Modeling, landscape analysis, and solving the capacitated single-allocation hub maximal covering problem using the GARVND hybrid algorithm

Abstract

In this paper, a new variation to the Hub Maximal Covering problem called the Capacitated Single-Allocation Hub Maximal Covering Problem (CSAHMCP) is addressed for the first time and a novel binary-integer mathematical model has been proposed. To analyze the features of the problem’s solution space and to determine the most effective heuristic approach to solve it, a comprehensive Fitness Landscape Analysis is performed which reveals that the problem is of ‘rugged plain’ type and can best be solved using an algorithm with good exploration and exploitation capabilities at the same time. Accordingly, we proposed a new algorithm named GARVND, which is a hybrid of the Genetic Algorithm acting as the main framework for diversification, and a variant of the Variable Neighborhood Descent algorithm called ‘Reduced VND’ acting as a means to improve individual solutions (intensification) by searching in the spaces generated by four types of neighborhood operators. We also introduced two original crossover and mutation operators that can be used for any hub location solution method. The parameters of GARVND are tuned toward less computational times and higher solution quality by using the Taguchi experiment design technique. We solved 114 CSAHMCP instances (several times each) from the Australian Post (AP) dataset using the proposed GARVND, as well as by the Genetic Algorithm, Variable Neighborhood Search, Simulated Annealing, Tabu Search algorithms, and a hybrid algorithm consisting of Grey Wolf Optimizer and Simulated Annealing, in addition to the Gurobi exact solver. Extensive computational results and statistical analyses showed that GARVND yields favorable solutions, outperforming all the compared algorithms by producing smaller gaps with global optimal objective values. In addition, to illustrate the practical value of the CSAHMCP and the GARVND method, we performed a cost-flow sensitivity analysis for the AP Central Sydney network and came up with the best expansion scenarios to be adopted by the management.