Approximating Permutations with Neural Network Components for Travelling Photographer Problem

Abstract

Most of current inference techniques rely upon Bayesian inference on Probabilistic Graphical Models of observations, and does prediction and classification on observations rather well. Event understanding of machines with observation inputs needs to deal with understanding of the relationship between sets of observations, and thus there is a crucial need to build models and come up with effective data structures to accumulate and organize relationships between observations. Given a set of states probabilisitcally-related with observations, 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. Our algorithm is able to solve The Travelling Photographer Problem with very small error. We demonstrate that by mimicking components of machine learning such as normalization, dropout, lambda layer with randomized algorithm, we are able to devise an architecture which solves TPP, a permutation NP-Hard problem. Other than TPP, we are also able to provide a 2-Local improvement heuristic for the Travelling Salesman Problem (TSP) with similar ideas.