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The seven papers included in this special issue represent a selection of extended contributions presented at the 16th International Conference on Soft Computing Models in Industrial and Environmental Applications, SOCO 2021, held in Bilbao, Spain, September 22nd-24th, 2021, and organized by the BISITE group and the University of Deusto. The SOCO 2021 international conference represents a collection or set of computational techniques in machine learning, computer science and some engineering disciplines that investigate, simulate, and analyse very complex issues and phenomena. This special issue is aimed at practitioners, researchers, and postgraduate students who are engaged in developing and applying advanced intelligent systems principles to solve real-world problems in the mentioned fields. [ABSTRACT FROM AUTHOR]

Combinatorial optimization problem (COP) is an NP-hard problem for which finding an optimal solution is difficult, especially as the problem size increases. The Traveling Salesman Problem (TSP), one of the COPs that can be formulated over a graph, is a well-researched area in operations research and computer science. Deep Reinforcement Learning (DRL) is now regarded as a promising approach for solving TSP and other NP hard problems. In this paper, we propose a novel Gated Deep Graph Attention Network (G-DGANet) which builds upon the existing Graph Neural Network (GNN) to solve TSP. The proposed G-DGANet uses gating mechanism between subsequent layers of the network to extract representations of nodes deeper in the network without loss in performance. G-DGANet also designs a novel aggregator to construct global graph embeddings from different embedding preferences. In addition, to effectively learn underlying structure of a graph, G-DGANet integrates node and edge information of the graph while updating node representations in the message passing mechanism. We used proximal policy optimization (PPO) to train G-DGANet on randomly generated instances. We conducted an experiment on randomly generated instances and on real-world road network data generated from digital maps to verify the performance of G-DGANet. The findings from experiments demonstrate that G-DGANet outperforms most traditional heuristics and existing DRL approaches, with high generalization abilities from random instance training to random instance testing and real-world road network instance testing. [ABSTRACT FROM AUTHOR]