Novel approach for solving integer equal flow problem
- Published
- Accepted
- Subject Areas
- Data Science, Optimization Theory and Computation, Theory and Formal Methods
- Keywords
- category theory, Fourier mortzkin elimination, transportation problem, integer equal flow problem
- Copyright
- © 2018 Kumar et al.
- Licence
- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Preprints) and either DOI or URL of the article must be cited.
- Cite this article
- 2018. Novel approach for solving integer equal flow problem. PeerJ Preprints 6:e27264v1 https://doi.org/10.7287/peerj.preprints.27264v1
Abstract
In this article we consider a certain sub class of Integer Equal Flow problem, which are known NP hard. Currently there exist no direct solutions for the same. It is a common problem in various inventory management systems. Here we discuss a local minima solution which uses projection of the convexspaces to resolve the equal flows and turn the problem into a known linear integer programming or constraint satisfaction problem which have reasonable known solutions and can be effectively solved using simplex or other standard optimization strategies
Author Comment
We use some techniques inspired from algebraic geometry and category theory to build an abstract framework for solving combinatorial optimisation and linear programming problems, we pick a specific case of transportation problem where we can actually achieve these deep theorems which can be applicable across all optimisation problems