Scalable Method for Linear Optimization of Industrial Processes

TL;DR

This paper introduces the apex-method, a scalable predictor-corrector algorithm for large-scale linear programming problems in industrial process optimization, with demonstrated parallel efficiency on cluster systems.

Contribution

The paper presents a novel apex-method for large-scale LP problems, including its formal description and parallel implementation, advancing computational efficiency in industrial process optimization.

Findings

Demonstrates scalability of the apex-method on cluster systems.

Provides formal description and parallel implementation details.

Shows improved solution efficiency for large-scale LP problems.

Abstract

In the development of industrial digital twins, the optimization problem of technological and business processes often arises. In many cases, this problem can be reduced to a large-scale linear programming (LP) problem. The article is devoted to the new method for solving large-scale LP problems. This method is called the "apex-method". The apex-method uses the predictor-corrector framework. The predictor step calculates a point belonging to the feasible region of LP problem. The corrector step calculates a sequence of points converging to the exact solution of the LP problem. The article gives a formal description of the apex-method and provides information about its parallel implementation in C++ language by using the MPI library. The results of large-scale computational experiments on a cluster computing system to study the scalability of the apex method are presented.