A Lattice Boltzmann Method-like Algorithm for the Maximal Covering Location Problem on the Complex Network: Application to Location of Railway Emergency-Rescue Spot

Abstract

Inspired by the core idea of the lattice Boltzmann method (LBM), which is successfully used in complex and nonlinear processes, we developed a lattice Boltzmann method-like (LBM-like) algorithm to effectively solve the maximal covering location problem with continuous- and inhomogeneous-edge demand on the complex network. The LBM-like algorithm developed has three key components, including the basic map, transfer function and effect function. The basic map is responsible for reasonably mapping complex networks with multiple branches and circles. Transfer functions are used to describe the complex covering process of the facility on the network, by splitting the entire covering process into several single-step covering processes, while the effect function is responsible for recording and processing the coverage effect of each covering process, based upon the requirement of an objective function. This LBM-like algorithm has good applicability to a complex network, intuitiveness, relatively low computational complexity, and open developability. Furthermore, the idea of the greedy algorithm was coupled with the LBM-like algorithm, to form two types of hybrid algorithms for improving the computational efficiency for the location problem, with multiple facilities, on a large-scale network. Finally, we successfully applied the LBM-like algorithm to the location problem of an emergency rescue spot on a real railway network, to underline the practicality of the proposed algorithm.