  The latency location routing problem integrates the facility location problem
and the multi-depot cumulative capacitated vehicle routing problem. This
problem involves making simultaneous decisions about depot locations and
vehicle routes to serve customers while aiming to minimize the sum of waiting
(arriving) times for all customers. To address this computationally challenging
problem, we propose a reinforcement learning guided hybrid evolutionary
algorithm following the framework of the memetic algorithm. The proposed
algorithm relies on a diversity-enhanced multi-parent edge assembly crossover
to build promising offspring and a reinforcement learning guided variable
neighborhood descent to determine the exploration order of multiple
neighborhoods. Additionally, strategic oscillation is used to achieve a
balanced exploration of both feasible and infeasible solutions. The
competitiveness of the algorithm against state-of-the-art methods is
demonstrated by experimental results on the three sets of 76 popular instances,
including 51 improved best solutions (new upper bounds) for the 59 instances
with unknown optima and equal best results for the remaining instances. We also
conduct additional experiments to shed light on the key components of the
algorithm.
