Cost-Flow Summation Algorithm Based on Table Form to Solve Minimum Cost-Flow Problem

TL;DR

This paper introduces a novel table-based algorithm for solving minimum cost-flow problems, efficiently handling large instances by summarizing graph information into a table and improving solution speed.

Contribution

The paper presents a new table form method that converts graph data into a summarized table, enabling a more efficient solution approach for large-scale minimum cost-flow problems.

Findings

Algorithm is highly efficient for large problems

Provides sufficiently good solutions on generated test cases

Introduces a novel data summarization technique for flow problems

Abstract

The minimum cost-flow problems have been attracted recently in optimization because of their applications in several areas of applied science and real life. Therefore, finding optima solution of these problems would be significant. Although some heuristic approaches have been proposed for solving the problem, but there is no any method to summarize information and converting from a graph form to a table. In this paper, at first all information of the problem are summarized in a table and then an efficient algorithm based on considering costs and flows is proposed. The algorithm is strongly efficient for problems with large size and it has sufficiently suitable results by solving some our generated problems.