This research proposes a hybrid Machine Learning and metaheuristic mechanism that is designed to solve Vehicle Routing Problems (VRPs). The main of our method is an edge solution selector model, which classifies solution edges to identify prohibited moves during the local search, hence guiding the search process within metaheuristic baselines. Two learning-based mechanisms are used to develop the edge selector: a simple tabular binary classifier and a Graph Neural Network (GNN). The tabular classifier employs Gradient Boosting Trees and Feedforward Neural Network as the baseline algorithms. Adjustments to the decision threshold are also applied to handle the class imbalance in the problem instance. An alternative mechanism employs the GNN to utilize graph structure for direct solution edge prediction, with the objective of guiding local search by predicting prohibited moves. These hybrid mechanisms are then applied in state-fo-the-art metaheuristic baselines. Our method demonstrates both scalability and generalizability, achieving performance improvements across different baseline metaheuristics, various problem sizes and variants, including the Capacitated Vehicle Routing Problem (CVRP) and CVRP with Time Windows (CVRPTW). Experimental evaluations on benchmark datasets up to 30,000 customer nodes, supported by pair-wise statistical analysis, verify the observed improvements.

Automated Heuristic Design (AHD) using Large Language Models (LLMs) has achieved notable success in recent years. Despite the effectiveness of existing approaches, they only design a single heuristic to serve all problem instances, often inducing poor generalization across different distributions or settings. To address this issue, we propose Automated Heuristic Set Design (AHSD), a new formulation for LLM-driven AHD. The aim of AHSD is to automatically generate a small-sized complementary heuristic set to serve diverse problem instances, such that each problem instance could be optimized by at least one heuristic in this set. We show that the objective function of AHSD is monotone and supermodular. Then, we propose Evolution of Heuristic Set (EoH-S) to apply the AHSD formulation for LLM-driven AHD. With two novel mechanisms of complementary population management and complementary-aware memetic search, EoH-S could effectively generate a set of high-quality and complementary heuristics. Comprehensive experimental results on three AHD tasks with diverse instances spanning various sizes and distributions demonstrate that EoH-S consistently outperforms existing state-of-the-art AHD methods and achieves up to 60\% performance improvements.

We introduce PLUME search, a data-driven framework that enhances search efficiency in combinatorial optimization through unsupervised learning. Unlike supervised or reinforcement learning, PLUME search learns directly from problem instances using a permutation-based loss with a non-autoregressive approach. We evaluate its performance on the quadratic assignment problem, a fundamental NP-hard problem that encompasses various combinatorial optimization problems. Experimental results demonstrate that PLUME search consistently improves solution quality. Furthermore, we study the generalization behavior and show that the learned model generalizes across different densities and sizes.

Decision Diagram (AOMDD) which represents all its optimal solutions.

Therefore, our algorithms can be extended to more general semiring based graphical models. We will fix all typos and presentation issues. We will extend the discussion in the paper to clarify this point.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

We are very thankful to all reviewers for their time and valuable comments. We agree that "lots of works have used GCNN for different combinatorial optimization We agree that our benchmark is artificial, and using real-world instances would bring value. Such datasets could be collected, e.g. We intend to include those new results in the final version of the paper. We agree that we should discuss references [a-c] in our literature review.

Neural Information Processing Systems http://nips.cc/

--Floorplanning is a critical step in VLSI physical design, increasingly complicated by modern constraints such as fixed-outline requirements, whitespace removal, and the presence of pre-placed modules. However, traditional floorplanners often overlook pin assignment with modern constraints during the floorplanning stage. In this work, we introduce Piano, a floorplanning framework that simultaneously optimizes module placement and pin assignment under multiple constraints. Specifically, we construct a graph based on the geometric relationships among modules and their netlist connections, then iteratively search for shortest paths to determine pin assignments. This graph-based method also enables accurate evaluation of feedthrough and unplaced pins, thereby guiding overall layout quality. T o further improve the design, we adopt a whitespace removal strategy and employ three local optimizers to enhance layout metrics under multi-constraint scenarios. Experimental results on widely used benchmark circuits demonstrate that Piano achieves an average 6.81% reduction in HPWL, a 13.39% decrease in feedthrough wirelength, a 16.36% reduction in the number of feedthrough modules, and a 21.21% drop in unplaced pins, while maintaining zero whitespace. Floorplanning is the first step in modern VLSI physical design as it needs to determine the shape and location of large circuit modules on a chip canvas, while assigning the pins to each module's boundary for inter-module connections, thereby laying the foundation for subsequent detailed placement and routing stages.