New deep learning method solves TSP faster and more efficiently.
problem Approximately solving the Travelling Salesman Problem on 2D Euclidean graphs.
method Uses Graph Convolutional Networks for efficient TSP graph representations and non-autoregressive beam search.
result Significantly reduces optimality gap for large problem instances.
Symmetric TSP is structurally equivalent to a constrained Group Steiner Tree Problem.
problem Finding the shortest tour in a symmetric TSP.
method Structural equivalence between symmetric TSP and constrained Group Steiner Tree Problem.
result Maximizing net weight in the cGSTP is equivalent to minimizing the TSP tour length.
Deep learning matches classical feature-based AS models for TSP.
problem Automated selection of algorithms for the TSP.
method Evolved instances, deep neural network, visual representation.
result Deep learning approach matches classical feature-based models.
SPG learns policies on permutation matrices using Sinkhorn layers.
problem Optimizing permutations for tasks like sorting, ranking, and matching.
method Introduces Sinkhorn Policy Gradient (SPG) algorithm with a temperature-controlled Sinkhorn layer.
result SPG agents perform competitively and are more data-efficient than baseline methods on matching tasks.
This paper surveys RL for combinatorial optimization, focusing on TSP.
problem Optimizing solutions for combinatorial optimization problems.
method Reinforcement learning applied to combinatorial optimization problems, specifically the TSP.
result Deep learning mechanisms enhance RL algorithms for near-optimal solutions.
Graph Pointer Networks and hierarchical reinforcement learning solve combinatorial optimization problems like TSP.
problem Traveling Salesman Problem (TSP) with constraints.
method Graph Pointer Networks (GPNs) and hierarchical reinforcement learning.
result GPNs and hierarchical RL find optimal solutions for TSP and TSP with time windows.
Graph Neural Networks and Guided Local Search improve TSP solutions.
problem Finding optimal solutions to the Traveling Salesperson Problem quickly.
method Hybrid approach combining Graph Neural Networks and Guided Local Search.
result Significant reduction in optimality gap for TSP solutions.
DeepCO uses deep learning for offline combinatorial optimization in warehouse operations.
problem Optimizing warehouse operation sequences in offline settings.
method DeepCO framework utilizing distribution regularized optimization for TSP.
result DeepCO reduces route length by 5.7% on average for TSP problems.
Neural network solves M-TSP with varying sets.
problem Generalizing TSP to M-TSP.
method Pooling networks combining set and graph elements, with new loss and layers.
result Outperforms leading solver's meta-heuristics.
Neural networks struggle with TSP beyond small instances, requiring new approaches.
problem Neural networks struggle to generalize to larger instances of the TSP.
method Unified pipeline to identify inductive biases and promote generalization.
result Zero-shot generalization requires rethinking neural combinatorial optimization.
Deep learning approximates TSP solutions for parking violations.
problem Solving the Travelling Salesman Problem for parking violation datasets.
method Converted TSP into a classification problem, designed a customised deep learning network.
result Empirically showed critical architectural components affecting network performance.
Improves heuristics for routing problems using attention models.
problem Improving heuristics for combinatorial optimization problems, especially for routing problems.
method Proposed a model based on attention layers and trained it using REINFORCE with a simple greedy rollout.
result Significantly improved results for TSP and other routing problems, close to optimal or specialized algorithms.
DPDP combines neural heuristics with DP for vehicle routing problems.
problem Vehicle routing problems with large scale.
method Deep Policy Dynamic Programming (DPDP) that uses a neural network policy to prioritize and restrict the DP state space.
result DPDP improves upon classical DP algorithms and outperforms neural approaches for TSP, VRP, and TSPTW.
This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city coordinates, predicts a distribution over different city permutations. Using negative t…
Deep RL learns 2-opt heuristics to improve TSP solutions.
problem Improving TSP solutions beyond initial heuristics.
method Deep reinforcement learning to learn 2-opt operations.
result Learned policies improve solutions faster than previous methods.
This research designs a data-driven partition to test independence between continuous variables.
problem Testing independence between continuous random variables.
method Empirical log-likelihood statistic and data-driven tree-structured partition.
result Strongly consistent test of independence over probability families.
Sym-NCO leverages symmetricities to improve DRL-NCO performance.
problem Improving neural combinatorial optimization methods.
method Sym-NCO is a regularizer-based training scheme that exploits universal symmetricities in CO problems and solutions.
result Sym-NCO significantly improves DRL-NCO performance across various CO tasks.
