Simplex Initialization: A Survey of Techniques and Trends

TL;DR

This survey reviews various initialization techniques for the simplex method in linear programming, highlighting current methods and future directions involving advanced learning technologies to enhance their efficiency.

Contribution

It provides a comprehensive overview of primal and dual simplex initialization methods and discusses potential improvements using modern learning approaches.

Findings

Summarizes existing simplex initialization techniques

Identifies gaps and challenges in current methods

Proposes future research directions with learning technologies

Abstract

The simplex method is one of the most fundamental technologies for solving linear programming (LP) problems and has been widely applied to different practical applications. In the past literature, how to improve and accelerate the simplex method has attracted plenty of research. One important way to achieve this goal is to find a better initialization method for the simplex. In this survey, we aim to provide an overview about the initialization methods in the primal and dual simplex, respectively. We also propose several potential future directions about how to improve the existing initialization methods with the help of advanced learning technologies.