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Permutation Picture of Graph Combinatorial Optimization Problems

Yimeng Min

TL;DR

This paper proposes a framework that formulates a wide range of graph combinatorial optimization problems using permutation-based representations, potentially opening up new avenues for algorithm design in neural combinatorial optimization.

Abstract

This paper proposes a framework that formulates a wide range of graph combinatorial optimization problems using permutation-based representations. These problems include the travelling salesman problem, maximum independent set, maximum cut, and various other related problems. This work potentially opens up new avenues for algorithm design in neural combinatorial optimization, bridging the gap between discrete and continuous optimization techniques.

Permutation Picture of Graph Combinatorial Optimization Problems

TL;DR

This paper proposes a framework that formulates a wide range of graph combinatorial optimization problems using permutation-based representations, potentially opening up new avenues for algorithm design in neural combinatorial optimization.

Abstract

This paper proposes a framework that formulates a wide range of graph combinatorial optimization problems using permutation-based representations. These problems include the travelling salesman problem, maximum independent set, maximum cut, and various other related problems. This work potentially opens up new avenues for algorithm design in neural combinatorial optimization, bridging the gap between discrete and continuous optimization techniques.

Paper Structure

This paper contains 53 sections, 51 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Supervised, Reinforcement and Unsupervised Learning
  3. Building Surrogate Loss using Ising Formulation
  4. Permutation
  5. Background
  6. Are Discrete Variables Differentiable?
  7. Learning to Reduce the Combinatorial Search Space
  8. Motivation
  9. Formulating Graph Combinatorial Problems using Permutation
  10. Travelling Salesman Problem
  11. Maximum Independent Set
  12. Definition
  13. Permutation-based objective function
  14. Proof
  15. Maximum Cut
  16. ...and 38 more sections

Figures (2)

  • Figure 1: Unsupervised Learning Framework for Graph Combinatorial Problems
  • Figure 2: Comparison of graph labellings and their adjacency matrices. The blue nodes are the solution of the MIS Problem. $A_1$ is the adjacency matrix of the left labelling and $A_2$ corresponds to the right one.