Machine learning reduces combinatorial optimization problem dimensions.
problem Reducing the complexity of large combinatorial optimization problems.
method Generalization of a machine learning model for problem reduction on TSP.
result Machine learning can predict which variables are not part of an optimal solution.
Two DRL policies collaborate to solve NP-hard routing problems.
problem Solving complex routing problems like TSP without expert knowledge.
method Learning Collaborative Policies (LCP) using seeder and reviser policies.
result Improves solution quality over single-policy DRL on various NP-hard routing problems.
Graph Neural Networks solve the decision variant of TSP with high accuracy.
problem Decision variant of the Traveling Salesperson Problem (TSP).
method Graph Neural Networks (GNNs) learn to solve TSP with minimal supervision.
result Graph Neural Networks achieve 80% accuracy in solving TSP with small cost deviations.
The paper solves a genome assembly problem by recovering hidden Hamiltonian cycles from noisy measurements.
problem Inferring an unknown Hamiltonian cycle in a genome assembly problem from noisy edge measurements.
method Introduced a linear programming relaxation (F2F LP) to recover the hidden Hamiltonian cycle with high probability.
result A simple linear programming relaxation recovers the hidden Hamiltonian cycle with high probability as no∞. We consider the learning of algorithmic tasks by mere observation of input-output pairs. Rather than studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping, we concentrate on tasks that are amenable to the principle of divide and conquer, and study what are it…
Perhaps surprisingly, it is possible to predict how long an algorithm will take to run on a previously unseen input, using machine learning techniques to build a model of the algorithm's runtime as a function of problem-specific instance features. Such models have important applications to algorithm analysis, portfolio…
Differentiable segmented models for non-stationary data.
problem Estimating change points in non-stationary sequential data.
method Formulated a relaxed variant of segmented models that enables gradient descent for all parameters, including segmentation.
result Successfully learned all tasks with standard gradient descent algorithms.
New CNN approach detects cell nuclei with prior information.
problem Challenges in detecting cell nuclei due to image quality and morphology diversity.
method Develops SP-CNN with trainable shape prior layer to guide CNN learning.
result TSP-CNN outperforms state-of-the-art alternatives on challenging datasets.
New method finds optimal training stop point with noisy labeled data.
problem Finding optimal training stop point with noisy labeled data.
method Analyzed training accuracy rate changes for different noise ratios to identify a training stop region. Developed a heuristic algorithm based on a small-learning assumption.
result Identified optimal training stop point at or close to maximum obtainable test accuracy.
Historical review of genetic algorithms for the TSP shows three distinct phases.
problem Optimizing routes for the Traveling Salesman Problem using genetic algorithms.
method Meta-data analysis of publications over time.
result Three distinct phases in the development of genetic algorithms for TSP identified.
DO uses DNNs to solve combinatorial optimisation problems.
problem Solving complex combinatorial optimisation problems.
method Combines evolutionary search with DNNs to learn and exploit problem structure.
result DO can solve problems like HTOP and MCparity that other algorithms cannot.
Study compares RL and SL for TSP, finds RL better for variable graph sizes.
problem Training deep neural networks for the Travelling Salesman Problem.
method Controlled experiments with supervised and reinforcement learning models on fixed and variable sized graphs.
result Reinforcement learning leads to better generalization to variable graph sizes.
GOTabPFN improves tabular model performance with compact tokenization for HDLSS data.
problem Making tabular models effective for high-dimensional, low-sample size data without retraining.
method Introducing Graph-guided Ordering with Local Refinement (GO-LR) and Neuro-Inspired Subunit Compression (NSC) to create compact meta-features.
result GOTabPFN improves stability and accuracy in tabular benchmarks with compact tokenization.
The paper tackles hierarchical reinforcement learning by approximating optimal solutions for the Traveling Salesman Problem.
problem Approximating optimal solutions for the Traveling Salesman Problem using hierarchical reinforcement learning.
method Mapping the problem into a Reward Discounted Traveling Salesman Problem and deriving approximate solutions using local policies.
result Three stochastic policies are proposed that guarantee better performance than any deterministic policy.
Combines TSP and SC to solve real-world vaccine distribution.
problem Combining TSP and SC for efficient vaccine distribution.
method Mixed Integer Programming (MIP) and machine learning.
result Machine learning approach improves solution efficiency.
