Most of the existing Knowledge Graph Completion (KGC) methods do not fully exploit the relational paths in the triple structure, and only consider the graph structure information; meanwhile, the existing models focus on considering the neighborhood information in the process of entity aggregation, and the learning of relations is relatively simple. To address the above problems, a graph attention model that integrates directed relations and relational paths was proposed, namely DRPGAT. Firstly, the regular triples were converted into directed relationship-based triples, and the attention mechanism was introduced to give different weights to different directed relationships, so as to realize the entity information aggregation. At the same time, the relational path model was established, and the relational positions were embedded into the path information to distinguish the relationships among different positions. And the irrelevant paths were filtered to obtain the useful path information. Secondly, the attention mechanism was used to carry out deep path information learning to realize the aggregation of relations. Finally, the entities and relations were fed into the decoder and trained to obtain the final completion results. Link prediction experiments were conducted on two real datasets to verify the effectiveness of the proposed model. Experimental results show that compared to the optimal results of the baseline models, on FB15k-237 dataset, DRPGAT has the Mean Rank (MR) reduced by 13, and the Mean Reciprocal Rank (MRR), Hits@1, Hits@3, and Hits@10 improved by 1.9, 1.2, 2.3, and 1.6 percentage points, respectively; on WN18RR dataset, DRPGAT has the MR reduced by 125, and the MRR, Hits@1, Hits@3, and Hits@10 improved by 1.1, 0.4, 1.2, and 0.6 percentage points, respectively, indicating the effectiveness of the proposed model.
In this paper, the military Petrol-Oil and Lubricants (POL) allotment and transportation problem was studied by introducing the concept of support time window. Considering the complicated restrictions of POL support time and transportation capability, the POL allotment and transportation model based on multiple time windows was proposed by using Constraint Satisfaction Problem (CSP) modelling approach. Firstly, the formalized description of the problem elements was presented, such as POL support station, demand unit, support time window, support demand, and support task. Based on the formalized description, the CSP model for POL support was constructed. The multi-objective model was transformed into single-objective one by using perfect point method. Finally, the solving procedure and its steps were designed based on Particle Swarm Optimization (PSO) algorithm, and an arithmetic example was followed to demonstrate the application of the method. In the example, the two optimization schemes obtained by the model given in this paper and got by the model in which the objective is maximizing the quantity supported were compared. In the two schemes, the transportation capacity both reached a maximum utilization, but the start supporting time of each POL demand in the scheme of the proposed method was no later than the one in the scheme of the single-objective model. By comparing different optimization schemes, it is shown that the proposed model and algorithm can effectively solve the multi-objective POL support optimization problem.