Recently, neural heuristics based on deep reinforcement learning have exhibited promise in solving multi-objective combinatorial optimization problems (MO-COPs).

While performing favourably on the independent and identically distributed (i.i.d.)

Recent neural heuristics for the Vehicle Routing Problem (VRP) primarily rely on node coordinates as input, which may be less effective in practical scenarios where real cost metrics-such as edge-based distances-are more relevant. To address this limitation, we introduce EFormer, an Edge-based Transformer model that uses edge as the sole input for VRPs. Our approach employs a precoder module with a mixed-score attention mechanism to convert edge information into temporary node embeddings. We also present a parallel encoding strategy characterized by a graph encoder and a node encoder, each responsible for processing graph and node embeddings in distinct feature spaces, respectively. This design yields a more comprehensive representation of the global relationships among edges. In the decoding phase, parallel context embedding and multi-query integration are used to compute separate attention mechanisms over the two encoded embeddings, facilitating efficient path construction. We train EFormer using reinforcement learning in an autoregressive manner. Extensive experiments on the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) reveal that EFormer outperforms established baselines on synthetic datasets, including large-scale and diverse distributions. Moreover, EFormer demonstrates strong generalization on real-world instances from TSPLib and CVRPLib. These findings confirm the effectiveness of EFormer's core design in solving VRPs.

Among the studied COPs, the Vehicle Routing Problems (VRPs) are often favoured and chosen to verify the effectiveness Existing neural heuristics often train a deep architecture of the NCO methods, especially the Traveling from scratch for each specific vehicle Salesman Problem (TSP) and Capacitated Vehicle Routing routing problem (VRP), ignoring the transferable Problem (CVRP). On the one hand, VRPs are widely applied knowledge across different VRP variants. This paper in real-world scenarios such as logistics, and drone proposes the cross-problem learning to assist delivery [Wang and Sheu, 2019; Konstantakopoulos et al., heuristics training for different downstream VRP 2022]. On the other hand, VRPs are known to be NPcomplete variants. Particularly, we modularize neural architectures problems, and many of them are challenging to be for complex VRPs into 1) the backbone solved efficiently. With the advances of deep learning and its Transformer for tackling the travelling salesman power to automatically learn neural heuristics, NCO methods problem (TSP), and 2) the additional lightweight have demonstrated notable promise against traditional heuristics modules for processing problem-specific features [Kool et al., 2018; Kwon et al., 2020; Li et al., 2021; Luo in complex VRPs. Accordingly, we propose to pretrain et al., 2023]. To further strengthen NCO methods, a number the backbone Transformer for TSP, and then of recent endeavors have been paid to enhance generalization apply it in the process of fine-tuning the Transformer capabilities, which attempt to ameliorate the performance of models for each target VRP variant. On the the neural heuristics in solving the VRP instances with distributions one hand, we fully fine-tune the trained backbone or sizes unseen during training [Geisler et al., 2022; Transformer and problem-specific modules simultaneously.

This article discusses the First International Symposium on Integrating Knowledge and Neural Heuristics, held on 9 to 10 May 1994 in Pensacola, Florida. The highlights of the event are summarized, organized according to the five areas of concentration at the conference: (1) integration methodologies; (2) language, psychology, and cognitive science; (3) fuzzy logic; (4) learning; and (5) applications. This trend has begun to pick up its momentum since the late 1980s, and both approaches have enjoyed many successful applications to real-world problems. This hybrid idea is largely a consequence of an increasingly strong belief that knowledge and neural models can complement each other beneficially. The growing community in this area convened at the First International Symposium on Integrating Knowledge and Neural Heuristics (ISIKNH) on 9 to 10 May 1994 in Pensacola Beach, Florida, for the first time on the international level.

One of the major problems faced by businesses in the 1990s is how to produce environmentally friendly products and stay profitable. A pioneering consortium at Carnegie Mellon University (CMU) is using AI, combined with operations research, environmental science, public policy, and other disciplines, to build tools for green engineering. Green engineering is an approach to product development that balances environmental compatibility against economic profitability. It looks at the entire life cycle of the product, from design to disposal, and seeks to extend this life cycle through remanufacturing, reusing, and recycling products and components. Today, industrial solutions to environmental problems focus largely on recycling, figuring out how to dispose of products at the end of their useful lives.

This article discusses the First International Symposium on Integrating Knowledge and Neural Heuristics, held on 9 to 10 May 1994 in Pensacola, Florida. The highlights of the event are summarized, organized according to the five areas of concentration at the conference: (1) integration methodolo-gies; (2) language, psychology, and cognitive science; (3) fuzzy logic; (4) learning; and (5) applications.