Xixi Zhu

The multi-objective traveling salesman problem (MOTSP) is a typical challenging multi-objective combinatorial optimization problem. Numerous advanced deep reinforcement learning algorithms have been developed to solve it. Existing learning-based methods can share information across subproblems through mechanisms such as parameter transfer. This paper investigates explicit graph-based modeling of preference relationships within a shared policy and proposes a graph-relation-driven deep reinforcement learning algorithm for MOTSP. The proposed algorithm trains a model to map problem instances to approximate Pareto sets under a collection of preference vectors. Specifically, the graph weight encoder combines global and objective-specific city representations with preference features learned on a fixed graph whose edges are defined by distances between weight vectors. A graph co-guided fusion module then combines global and objective-specific city embeddings with the learned preference representations to generate preference-conditioned city embeddings. The resulting problem embeddings and contextual embeddings are supplied to the decoder to generate candidate tours in parallel, providing an approximation to the Pareto set. Furthermore, a Top-p training baseline is introduced to adaptively select reference candidates according to their scalarized costs. Finally, extensive experiments are conducted on various MOTSP instances. Comparisons are carried out between the proposed algorithm and heuristic and learning-based algorithms. Experimental results demonstrate the solution quality of the proposed algorithm on the evaluated multi-objective traveling salesman problems. Its computational cost is reported under the specified hardware, decoding budgets, and evaluation settings.

The ontology knowledge base (KB) can be divided into two parts: TBox and ABox, where the former models schema-level knowledge within the domain, and the latter is a set of statements of assertions or facts about instances. ABox reasoning is a process of discovering implicit knowledge in ABox based on the existing KB, which is of great value in KB applications. ABox reasoning is influenced by both the complexity of TBox and scale of ABox. The traditional logic-based ontology reasoning methods are usually designed to be provably sound and complete but suffer from long algorithm runtimes and do not scale well for ontology KB represented by OWL DL (Description Logic). In some application scenarios, the soundness and completeness of reasoning results are not the key constraints, and it is acceptable to sacrifice them in exchange for the improvement of reasoning efficiency to some extent. Based on this view, an approximate reasoning method for large-scale ABox in OWL DL KBs was proposed, which is named the ChunfyReasoner (CFR). The CFR introduces neural-symbolic learning into ABox reasoning and integrates the advantages of symbolic systems and neural networks (NNs). By training the NN model, the CFR approximately compiles the logic deduction process of ontology reasoning, which can greatly improve the reasoning speed while ensuring higher reasoning quality. In this paper, we state the basic idea, framework, and construction process of the CFR in detail, and we conduct experiments on two open-source ontologies built on OWL DL. The experimental results verify the effectiveness of our method and show that the CFR can support the applications of large-scale ABox reasoning of OWL DL KBs.