A novel hybrid genetic algorithm for the location routing problem with tight capacity constraints

Location routing problem (LRP) is a popular and challenging topic in the field of logistic systems. LRP needs to address the depot location problem and vehicle routing problem at the same time. Till now, different LRP variants have been formulated to better meet realistic requirements. In this study, we focus on the capacitated LRP (CLRP) with tight capacity constraint on both depots and vehicles. To cope with the tight constraints, a hybrid genetic algorithm (HGA) is developed to search not only feasible solution space but also infeasible solution space. The proposed HGA combines the wide exploration capacity of GA, and the fast exploitation capacity of neighbourhood local search. To evolve GA for CLRP, solutions are represented by sets and sequences, and accordingly, a multi-sequence-based crossover is designed for the offspring generation. Moreover, a population management scheme is designed to facilitate GA’s evolution. Experiments are conducted on two benchmark sets and the results show that HGA is quite competitive with existing well-known CLRP algorithms on the classical instances. Furthermore, HGA is able to obtain quite a number of new best solutions on the real-life-like instances with tighter constraints.