Limited Resource Optimal Distribution Algorithm Based on Game Iteration Method

TL;DR

This paper introduces an iterative game-based algorithm for solving linear programming problems efficiently, demonstrating high convergence rates and potential for integration into optimal control systems.

Contribution

It presents a novel iterative method transforming LPP into a game problem and provides a computer implementation with proven convergence and accuracy.

Findings

High solution convergence rate observed

Algorithm achieves acceptable accuracy with fractions or unities

Suitable for integration into optimal control systems

Abstract

The article provides a solution algorithm for the linear programming problem (LPP) with the latter being presented as an antagonistic matrix game so the game's further solution is based on the iterative method. The algorithm is presented as a computer program. Having applied necessary accuracy, the author has researched the solution assessment convergence rate in relation to the actual value. Program implementation demonstrates high rate of the LPP solution receipt, with the acceptable accuracy being fractions or unities. It allows using the algorithm in the integrated systems for the purpose of their optimal control.