Approximating Permutations with Neural Network Components for Travelling Photographer Problem

TL;DR

This paper introduces a neural network-inspired approach to approximate permutations in complex problems like the Travelling Photographer Problem and TSP, enabling efficient solutions to NP-hard permutation challenges.

Contribution

It proposes a novel architecture that mimics machine learning components for permutation approximation, improving solution efficiency for NP-hard problems.

Findings

Successfully solves the Travelling Photographer Problem with minimal error.

Provides a 2-Local improvement heuristic for the Travelling Salesman Problem.

Demonstrates the effectiveness of neural network-inspired architectures for permutation problems.

Abstract

Most of the current inference techniques rely upon Bayesian inference on Probabilistic Graphical Models of observations and do predictions and classification on observations. However, there is very little literature on the mining of relationships between observations and building models of the relationship between sets of observations or the generating context of the observations. Moreover, event understanding of machines with observation inputs needs to understand the relationship between observations. Thus there is a crucial need to build models and develop effective data structures to accumulate and organize relationships between observations. Given a PGM model, this paper attempts to fit a permutation of states to a sequence of observation tokens (The Travelling Photographer Problem). We have devised a machine learning inspired architecture for randomized approximation of state permutation, facilitating parallelization of heuristic search of permutations. As a result, our algorithm can solve The Travelling Photographer Problem with minimal error. Furthermore, we demonstrate that by mimicking machine learning components such as normalization, dropout, and lambda layer with a randomized algorithm, we can devise an architecture that solves TPP, a permutation NP-Hard problem. Other than TPP, we can also provide a 2-Local improvement heuristic for the Travelling Salesman Problem (TSP) with similar ideas.