance are key factors to benefit the local area or national transportation capability and economic development. This paper presents a method based on the weighted algebraic connectivity to optimize and analyze the network. The indispensability of the weighted adjacent matrix and weighted Laplacian matrix in airport transportation network performance study is emphasized in this paper. According to practical operational viability, we formulate the weighted algebraic connectivity application as the flight routes addition/deletion problems. The greedy perturbation heuristic by Ghosh and Boyd is analyzed and extended into the Modified Greedy Perturbation Algorithm (MGP) to provide a local optimum in a fast iterative manner. The unweighted tabu search applying algebraic connectivity to airport transportation network by Vargo and Kincaid is re-designed as the Weighted Tabu Search (WTS) to fit the new weighted flight routes addition/deletion problems, potentially offering a global optimum with much longer running time. The simulation results indicate the trade-off between the Modified Greedy Perturbation and the Weighted Tabu Search, with which we can decide the appropriate algorithm to be used for enhancing the performance of an airport transportation network.