Graph colouring model uses GNN to solve NP-Complete problems.
problem Solving NP-Complete problems like graph colouring.
method Simple GNN architecture trained on random instances, generalizes to diverse graph distributions.
result GNN model outperforms Neurosat, Tabucol, and greedy baselines for some graph distributions.
Euclidean metrics without conjugate points are proven to be flat.
problem Proving the flatness of metrics without conjugate points.
method Analyzing asymptotically Euclidean metrics.
result Asymptotically Euclidean metrics without conjugate points are isometric to the Euclidean metric.
Complete classification of metric fibrations in Euclidean space.
problem Classifying metric fibrations in Euclidean space.
method Completed a minor gap in Gromoll and Walschap's classification.
result Completed the classification of Riemannian foliations on Euclidean spaces.
In this paper we demonstrate how the geometrically motivated algorithm to determine whether a two generator real Mobius group acting on the Poincare plane is or is not discrete can be interpreted as a non-Euclidean Euclidean algorithm. That is, the algorithm can be viewed as an application of the Euclidean division alg…
The study of Euclidean submanifolds with incompressible canonical vector fields.
problem Characterizing Euclidean submanifolds with incompressible canonical vector fields.
method Analyzing the canonical vector field properties and conditions for incompressibility.
result Necessary and sufficient conditions for the canonical vector field of a Euclidean submanifold to be incompressible.
4-manifolds with non-positive curvature are essentially Euclidean.
problem Understanding the structure of 4-manifolds with specific curvature properties.
method Proving homeomorphism to Euclidean space using globally non-positive curvature.
result CAT(0) 4-manifolds are homeomorphic to Euclidean space.
The study characterizes Euclidean submanifolds with a conformal canonical vector field.
problem Characterizing Euclidean submanifolds with a specific vector field property.
method Investigating properties of the canonical vector field and its conformal nature.
result Characterization of Euclidean submanifolds with conformal canonical vector fields.
The study shows how strictly convex domains in Euclidean spaces are rigid.
problem Understanding the rigidity of strictly convex domains in Euclidean spaces.
method Proved a rigidity theorem for smooth strictly convex domains in Euclidean spaces.
result Smooth strictly convex domains in Euclidean spaces are rigid.
Prove Gromov's Euclidean endpoint C0 rigidity conjecture for positive mass theorem.
problem Prove Gromov's Euclidean endpoint C0 rigidity conjecture for positive mass theorem. method Prove Gromov's Euclidean endpoint C0 rigidity conjecture for positive mass theorem. result Prove Gromov's Euclidean endpoint C0 rigidity conjecture for positive mass theorem. Researchers describe a specific type of submanifolds in Euclidean space.
problem Understanding inhomogeneous almost symmetric submanifolds.
method Completely describing submanifolds as unions of parallel symmetric submanifolds.
result Described inhomogeneous properly embedded almost symmetric submanifolds as unions of symmetric submanifolds.
Study classifies graphs in Euclidean and non-Euclidean spaces with specific curvature conditions.
problem Classifying graphs with prescribed curvature in various spaces.
method Proves rigidity and classification results for graphs in Riemannian manifolds, focusing on R2 and R3. result Provides general splitting theorems for graphs in these settings.
We calculate Euclidean distance degrees for common manifold optimization types.
problem Optimizing on manifold structures.
method Closed-form expressions for stationary points of Euclidean distance function.
result Closed-form expressions for all stationary points on manifold optimization.
Flat subsets in Euclidean buildings are contained within apartments.
problem Understanding the structure of flat subsets in Euclidean buildings.
method Proving containment within apartments.
result Convex flat subsets are contained in apartments.
Direct proof for all conformally flat isoparametric submanifolds in Euclidean space.
problem Classifying conformally flat isoparametric submanifolds in Euclidean space.
method Direct proof approach.
result Complete classification of conformally flat isoparametric submanifolds of Euclidean space.
The paper classifies conformal solitons in pseudo-Euclidean spaces.
problem Classifying conformal solitons in pseudo-Euclidean spaces.
method Classification through pseudo-Riemannian hypersurfaces and position vector fields.
result Complete classification of conformal solitons in pseudo-Euclidean spaces.
Proves metric spaces with Euclidean heat kernel are isometric to Euclidean space.
problem Characterizing metric measure spaces with specific heat kernels.
method Analyzes Dirichlet forms and heat kernels to prove rigidity.
result Metric measure spaces with Euclidean heat kernel are isometric to Euclidean space.