the Traveling Salesman Problem
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Hybrid Metaheuristic Combining the Dragonfly Algorithm and Tabu Search for the Traveling Salesman Problem
Announce Type: new Abstract: The Traveling Salesman Problem (TSP) is a classical NP-hard combinatorial optimization problem that aims to find the shortest Hamiltonian cycle visiting each city exactly once and returning to the starting point. This paper proposes a hybrid metaheuristic for the TSP by combining the Dragonfly Algorithm (DA), a swarm-intelligence-based global search method, with Tabu Search (TS), a memory-based local search technique. The proposed method follows a High-Level...
IDEQ -- Improving Diffusion Models for the Traveling Salesman Problem (TSP) by Leveraging the Structure of the Solution Space
arXiv:2412.13858v2 Announce Type: replace Abstract: We investigate diffusion models to solve the Traveling Salesman Problem. Building on the recent DIFUSCO and T2TCO approaches, we propose IDEQ. IDEQ improves the quality of the solutions by leveraging the constrained structure of the state space of the TSP.
On Fr\'echet Traveling Salesmen Problems
arXiv:2606.01147v1 Announce Type: new Abstract: The Fr\'echet distance is a well-studied distance measure between two curves. In this work, we demonstrate that the merit of Fr\'echet distance extends beyond evaluating similarity, and introduce a new setting in which it proves useful. Consider a situation where two agents are required to visit a given set of sites, while staying close to each other throughout their traversal.
ASAP: Exploiting the Satisficing Generalization Edge in Neural Combinatorial Optimization
Announce Type: replace Abstract: Deep Reinforcement Learning (DRL) has emerged as a promising approach for solving Combinatorial Optimization (CO) problems, such as the 3D Bin Packing Problem (3D-BPP), Traveling Salesman Problem (TSP), or Vehicle Routing Problem (VRP), but these neural solvers often exhibit brittleness when facing distribution shifts. To address this issue, we uncover the Satisficing Generalization Edge, which we validate both theoretically and experimentally: identifying a...
MViewRouter: Internalizing Geometric Equivariance via Multi-view Alternating Attention for Combinatorial Routing
Announce Type: new Abstract: Combinatorial routing problems such as the Traveling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) are fundamental NP-hard problems with broad real-world applications. While recent deep reinforcement learning methods have shown promising performance, they typically handle geometric symmetries only through data augmentation, resulting in inconsistent decisions and limited generalization. To address this issue, we propose MViewRouter, a...
Towards Implementable Quantum Divide and Conquer: A TSP Solver with Improved Exponential Base over Held-Karp
Announce Type: cross Abstract: The traveling salesman problem (TSP) is a significant classical NP-hard combinatorial optimization problem. In this work, we demonstrate that combining classical dynamic programming with quantum search can yield an achievable quantum advantage for TSP on the basis of excellent work by the authors of~\cite{ambainis2019quantum}. We design the quantum divide and conquer strategy to provide a parameterized spectrum for this combination.
Leveraging Structural Constraints for Diffusion-based Neural TSP Solvers
arXiv:2606.09343v1 Announce Type: new Abstract: Neural combinatorial optimization has recently achieved strong results on the Euclidean Traveling Salesman Problem (TSP) using generative models such as diffusion and consistency models. State-ofthe-art approaches like FT2T combine fast consistency-based prediction with gradient-based inference time refinement. However, gradient search often incurs significant computational overhead and may not align with the discrete structure of feasible...
Diffusion-Robust Optimization over Graphs
arXiv:2605.30853v1 Announce Type: cross Abstract: We introduce a diffusion-based uncertainty model for robust optimization on directed graphs, in which perturbations of edge weights propagate along adjacent edges and satisfy conservation constraints at nodes. This topology-aware structure is natural in networked systems where uncertainty is induced by flows and local interactions, including transportation, logistics, communication, and energy networks. We analyze how such diffusive...
Adversarial Instance Generation and Robust Training for Neural Combinatorial Optimization with Multiple Objectives
arXiv:2601.01665v2 Announce Type: replace Abstract: Deep reinforcement learning (DRL) has shown great promise in addressing multi-objective combinatorial optimization problems (MOCOPs). Nevertheless, the robustness of these learning-based solvers has remained insufficiently explored, especially across diverse and complex problem distributions. In this paper, we propose a unified robustness-oriented framework for preference-conditioned DRL solvers for MOCOPs.
Lean 4 Machine-Verified Proof of P = NP via the Pedigree Polytope Membership Problem
arXiv:2606.03194v1 Announce Type: new Abstract: The Membership Problem for Pedigree Polytope (M3P) asks, given $X\in\mathbb{Q}^{\binom{n}{3}}$, whether $X\in\mathrm{conv}(P_n)$, where $P_n$ is the set of all pedigrees. A pedigree is a structured encoding of a Hamiltonian cycle construction in $K_n$. We establish that M3P is solvable in strongly polynomial time via a recursively constructed layered network $(N_k, R_k, \mu)$ and a multicommodity flow problem MCF$(k)$. The necessary and...