Multiobjective combinatorial optimization (MOCO) problems can be found in
many real-world applications. However, exactly solving these problems would be
very challenging, particularly when they are NP-hard. Many handcrafted
heuristic methods have been proposed to tackle different MOCO problems over the
past decades. In this work, we generalize the idea of neural combinatorial
optimization, and develop a learning-based approach to approximate the whole
Pareto set for a given MOCO problem without further search procedure. We
propose a single preference-conditioned model to directly generate approximate
Pareto solutions for any trade-off preference, and design an efficient
multiobjective reinforcement learning algorithm to train this model. Our
proposed method can be treated as a learning-based extension for the
widely-used decomposition-based multiobjective evolutionary algorithm (MOEA/D).
It uses a single model to accommodate all the possible preferences, whereas
other methods use a finite number of solutions to approximate the Pareto set.
Experimental results show that our proposed method significantly outperforms
some other methods on the multiobjective traveling salesman problem,
multiobjective vehicle routing problem, and multiobjective knapsack problem in
terms of solution quality, speed, and model efficiency.

本文通过神经组合优化的思想，提出了多目标组合优化问题的学习方法，模型可直接生成逼近帕累托前沿的解，证明了该方法在多目标问题上的有效性。