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Learning-based heuristics for solving combinatorial optimization problems hasrecently attracted much academic attention. While most of the existing worksonly consider the single objective problem with simple constraints, manyreal-world problems have the multiobjective perspective and contain a rich setof constraints. This paper proposes a multiobjective deep reinforcementlearning with evolutionary learning algorithm for a typical complex problemcalled the multiobjective vehicle routing problem with time windows (MO-VRPTW).In the proposed algorithm, the decomposition strategy is applied to generatesubproblems for a set of attention models. The comprehensive contextinformation is introduced to further enhance the attention models. Theevolutionary learning is also employed to fine-tune the parameters of themodels. The experimental results on MO-VRPTW instances demonstrate thesuperiority of the proposed algorithm over other learning-based anditerative-based approaches.

MODRL/D-EL: Multiobjective Deep Reinforcement Learning with Evolutionary Learning for Multiobjective Optimization